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Number conversion and binary artihmetic

teacher avatar Inside Code, Content creator

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Taught by industry leaders & working professionals
Topics include illustration, design, photography, and more

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Taught by industry leaders & working professionals
Topics include illustration, design, photography, and more

Lessons in This Class

32 Lessons (2h 8m)
    • 1. Course introduction and content

      0:51
    • 2. Introduction to number systems

      1:37
    • 3. Introduction to decimal system

      3:39
    • 4. Decimal to binary conversion

      9:27
    • 5. Decimal to octal conversion

      4:53
    • 6. Decimal to hexadecimal conversion

      6:18
    • 7. Introduction to binary system

      3:36
    • 8. Binary to decimal conversion

      3:17
    • 9. Binary to octal conversion

      4:27
    • 10. Binary to hexadecimal conversion

      4:44
    • 11. Introduction to octal system

      3:28
    • 12. Octal to decimal conversion

      3:07
    • 13. Octal to binary conversion

      1:21
    • 14. Octal to hexadecimal conversion

      2:17
    • 15. Introduction to hexadecimal system

      3:51
    • 16. Hexadecimal to decimal conversion

      2:57
    • 17. Hexadecimal to binary conversion

      1:24
    • 18. Hexadecimal to octal conversion

      2:17
    • 19. Decimal to BCD conversion

      1:38
    • 20. BCD to decimal conversion

      1:46
    • 21. Binary to ASCII conversion

      2:22
    • 22. ASCII to binary conversion

      1:45
    • 23. Binary to gray conversion

      3:07
    • 24. Gray to binary conversion

      2:27
    • 25. Binary to IEEE-754 conversion

      7:53
    • 26. IEEE-754 to binary conversion

      6:35
    • 27. Binary addition

      5:46
    • 28. Binary subtraction

      6:31
    • 29. Binary subtraction with two's complement

      7:27
    • 30. Binary multiplication

      7:48
    • 31. Binary division

      8:43
    • 32. Conclusion

      0:20
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About This Class

This is a course about numbers conversion and binary arithmetic, it contains 44 lectures for a total of 2 hours

Number converter : http://bit.ly/numberConverter

Why would you take this course :

- Simple explications

- A lot of examples/practice

- Additional corrected exercises

- By taking this course, you will be able to :

      1. Understand the concept of number systems

      2. Convert from/to decimal, binary, octal, and hexadecimal system quickly

      3. Convert from/to IEEE 754, BCD, ASCII and gray quickly

      4. Solve binary arithmetic operations (addition/subtraction/multiplication/division) quickly

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Inside Code

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Transcripts

1. Course introduction and content: Welcome to the scores about numbers conversion and binary arithmetic. Through the scores, we will see. What does a number system mean? We will see the decimal system, the binary system, the octo system on the hugs at a simple system on how to convert a number from a system to another. Then we'll see other conversions, like BCD asking Great on our trip. Police 7 54 On Finally, we will see how to do binary arithmetic, addition, subtraction, multiplication and division. So be ready to follow the course and to practice because practicing is very important to improve your solving skills before starting. I want to let you know that I made a number converter that will help you here. Is it? You put the number in any system and you get the conversion in other ones. I will put the link in the description. See you in the first video. 2. Introduction to number systems: Hello, everyone. In this video we will see a quick and production to number systems. First, you have to know that a number system is just a way to represent numbers. For example, we have a number 12 represented like this in decimal. But we can also represent it in other number systems like binary we can represented by this form. We will see that in future videos. Now we're just focused on what does a number system me second thing. The most known number system is the decimal system, the one that we use in our daily life as humans. Also called based 10 it has 10 possible digits. 012345678 of mine who have Onley these digits on. Also, each number system has a set of possible digits. For example, the base 10 also called the decimal system, has 10 possible digits. 0123456789 But the base to the binary system has Onley to possible digits. 01 and you have to know that there is not only the symbol system. There is older ones like binary system, Octel System Exile, A simple system everyone has its utility on. We will see them in future videos, and also we can converse a number from a base to another base. For example, 13 in the symbol is represented by 1101 in binary on it's also represented by in 15 in Octel. See you in the next videos. 3. Introduction to decimal system: Hello, everyone. In this video we will see a quick and production to the simple system. The decimal system is the most known number system. It's the one that we use in our daily life. For example, to count money to Maju thinks on to do all the things The decimal system has 10 possible digits. 012345678 Line on Leah. These ones we can to compose a number in the simple system toe waits. Each weight represents a power of 10. We'll see that in examples to go from away to hire one will multiply by 10 and from away to a lower one with divide by item, we can name waits in the simple system depending on what they represent. You can see here that from here we have once then we have tense. Then we have hundreds. Then you have thousands. Then you have 10 thousands on the decimal point. And from here we have tense hundreds on so on. For example, this one represents how much units or once we have in the number, this digit represent how much we have tense this Did it represent how how much we have hundreds and so on. We can see that it's all powers of 10 here we have to expand zero, which is one than 10 explained to one which is tan tense. Then we have explained to which is hundreds and so on. Same thing from here. Examples. We have the number 3000 and 856 six represents the number off units or wants then explain on 05 Represents. The member of Tense eight represents the member off hundreds and three represent the number off thousands. So three thousands and 856 It's three times 1000 plus eight times 100 plus five times 10 plus six times. One second example, A fractional number. This time this one represents 10 exponents 0 10 exponents. One then explained to and from hair 10 exponents minus one, which is 0.1 10 explained minus two, which is 0.1 So this number means four times 100 plus three times 10 plus two times one plus one time. 0.1 plus five times syrah 50.1 There is a logic, while counting in the simple system. If we arrive to the highest possible digit, which is nine like we've seen in the set of possible digits and we want to add one. We put the number off that weight at zero, and we add one to the next. Wait, for example, we're counting. We have seven than eight and nine, and now we want to add one. But the mind is the highest possible. Did it? So we put 90 and we add one to the next. Weight on it becomes Stan 10 Here we put zero and we add one here. Second example, we have 49 toe add 1 to 49 9 is the highest possible digit. So line become zero. And here we add one, it becomes 50 third example We have 199 here we have zero and we add one here. But also this one is the highest possible digit. So we also put zero here and we add one hair on it becomes 2000. I hope you understood this one. See you in the next videos 4. Decimal to binary conversion: Hello, everyone. In this video we will see how to convert from decimal to binary in two different methods. First method. The successive division one of the number is strictly superior with divided by two and write the remainder At the end. We read remainder from bottom to the top and we get the binary number. We'll see that in examples. For example, we have the number 13. 13 is two times six +11 is the remainder. Now we take this number on, we do the same thing. Six is two times three plus zero. This time we have zero as remainder. We take three. We do this until we get zero in a caution. Three is to a time swan plus one, and now one is two times zero plus one. Here we have zero in the caution. So we stop and we read from the bottom to the top and we get 1101 second example, we have 34. 34 is two times 17 plus zero. 17 is two times eight plus one eight is two times for plus zero four is two times two flat zero to his two times one plus zero and one is two times zero plus one. And here we have zero. So we stopped on. When we read from the bottom to the top, we get 100010 third example, we have 287 287 is two times 143 plus one. 143 is two times 71 plus one. 71 is two times 35 plus one. 35 is two times 17 plus one. 17 is two times eight plus one eight is two times for zero. Fuller is two times two plus zero two. It's two times one plus zero and one is two times zero plus one. Here we have zero. So we stop and when we read from the bottom to the top, we get 100011111 Now we will see how we deal with fractional numbers. We will first do the integral part. Then we will treat the fractional part. The into their part is 11. In this first example, 11 is two times five plus one five is two times two plus one two is two times one plus zero and one is two times zero plus one. Here we have zero. So we stop and were it from the bottom to the top? We have 1011 and now we will do this part zero points 5000 and 625. This time we won't divide by two. We'll multiply by two by multiplying this number by two We get one 0.125. We just take the integer part which is one and we'll write zero point the rest off the result and we do the same thing multiplied by two This number is 0.25 on the integer part is zero with the same thing 0.25 multiplied by 20.5 The integer party zero and 0.5 multiplied by two is 1.0 and the integer part is one And here we have zero. So we stopped and we did this time from top to the bottom. We don't read from the bottom to the top word from top to the bottom. So we have 11.5000 and 625 is 1011.1001 And here we have the number second example, we have 28.3. First, we do the integral part. 28 is two times 14 plus zero. 14 is two times seven plus zero. Seven is two times three plus one. Three is two times one plus 11 is to time zero plus one and we get 11100 because read from bottom to the top. Now we do the fractional part. 0.3, multiplied by two is 0.6 is the integral part zero. This number 0.6, multiplied by two, is 1.2. The integer part is one zero 0.2 multiplied by 204 The integer party zero 0.4 multiplied by 20.8. The integer part is zero 0.8 multiplied by two is 1.6. The integer part is one on. Do we take 0.6? We can see that now we'll have the same result. So this division is an infinite division. Evan, we continue. We'll have the same Siri, which is 10011001 So we can decide to stop after five digits, for example. And we have their 1001 So our number and Byner is 11100.1001 Now, the second method, the powers of two first step will write powers of two that are unfair are equal to the number and second step. We compared the number with each power beginning from the biggest one. And if the number is superior that the power equal will write one on we subtract the power from the number else would just ride zero and we continue. For example, we have 91 The power's off Do that are inferior than or equal? The 91 are 64 32 16 84 to 1 on. Now we begin. 91 is bigger than 64. So we write one and we subject the power from the number and you get 27. Now we will work with this number. Not this one. This number This number is inferior than 32. So we ride zero on we continue. This number is super than 16. So right, 100 subtract. We get 11. 11 is superior than eight. So we write one. And here they have three threes in Federer than four right zero disrepair than to write one . And here we have one. It's equal. So it right one. And when you subtract, we have zero and we have no more powers. So this is our binary number 101101 second example, we have 4000 and 846. The powers that are inferior equal to this number R 4000 and 96. 2000 and 48. 1000 and 24. 512. And so on until one We just divide by two each time. Now we begin. This number is superior than 4000 and 96. So we write one. And when we subtract, we get 760 in failure than this one. Right zero. Also infer that this one right zero here. Hey, superior. So we have one and we're on. We subtract 5000 and 12 we get we get 2000 and 48 in further than 256. So we ride zero superior than this one and we have 120. Also superhero. That this one? Then we have 56 also superior. We have 24 also superior. We have one I do have. Then you have AIDS. It is equal. So at one and it becomes zero in fairer in Syria. Incident 000 because our number became zero and we have our binary number. 1001011111000 I hope you understood and see in the next videos. 5. Decimal to octal conversion: Hello, everyone. In this video we will see how to convert from the symbol, toe octo and a simple way to get the ocular presentation off a decimal number. We just do the Euclidean division each time. For example. Here we have 13. It's one time. It's one time eight plus five. Then we take this one. The caution one we divided by eight. One is zero times eight plus one. Here we have zero in the course in so stop and we read from the bottom to the top on. We have 15 second example We have 100 on 56. We do the division 156 by eight. Here we have one. When do we have seven? We take the six here we have line minus 72 and we have four. So 156 is 19 times eight plus four. Then we take this Number 19 is two times eight plus three to is zero times eight plus two. And here we have zero. So we stopped and were it from the bottom to the top. And we get to 234 A Now will treat fractional numbers. First, we will do the integral part of this example, which is 21. 21 is two times eight plus five. And to is zero times eight plus two. And here we have zero. So we stop and were it from the bottom to the top. Now we will do this part 0.75. Now, each time we multiply by eight until we get zero in the fractional part of the result. For example, here, 0.75 mighty multiplied by eight is 6.0. They take her part. It's six on here we have zero. So we stop and were it from the top to the bottom. So this number is 25 0.6 second example, we have 78.65 78th as nine times eight plus six 100 line. His one time eight plus one undo on is zero times eight plus one. Here we have zero. So we stopped. So 78th. This part is 116 116. Now we will do this. Part 0.65 multiplied by eight is 5.2. Well, let the integral parts and we use 0.2 0.2 multiplied by eight is 1.6. The integer part is one, and we use 0.60 point six. Multiplied by eight is for 0.8. We have four here and we use 0.8 0.8. Multiplied by eight is six points. For here we have six, and here we have 0.4 0.4 months. Supplied by eight is it's three point to the integer part is three on here? We have 0.2, but we can see that it's the same that this multiplication. So this is very we'll just repeat to the NFL. It's one for 63 and we can decide to stop after, For example, five digits and we get 116.51 for six Tree. I hope you understood and see you in the next videos 6. Decimal to hexadecimal conversion: Hello, everyone. In this video we will see how to convert from decimal toe, said Ismael, in a simple way like we did from this Moto Otto will do the A clearly in division by dividing each time by 16 until we get zero in the quotient. Here we have the first example. It's 90 on the 90. It's equal to 16 farms, five plus. Then we take this number. The questions on we repeat the operation five is 16 times zero plus five and we have zero in the portion. So we stop and we read from the bottom to the top. So we have 19 is five a. Because we can't right on as a decimal. 10 is represented by a second example. We have 588 now we will do the division 500 and 88 divided right? 16. We take to a numbers because here we have to 58 in 58 we have three times 16 3 33 multiplied by 16. It's 48 and when we do this obstruction, we get 10 and we take the next digit in 108. We have in 108 to have six times 16 six multiplied by 16 is 96 and here the half 12 but 12 is inferior than 16. So we stop on we right? 500 Uh, 88 is okay. 36 times 16 plus 12 and now will think this number and repeat the same. Operation 36 is two times 16 Los four. We take this number again to is zero times 16 plus to And here we have zero in the question . So stop and we're to for and 12 is represented by sea. So 588 is two for C in decimal. Now we will do the same thing with fractional numbers. First, we will do the integral part 14 is zero times 16 plus 14 and we stop here. They have zero of the caution and 14 is a so 14 Is he in exhibit? Similar. And now we will do the fractional part. This part will multiply each time by 16 until we get zero in the fractional part off the result 0.3 on two sighs multiplied by 16 is equal to five point zoo. We take the integral part and here we have zero in the fractional part of the results. So and were it from the top to the bottom in the integral part Word from the bottom to the top. And here we read from the top to the bottom on 14.3125 is e point Fine. Second example, we have 28.54. 28th is one time, 16 plus Well, just see. And one is zero times 16 plus one on here we have there so stop and 28 is praise from from the bottom to the top it's one see because 12 is represented by sea in exit a symbol. Now we will do this part which is zero point 54 one will multiply it by 16 We get eight 0.64 right? The integer part here and we take the fractional part 0.6 default. We multiplied by 16 we get sen points 24 We take the integer part on here we have the fractional part 0.24 multiplied by 16 is three points 80 We take the integer part on we do the same operation until we get zero. Him zero 0.84 multiplied by 16 Is sir seeing points 54 on the integral part is 13 zero point 44 multiplied by 16 is seven point zero four. Take the seven. Andrea let fractional part 0.4 multiplied by 16 is 0.64 and you take the integer part zero . But we can see that we will repeat the same operation as this one. So we'll get 10 3 13 70 10 3 13 70 until infant. So we can decide to stop here after five digits and we have 20. 28.54 is one. See 10.8 a three d seven. We can continue, but we can't stop here. See you in the next video. 7. Introduction to binary system: how everyone in this video, we will see a quick introduction toe binary system. The binary system is the most known number system after the symbol system. It's used by the most common Elektronik systems computers, calculators on other ones. The binary system has only two possible digits, also called bits. We will use this word a lot of times. In this course they are Onley zero and one. We can use Onley, these two possible digits. Who used the binary system? A lot of electron ICS because zero and one represent the state off the electric current one if it passes zero if not one and zero are also used in Bullen algebra. One represents the true statement, and zero represents the full statement we can to compose a number in binary system to weights each way to represent the power of to to go from away to a higher one. We multiply by two, and from away to a lower one, we divide by two. As we can see here from here, we have to expand zero to expand one to expand to to explain, three. To explain. For on here we have the binary point and in the fractional part of two exponents minus one to expand minus two to expand 13 and so on. We can continue to infinity. There is a logic while counting in binary system. If we arrive to the highest possible digit, which is one we can't use two or three or more. And we want to add one. We put the number off that Wait a zero and we add one to the next. Wait, for example, we have one, and we want to add one. We put this weight at zero and we had one here It becomes 10 10 and binary. Second example, We have 11 When we add when we want to adhere, we put this 10 and we add one here. But same problem. One is highest possible digit. So we put also zero here and we add one. It becomes 100 Here we have 101 Here we have one and we want to add one. So this one become zero and we had one here. It becomes 110 Now we see some examples. Hey, we have 101101 This one represents to explode. Zero to explain it. One to explain to to explain three. To expound for and to expand. Five To get the powers of two would just multiply each time. By 21 we move to the left. So here we have one, then two, then four, then eight and 16 than 32. So this number means one time. 32 plus zero times 16 plus one time eight plus one time. Four plus zero times two plus one time. One second example Who have won 10.101 This one represents to expand zero to expand toe to explain to aunt from here to expound minus one, which is 0.5 to expand minus 20.25 2 exponents minus 30.125. So this number represents one time four plus one time two plus zero times one plus one time . 0.5 plus zero times 0.25 1 Time Sarah 10.125. I hope you understood. See you in the next videos 8. Binary to decimal conversion: Hello, everyone. In this video we will learn how to convert from binary to decimal in a simple way. First, you have to know that in a binary number, each bit represents the power of to, for example, here this first bid from the right represents to explore and zero which is one then this wrong represents to explain it one which is to then this one represents to expand to which is for and so on. So, each time to get the next power, we just multiply by two and the next step together the symbol number. We just add each power off to when we have one here. So for example, in this binary number, which is 110 we have four plus two. We don't add one, because here we have zero on. We get six second example who have won 1011 This one represents one, then two, then fourth and eighth and 16 on Now, second step, we add we at 16 plus eight plus two plus one. We don't at four, because here we have zero and we get our decimal number, which is 27 third example, have won 1011001 it represents 1248 16 32 64 128. So we add, we add 128 plus 64 plus 16 plus eight plus one. And we get 217 last example we have +10010101 same powers because thes two numbers have the same the same number off bits. So we add 128 plus 16 plus four plus one, and we get 149. And now we move to fractional numbers the numbers which have a fractional part. But it's the same thing because in the fractional part, each each bit represents the power of to but negative exponents. So here we have two exponents, minus one toe exponents minus two to explore in minus three. You can see this table to know the values of the most important powers of two. So here, to explain minus one is 0.5 than to expand minus two. Is there a 20.25 so on. So here we have from here 1248 16 on from here we have 0.50 point 25 therefore 10.125 and we add as we did in the previous examples, we have 16 plus 2 10.5 plus 0.125 and we get 19.625 2nd example, we have 1011.1101 from here it represents +1248 And from here we have 0.50 point 25 0.125 0.0, 625. And we just add we at eight plus two plus one plus 0.50 point 25 plus 0.0, 625 and we just get 11.8000 and 125. See you in the next video. Try to do more examples to practice. It's very important 9. Binary to octal conversion: everyone. In this video, we will learn how the convert from binary toe octo and simple way. We just have to split our binary number into groups off three bits. And then we will convert each group into a one digit Octel number. For example. 000 become 0001 becomes 10 on their becomes two and so on. In this first example, which is 111 we have on Lee one group because we have only three bits and 111 become seven . Because it's four plus two plus one second example, we have the first prepare on the 2nd 1 In the 2nd 1 we can see that we have on Lee to bits , but it's not a problem because we can fill the remaining bits by zeros and it's the same thing. So 110 become six and 010 becomes too. So it's 26 Octel third example. They have this group, and this group 001 is 1011 is three fourth example. We have first group second group on 1/3 group. 110 is six because it's four plus 2101 is five on 1106 So it's 600 on 56 last example. We have this group, this one this one This one This one on this one. This one is the same as 001 So it will we have 100 It's 4110 is six there is there. Want is one on ones. Every 6010 is 2001 is one. So we got our octo under. Now we will do the same thing with fractional numbers and fractional numbers will do the same thing for both parts. In the integral parts we do the same thing. For example, here we start from the binary point and we go to the left. We split from the the integer part into groups off three bits, for example, Here we have only one. We could continue from here. Then we do the fractional part from the binary point to the right And here we have all the one group and we convert 001 becomes one. Then we have the point. Then 110 becomes six. So it's 6.1 second example we start from here to the left. First you do this part. You have this group on this group. Same thing here. 001 Then from the Visionary point to the right to do the fractional part. You have this group on this group something here who feel the remaining bits by zeros. So this group is 010 010 is too. Don't do the mistake that you can think that this group is 001 It's wrong. You have to continue by serves. So it 010 01 want is three have the point 011 is three and 001 is one third example. You have this group and this group And from here we have this group on this group. 100 is four 110 is six. We have the point. 100 is 4001 This one third example We have only one group here in this part on in this part you have one group to three groups. Zero on zero is 2100 is four 1106 We do the 0.110 is six. So it's 6.642 last example. In this video we have in the sport to have first group and second group. And in the fractional part we have this group, this one this one this one on this 1110 is sits. 1117 11060000 001 is one we do the point 010 is two and 001 is one. So it's 12.10676 See you in the next video and try to practice more examples. 10. Binary to hexadecimal conversion: Hello, everyone. In this video you will see how to convert from binary toe executable in conversion from binary toe octo. We said that we have to split the number into groups off three bits. This time we'll do the same thing, but by groups off forbids. So we will split the binary number in groups off forbids. Then we will convert each group in a one bit exact symbol number following this table, for example, we have 0000 become zero 101 warms it becomes be the 11 on other conversions. So in this first example which is 110 we have only one group. We have only this one and we have only three bits here. So we feel the remaining bits by zero. So 0110 becomes six and we got our exit decimal number. Second example, we have two groups have the 1st 1 Then the 2nd 1 The 2nd 1 is 0001 So 100 war is nine because it's eight plus one and 0001 is one and we get 19 third example, we have first group second group 0110 is 60011 is three fourth example. You have this group on this group on the third group, 1110 is E, which is 14 but we can't write 14 right assemble that represents 14 in Exit the Symbol, which is 1010 Ystad because it's eight plus two but 10 is a sore right. A here and 0001 is one last example. You have first group second group third group on fourth quarter 0100 is for we have 01117 because it's four plus two plus 17 1100 is 12. So following this table, it's C because we can try 12 1010 istan. So we write a on We got our exit decimal number, which is a C 74. Now we'll do the same thing with fractional numbers. First we do the integer part. We split into groups of four bits. Then whether the fractional parts also a spirit in groups of forbids. Here we have one from each side. 0110 is six. Then we do the point 0010 Don't forget zero hair to complete the four bits 0010 is too. I'm not one second example in this side we have only one group. And from here we have this group. Uh, this one. This one is 1000 Which is it? This one is 0110 which is six. We do the points and we have 1011 which is 11 because it's eight plus two plus one and 11 is be So were I to be You have be born 68 third example will have one group and one group 1101 is the it's 13 because it's eight plus two plus one. So we right d we do the 0.1100 is 12. So it see, so is see pointing. This binary number is represented in exit decimal by sea pointed the We have this example We have one group here 01106 And from here we have one group on two groups. 0001 is 11101 is D which is 13. We do the point 0110 is six. It's for us. Last example. We have one group from here and from here have one to three. And for this one is want one zero zero 1100 is 12. So it see 01117 0011 is three 0010 is too. We do the point on 1010 is 10 so right. Hey! And we finished our examples. See you in the next videos. 11. Introduction to octal system: Hello, everyone. In this video, we will see a quick introduction toe Octel system. The actual system is one off the different number systems. It is often used to reduce binary numbers length. For example, here we have 110001111 it becomes 617 We reduced the length from nine digits to three digits. The binary system has eight possible digits. 01234567 In the only days of computing, Actos often used to shorten 12 bit, 24 bit or 36 bit words. It was very important to have a short length articles also used by some Native American tribes, because they were using spaces between fingers to count or in the Avital film, where characters had four fingers. So they have to you the Octel system. We can to compose a number and octo system to wait. Each with represents a power off eight to go from away to a higher one. We multiply by eight and from away to a lower one, we divide by eight. So from here, for example, from here we have eight expand zero, which is one then we have a exponent 18 explained to and so on. Same thing from here. It exponents minus one. It explained, minus to answer. We'll see that in examples. There is a logical counting and Octel system. If we arrive to the highest possible digit, which is seven and we want to add one who put the number off that weight at zero and we add one to the next week. For example, we have seven and we want to add one. Here we put zero and we add one here and it becomes a 10 2nd example we have 37 7 and we want to add one. We put zero here and we add one here it because for Joe here we have 77. And if we want to add 17 become zero. And we had one here, but same problem. So we put zero here and we add one. It becomes 100 examples. And Octel, we have 7000 and 325. This one represents eight exponents. Zero x eight exploring 18 explained to it. Expand three. We can see the values of each power here. The most used wants. So for example, here we have 512 multiplied by seven plus 64 multiplied by three plus eight multiplied by two plus one multiplied by five. And if we add these numbers who have the decimal representation off this Octel number? Second example, we have 25.46 from here. We have one Have this one represents eight. And here we have eight explained minus one, which is this number on eight explained minus two. Which is this number now we And this number represents two times eight plus five times one plus four times it explains minus one, which is 0.125 on six times eight exponents minus two. I hope you understood it and see you in the next videos. 12. Octal to decimal conversion: However, one in this video we will learn how to convert from Actel two decimal. First you have to know that in Octel number each digit represents a power off eight. For example, the 1st 1 from the right represents eight exponents zero which is one then This one represents at eight exponents one which is eight. So now we have the powers. Then we do the audition. We multiply each power by value off the digit. So for example, here we have eight multiplied by four plus one multiplied by six and we get 38 in decimal. So 46 in Octo is 38 in decimal. Second example, we have 257. This one represents eight explosion zero which is one then we have eight. Then we have 64. So here we have the powers on. Now we will do the audition. We have 64 multiplied by two plus eight times five plus one time seven and we get 175. Third example. We have 3000 and 504 here We have one than eight than 64 than 512 and now we do the addition. We have 5 12 multiplied by three blast 64 multiplied by five plus one multiplied by four. We don't at eight, because here we have zero. So we don't multiply because eight multiplied. Baser Ezio. So now, when doing the addition, we have 1000 and 860 last example. We have 2000 and 167 this one same powers, because thes do numbers have the same number off digits. So now we did addition, we have 5000 and 12 multiplied by two plus one time, 64 plus eight times six plus one time seven and we get 1000 and 143. Now we will do the same thing with fractional numbers. So in this table you can see the values of the most used powers off eight. In this first example, we have 14.7. This one represents eight exponents minus one, which is 0.125. Then here we have one. Then we have eight. And now we do the addition as we did in previous examples. We have a time one plus one time for plus 0.125 multiplied by seven. And we get 12.875 second example. We have 45 do 450.0 tree. This one represents one than eighth and 64 on. From here it represents 0.125. This one represents this number, as you can see in this table. So now we do the multiplication who have 64 multiplied by four plus eight times five plus one time, two plus three times this number and we get this number in the symbol. See you in the next videos. 13. Octal to binary conversion: Hello, everyone. In this video we will see how to convert from Actel toe binary conversion from octo toe binary is really easy because you just have to convert each digit in the Octel number into a three bits binary number following this table, for example, Here we have five becomes 101 and seven becomes 111 because it's four plus two plus one and we get our binary number. Second example, we have 167 1 becomes 0016 becomes 110 and seven becomes 111 and we have our number. Third example, we have 7000 and 24 7 is 111000020104 is 100 and we get our number. Fourth example. This time we'll have a fractional numbers. But we will do the same thing on we at the point 10013 is 0115 is 101 We do the point and four is 1005 is 101 last example. You have this number on. We will do the same thing to get this number and we just finished. The conversion is really easy. See you in the next video. 14. Octal to hexadecimal conversion: Hello everyone. In this video we will see how to convert from Octel to exit decimal to convert from Octel To exert a simple we have to do two steps in the first step will convert from Octel Tobin a reforming this table than in the second time. We will convert the binary number that we got to exit a symbol following this table. First example would have 52 five becomes 101 and to become 010 we got the binary number. Now we converted to eggs decimal by splitting it in. Groups off forbids we have first group Second group 1010 is 10 but done in exit Decimal is represented by a It's all right, eh? And 0010 is too second example We have 4000 and 51. Four becomes 1000 become 0005 becomes 101 and one becomes 001 We got the binary number on now were converted to exile a symbol 100 on his line. 0010 is too. 1000 is eight And now we got exit the similar representation off this Octel number Third example, We have a fractional number, but it's the same method we have 4.25 for Becomes 100 We do the point. Two becomes 00 and five becomes 101 on we get this binary number now we converted to exit the symbol In this part we have only one group and in the fractional part of you have two groups. 0100 Don't forget the zeros here to complete the forbids 0100 becomes four 0101 becomes five. The 50.100 becomes for last example. This number in binary becomes this'll one. Ah, Now we split one group here and here have two groups. 0011 is 31110 is 14. But but well, right e the 0.101 is five and we just finished the conversion. See you in the next videos. 15. Introduction to hexadecimal system: Hello, everyone. In this video, we will see a quick introduction toe exit decimal system. The exact decimal system is one of the different number systems it is often used to reduce binary numbers length. For example. 111101001001 becomes F for mine from 12 digits to three digits. We will see why we wrote half here. The eggs are decimal system has 16 possible digits. 0123456789 a b c D E f. Here because we have 10 11 12 13 14 15. But we don't have symbols like this to represent them. So we used letters, an exact a symbol system. We need digits that are greater than line, so use letters to represent them, then becomes a 11 becomes B 12 becomes C 13 becomes the 14 becomes E and 15 becomes F. You really have to know this. An exit decimal digit is also called a nibble. Nibble is the group off four bits. We can also represent colors in exile decimal, for example. White is F F F F F F Black 000000 This green is 63538 On this bank is FC three, the F line we can to compose a number in exile a symbol system to weights. Each weight represents a power off 16 to go from away to a higher one. We multiply by 16 on from away to a lower one. We divide by 16 as we can see here, Here we have 16 exponent, zero number of times that we have 16 exponent, one number of times that we have 16 expo in two and so on. And same thing from here There is a lot of coil counting and exit decimal system. If we arrived to the highest possible digit which is F 15 on, we want to add one. We put the number off that way a zero and we add one to the next. Wait, for example, we have and we want to add one to go to 16. We put this 10 and we add one Here it becomes 10 So 16 is 10 eight f and we want to add one . This one become zero and here we add one, it becomes 90 third example, Have 1/2 half Harry. What we want to add one. So here we we put zero and we add one here. Same problem here. So it puts zero and we add one here, and it becomes B 00 Example of exotic symbol system. The composing will have six. A seven e e means that we have 14 times 16 exponents. 07 means we have seven times 16 exponents. One A, which is 10 means we have 10 times 16 explode into and six minutes. We have six times 16 Explain three, which is 4000 and 96. So we have that. The composition. Six Time 4000 and 96 plus 10 times 256 plus seven times 16 plus 14 times one second example Have B 2.3 C. It means we have 11 times 16 exponents, one plus two times 60 and expand zero plus three times 16 explained to minus one plus 12 times 16 exponents minus two. I hope you understood it and see you in the next video 16. Hexadecimal to decimal conversion: Hello, everyone. In this video we will see how to convert from Eggs are a symbol to the symbol. You have to know that exact decimal number. Each digit represents the power off 16. For example, the 1st 1 represents 16 exponents zero, which is one. And this one orb isn't 16 exponents, one which is 16 at now. Second step, we multiply each power by the value off the digit. For example. Here we have 16 multiplied by three plus one multiplied by six and we get 54 second example . We have three C eight c is 12. We have three times 16 expo in two and 12 times 16 exponents one and eight times 16 expand 1 16 exposed to is 256 and we get by adding the powers multiplied by the value of the digit . 968 3rd example have the zero being line. Here we have the is 13. Here we have 30 and multiplied by 16 exposed three plus 11 multiplied by 16 exponents. One blast line times 60 and expand zero, which is one 16 Expo in three is 4000 and 96 and we get by adding we get 53,000 and 433 in the symbol. So this the similar representation is the representation of this exit. A symbol number. Last example. We have 488 e same powers because these two numbers have the same number off digits. Now we multiply four times 4000 and 96 plus 10 times because a istan 10 times 236 plus 16 times a eight plus one time E e is 14 and we get 19,000 and 86 now we will do the same thing with fractional numbers. It's the same thing here. Visited. It represents 14 times because he's 14 14 times 16 exponents minus one, which is zero 0.0, 625. So in this number we have eight times 16 exponents, one plus 12 times 16 exploring zero plus 14 times 16 exponents minus one, and we get 140.875 second example. We have a 5.2 b, so we have 10 times 2000 and 56 plus five times one plus two times this number, which is 16 exponents minus one plus 11 times this number, which is 16. Expand minus two and we get this number. I hope you understood and see you in the next videos. 17. Hexadecimal to binary conversion: how everyone in this video we will see how to cover it from exile. A symbol toe binary to convert from exact a symbol to binary. We just convert each digit toe a four bids Binary number following this table, for example, nine in binary is 1001 and three is 0011 So we joined them and we get the binary representation. The zero tree is 11010000030011 who joined them? And we get the vinyl representation. So this one represents these forbids. This one represents these forbids and this one represents these four bits. Third example have see 6 to 8. We have C becomes 11006 becomes 0110 to become 0010 and eight becomes 1000 And with John them same thing for fractional numbers we have here before. 0.55 b becomes 1011 for become 01005 become 0101 And we don't forget the point here between the two parts last example we have this number by following the same method. We get this binary representation. See you in the next videos 18. Hexadecimal to octal conversion: Hello everyone. In this video we will learn how to convert from exit decimal toe octo to convert from Exodus Emoto Octo We must do two steps. 1st 1 is to convert from exile a symbol to binary following this table and second step is to convert from binary toe Octel, for example. Here we have a six in his arsenal A is 1010 and six is 0110 Now we got the binary number. We will split it in groups off three bits to get the Octel Representation First Group, Second World and third group This group is 010 We have won 10 which is six 100 which is four 010 which is to second example have nine for de to mine is 1001 for 0100 There is 1101 and 20010 Now we'll split 12 three, four, 56 Here we have to another two three to 11 third example we have seven point C four seven becomes 0111 c becomes 1100 on four becomes 0100 Here we have one group and from here we have 12 groups. 001 is 11106.1117 last example, which is be 0.0 f b is 1011.0 and f is 1111 We got the binary number and now we split. We have 12 groups and from here we have one, 23 groups From here we have 110 which is 6011 is 30000 0.11 is 3001 is on on. We got the octo representation off this exit. A symbol number. See you in the next videos. 19. Decimal to BCD conversion: Hello, everyone. In this video, we will see how to convert from the simple to obesity or binary coded decimal to convert from decimal to obesity. We just have to convert each digit from the decimal number toe a four bits representation, for example. Zero become 00001 becomes 0001 and so on for for the nine digits. So, for example, here we have two to become 0010 and five become 0101 and we just write him on. We get our BCG representation. Second example, we have 461 4 become 01006 becomes 0110 and one become 0001 third example, you have 307 three become 0011 and zero. Become 0000 and seven become 0111 Andre. Get the representation. Fourth example, who have 7000 and 953. It's becomes this number. We just convert each digit toe a four bit representation and binary. Obviously last example who have 816840 eight becomes 10001 become 00016 becomes this. It becomes this and for becomes this and zero becomes this and we just get the representation. See you in the next videos. 20. BCD to decimal conversion: Hello, everyone. In this video we will see how to convert from Bay City two decimal to convert from basically two decimal. We just have to split the number into groups off forbids. Then we will convert each group into a one digit. The symbol number following this table in this first example will have the first group begin. We begin from the right of the first group and the second group. The second group has only one digit, but it's 0001 1000 becomes eight following this table and 0001 becomes one and we have 18 2nd example We have first group, second group, third group this 10111 and we get following this table. We get the representation in the symbol because they're 111 becomes 71001 becomes nine and 011 will become seven third example who have first group's second group and third group. This one becomes four. Here we have zero and here we have eight. This example First group Second group, Third group fourth quote. Here we have six have five here we have three. And here we have to. It's 0010 last example. Have this group this one? This one. This one. This one and this one. Hey would have seven and we have seven Here. We have line here. We have eight here. We have seven on here. We have four. And we got our decimal number, which is for 78977 See you in the next videos. 21. Binary to ASCII conversion: Hello, everyone. In this video we will see how to convert from binary toe asking. Asking is the American standard code for information interchange and we will use the escape table to do the conversion. The escape table contains each character and its decimal value are executable or octo value . For example, we can see here that the value of the upper case A is 65. The value of the plus sign is 43 and the value of the lower case oh, is 111 on last example the value of the equal sign is 61 to convert from binary. To ask you, we convert first we convert each bite group of eight bits to the symbol. For example, if we have 1501000 zero zil one, this one becomes 65 because we have 64 plus one. Then the second step is to use the escape table to get the character off each decimal value . Now we will do an example. For example, we have this binary string we will convert bite by bite. For example, we have the first bite. 01000001 It's 64 plus one. It's 65 we get the upper case. A second character. Second bite we have 01010011 We have 64 plus 16 plus two plus one. It's 83 and 83 is the letter. The uppercase s third bite will have 01000011 who have 64 plus two plus one. It's 67 on we get the letter. The upper case c fourth by to have 01001001 It's 64 plus eight plus one. It's 73 in 73 we have the upper case. I the last, but is the same other previous one. So it's also the upper case I and we get the world asking See you in the next video. 22. ASCII to binary conversion: Hello, everyone. In this video we will see how to convert from. Ask a tow binary. First, we will use the ask your table to get the SK value off each character. And then we will convert each value to binary in eight bits. Obviously, here we have the escape table and we will convert the word Valtteri. The value of the upper case B is 66 66 64 plus two. So it +01 0000 10 Here is it The second letter is I lowercase I It's asking. Value is 105 105 is 0110100 1/3 letter. We have add lower case and it's asking value is 110 and by converting it toe binary we get 0110111 0/4 letter is lowercase A It's asking value is 97 by converting it to binary and eight bits. We get 01100001 fifth letter is lower case Are the decimal value off? Lower case R is 114. By converting it to binary, We get 01110010 on last letter is why lower case? Why the SK value off? Lower case. Why is 121? And by conversion we get 01111001 on Dhere. We converted the world binary into binary. See you in the next videos. 23. Binary to gray conversion: Hello, everyone. In this video we will see how to convert from binary to gray. Also called reflected binary code. The method is easy. First were right the MSP the most significant bit. Then for each bit If it's different than the previous one, right? One else, Right? Zero. We'll see that in examples. First example, we have 1001 Right. The MSP which is one this one. If it was here, we would ride zero. Then we can see that zero is different than one. So we write one. It means that we change the value, the value chance. Then we have zero. It's the same as the previous one. So we ride zero. We didn't change the value. Now we have one. It's different than the previous one. So we write one and we got our conversion. You must know that the binary number and it's great representation have the same number off bits. So here is for and we have four bits here. Second example, we have 1100 who are the most significant bit. And hey, we have one. It's the same value than the previous one. So we didn't change and we right there Now we have zero. It change its alright one And now we have zero. It's the same other previous one This one 00 So right zero Because we didn't attend the value. Third example, we have Juan Juan, Juan Juan. We have one here now we have zero because it didn't change. We have also zero and they have also zero. It didn't change at all. We have 1000 We have one than zero. So it Jen So we're right on. Then we have zero. It didn't change. So we have zero and zero because it's the same value than the previous one. We have 1011101 Here we have one than zero. So it Trent, we have one. So here we have one is the same value. So zero zero one zero one Because it chanced it was zero. It became one. Now we have 0101000 Now we start by zero. The most significant bit. We have one chance. It also changed. Also here also here. But now we have 00 because it's the same values of the previous one last example, we have won 10 Their 10111 there. 1011 You can do it very quickly with practicing. Ever have one zero one 01 one 10 zero 111100 And here we finished Our examples. See you in the next video. 24. Gray to binary conversion: Hello everyone. In this video we will see how to convert from Graito Binary. The method is easy to convert from greater binary. First we write the MSB the most significant bit than for each bit. If we have one, we change the value and write it else will write the same value as previous one. We will see that in examples For example, we have won 101 right? The MSP, which is one in this case. If it was your, we would write zero then. Now we have one. So we change the value. Right? Zero Now I have zero, so we don't change. And now we have one. So we change. Have 100 The gray number and the binary number have the same number of pits. Second example, we have 1001 We write one Then we have there. So we don't change. We don't change. Yeah. Once a witch and third example of 1111 Who are the AMA's B which is one one Then we have one. So we Chand, we turned and we change. We get 1010 fourth example, we have 010 here we have zero one So we change. Zero means we don't change. One means we change. You can do the conversion very quickly. You have 1010101 one You don't change. We change. We don't change. We chained. We don't change and we change. 0101011! We have zero. We Chand, We don't chant You change! You don't chant! We change on we change again. Last example We have won 1011011101011! We have one. We tend Don't change We turned We change again. We don't change We chant Chand! It turned! They're here! We don't change, We chant We don't change rich and which end on we change again on we finished our examples . See you in the next video. You can't practice with more examples to get to get the conversion very quickly. 25. Binary to IEEE-754 conversion: Hello, everyone. In this video we will see how to covert from binary or decimal toe I triple e 7 54 Standard . First, I will begin by simple precision. It means that we will get the representation in 32 bits. The first step is to convert the number into binary. If it is not already second step, we write the scientific notation of the number. It means to write it in this form wine point. The rest of the number multiplied by to expand and examples. We have this number. It becomes 1.11001101 multiplied by two exponents five y five Because we moved the point by five positions to the left. Second example, this number becomes 1.101011 multiplied by two Excellent minus four. Why minus four? Because we moved the point by four positions to the right this time not to the left. When When? When we move to the right, it's minus third example This one becomes 1.1001110 multiplied by to expand 00 because we didn't move the point. Same thing for fourth example, we have minus 1001011 It becomes minus 1.1011 multiplied by two exponents six because we moved the point by six positions to the left. The point is, here we don't see it. See it? But it is here because it's the end of the numbers. So we moved by 123456 Third step is to use the scientific notation to get the I triple e 7 54 representation in this form. First, we have one bit for the sign. It's zero if the number is positive and one if the number is negative, we have the exponents. So we add this number. Exponents were added to 127 on. We write it in binary in eight bits, and third part is the Monte, so represented in 23 bits. It's this part after the point in the scientific notation and we add zeros to fill 23 bits . We'll see that in examples. For example, we have this number 1100110.1011 We have to get the scientific notation. We have to move the point by six positions. 123456 to the left. So it becomes 1.1001101011 multiplied by to expand six. Now we got the scientific notation. Now we'll get the exponents we add six explained this 1 to 127 and we get in binary ones in eight bits. Obviously 10000101 And now well, we feel the representation. The number is positive. So we have zero in the sign bit. We write the exponents in eight bits in the second part on now we wrote this part here, and we fell by zeros to get 23 bits in this part and we got the I triple E 754 representation off this number, This binary number second example have minus 0.1001011 Now we have to move the point by four positions to the right. 1234 to get one point of the rest multiplied by two exponents minus four. And now we will add it to 127. This is a scientific notation and we will add minus four plus 127. We get 123 represented in via Larry. It's in eight bit it. 01111011 And now we'll get the I Tripoli representation in the sign bit. We put one because as you can see, the number is negative. Then we have the exposing in this part eight bits, it goes here. Then we have this part off after the one point it goes here and we filled by zeros. Toe get 23 bits in the months and we got our representation. Third example, we will do it by hand. We have 1100011101 So the binary point is here. We can see it, but it is here. We have to move it by 1234567899 Positions line and the Now all right. The scientific notation it equals to 1.1 00 0111 01 multiplied by two exponents line. And now we'll search for the exposing we add 127 plus mine. They get 136 which is in binary 128 plus eight. So in binary is it's an eight bits. 100 01 000 on. Now we get the representation. The number is positive. So we have zero in the sign bit. Second part, we put the exposing in eight bits. The eight bits off the exposed 1000 100 and the third part It's this part. 10 zero 11101 And now we add zeros to feel 32 bits you have when you count here, all the all the bits from here to the end, you have to find 32 to stop putting zeros. Now we'll do the same thing for double precision. Double persistent mean We'll get means We will get the representation in 64 bits. Step one. Convert the number in turbine er, same us for simple precision. Second part will ride the scientific notation. Same examples. The third part changes a little bit because the I triple E 745 and 54 representation in double precision who write it in 64 bits, not 32. So have one bit for the sign. Same thing. One is if it's negative. Zero. It's positive. 11 bits for the exponents on not eight and we have 52 for the month is so we'll see an example. We have this number and we must represent it in 64 bits. Remove the point by 12345 positions to the left. So positive on we write the scientific notation This number multiplied by to expand five. Now who was search for the exposed, which is 101,000 and 23. Now we don't add 127 and double precision. We have explained to 1 1000 and 23 we get 1000 and 28 in binary in 11 bits. It's 10000000100 And we feel this phone. So we have zero hair in the sign bit because the member is positive. We have this part goes here on this this one. Those here on obviously were filled by zeros to get wanted in 52 bits. Onda, we finished our work. See you in the next videos 26. IEEE-754 to binary conversion: Hello, everyone. In this video we will see how to covert from Tripoli. 754. Standard toe binary or decimal and simple. First, we will do a simple precision. We have the simple precision Form one before the sign. A bit for the exponents and 23 bits for the Mounties. We have 32 bits. First step right. The exponents in the decimal form have the this exponents on. We'll write it in the decimal form we converted from binary to decimal second step who write the number In the scientific form, it means one point the Mount Isa This part multiplied by two exponents. The number we got here minus 127 and third step will write the number in the normal form by moving the binary point. If we have a positive number here who move the point to the right and if we have a negative number, will move the point to the left fourth step. We add the minus sign before the number. If the sign bit is one, because if the sign bit is one, it means that the number is negative. Last step would just convert the number two decimal. We can let it in binary, but we can convert it to decimal. Let's see an example. We have this number. This number is in 32 bits and I triple is 754 and simple precision. We split it like that one bit for the sign. Here it 08 bits for the exponents and 23 for the month is here. We have zeros of the number is positive. Then we have the exponents. 10000111 We will convert it to decimal. It means 128 plus four plus two plus one. It becomes 135 now we just subtract 127 from it and we get eight. So now all right. The scientific for its one point this part. We don't have to have this extra zeros multiplied by two exponents. Eight the number we got here and now we move the point by eight positions to the right because this number is positive. Remove 12345678 And we get 110111010101 123456780.1 and now we converted to the symbol on we get 442 points. 25. Let's see a second example. We will do it by hand. This time we have one. So the member is negative, who have the exponents which is 01111010 And to have the Matesa first, we convert the exponents of the decimal form. We have 64 plus 32 plus 16 plus eight plus to it gives us 122. And now by doing 122 minus 127 we get minus five. So now were right. The scientific form one point This part. We don't have to add extra zeros. 111101 multiplied by two Ex Poland This number minus five. So now we just move the point by five positions to the left. So 12345 So we have to add zeros. It's become zero point zero zero 00 one Onda, we continue this part 11110 one because we moved the point by five positions to go to the left. Here we have the point. 12345 And now we go the number. But the sign bit is one. So the number is negative and we don't forget to add the minus sign. And we got the binary representation off this number on. You can convert it to the simple if you want. Now we will do the same thing with double precision. Now I have the number in 64 bits. One for the sign, 11 for the X Poland, and not eight and 52 for the Mantis. Third step right. They x Poland in the decimal phone. It's the same steps, a simple precision. But just in the man Tissa, we calculate exponents minus 1000 and 23 on not 127. But you have the same steps and now we will see an example. We have this number in 64 bits. The sign bit zero. So the number is positive and we have the exponents in 11 bits. So we calculated were converted to decimal. We have 100 24 plus eight. Here we have AIDS lost to plus one. We get 1000. Um, 35. And now we subtract 1000 and 24 from it, and he gets well, so we ride the scientific innovation. 1.10 01010 one multiplied by two exponents. Well, you just wrote this part after the one point, and now we move the point by 12 positions to the right because this number is positive. 123456789 And now we have to a zoo Juan 10 So, Juan 10 one. The point was here. 123456789 10 11. Well, and now we got the vinyl representation off this number to you in the next videos. 27. Binary addition: Hello, everyone. In this video, we will see how to do the addition between two binary numbers. First, before we get started, there is basic operations. In addition that you need to know. Then we will able to do examples first. There is zero plus zero. We get zero 2nd 1 we have one cause zero. It gives us one, obviously. Then we have zero plus one. It gives us one. Then we have one plus 11 plus one is two. But we can't right to here because we're in binary and two is represented by 10 So right, zero here. And we get one As Carrie. Fourth operation. We have the carry one plus zero plus zero. It gives us one. Then we have one of the carry plus one plus zero. We get too. So it's +10 So I write zero and we have one as a carry. Then we have one off the carry plus zero plus one. Same thing. We get zero and one as a carry for the next operation and less one. We have one plus one plus one. We get three, which is 11 So we write one here and we let one as a carry. Now we can start to do examples. First we have 10 plus one. We will add bit by bit. First we start from here We have zero plus one. It's one Then you have one plus nothing. Zero It's one and we get 11 2nd example who have 11 +11 plus one is two. So ride zero here and we get one as big carry and one plus one is two. So we have +10 But we have no more operations. Override +01 here and we get 100 which is for in binary. Third example have 101 plus 11 one plus one is two so right zero here on right one as I carry one plus zero plus one is also too. So we have zero plus one here and one plus one plus zero is 10 So we write it here because we have no more bits to add. 4th 1 have 11101 plus 110011 plus one is two. So we have zero plus one and occur in the carry here one plus zero plus zero is one 10 is 11 plus one is zero on one Here, one plus one plus one is three, which is 11 in binary. So we righted here because we have no more bits to add. It's the last one fourth example we have 111 plus 111 plus 10 and you have one here, one plus one plus 11 And we put one here and one plus one have 10 who have 1010 plus 11100 plus zero is 01 plus 10 and we put one here one plus zero plus 10 and we put one here. One plus one plus one is three. So we put 11 last example. We have a long example, but it will be easy because we will repeat the same operations for each bit and we'll get the final number one plus 10 and one here one plus zero plus 10 And we have one here one plus one plus one. We have one on one here. One plus zero plus one have zero and one here zero and one here. One one Hair zero one here. Zero on one hair. 11 What? One one 11 zero on 10? Because it's the last one and we get the number. Now we will do the same thing with fractional numbers. It's the same thing for fractional numbers. We will do the addition normally, and we just at the point in its place. For example, here we have one plus one is zero and we have one hit. We have one here in the next one. You have the 0.1 plus zero plus 10 and we have one here. One plus zero plus one. Same thing here and one plus one is 10 So we have 4.5 plus 3.5. It's equal to eight just in by them. Second example, we have 110.1 plus 111.1 one plus nothing. It's equal. It equals to 10 plus one Same thing. The 0.0 plus 111 plus 10 And here we have 11 plus one plus one. It's 11 third example. Have one plus zero. It's one on +10 as we put one here as a carry the point one on the one hair. Same thing here and here we have 11 last example. We have 1.1101 plus 1.10011 plus one is zero. And here we have one one plus zero plus zero. It's one same thing here have zero and one here we do the point at the same position at one plus one plus one is three so right one on because it's the last one and seal in the lax videos. 28. Binary subtraction : Hello, everyone. In this video we'll see how to do the subtraction between two numbers and binary. First, there is basic operations that you need to know before we move Two examples. Here we have zero minus zero. It's zero. Obviously add one mind zero, It's one and one minus one is zero. And when we have zero minus one, when you have this number smaller than this number, we can do the subtraction. So we had to hear and we put one here for the next operation. So here we add to here. So we have two minus one. It's one and we'll add one here in the bottom for the next operation. 4th 1 would have zero minus one with a carry on on. It means here we have two on not only this one, because we have one. As the previous carry we have, we have zero minus two. But we can do because this number is smaller than this one. So we had to hear and two minds to it. Zero, and we add one here for the next operation when we have one minus zero, but with the carry. So it means it's one minus one. So it's zero last one. We have one minus one with the carry. So here we have two on one minus two. We can't because this because one is smaller than two. So we add to and we had one for the next operation and two plus one because here we have three three minus two. It's one Andi I'd want Now we can do examples. 11 minus 101 minus zero. It's one and the one minus one. It's so 10 minus 10 minus one. We can't. So we add to here and we had one here. Tu minus one. It's one and one minus one. It's still third example We have 100 minus 110 minus one. We can So we act to here. Onda, we add one here to minus one. It's one zero minus. Do we can. So we had to hear and we add one here to minus two. It zero Here we have to because one on this one one minus one. It's ill. So we get one 11101 minus 101111 minus one. It's still here. We can. So we had to and we had one here. Tu minus one. It's one one minus two. We can't. So we add to here on one here. Three. Here we have three minus two. It's one one minus 10 plus 11 minus one. It's zero and one minus one. It's you. Fourth example, we have 1011 minus 101 one minus one. It's so here we have one here. We can so it at under. Add one. Here, one do 1110 minus 1011 Here weekend. We had to at one here to minus one. It's one. Him one minus two. We can't. So at two. And we have one here. Three minus two. It's one on minus one. It's zero on a minus one. It's here. Last example along 10 minus one. You can't. You have to. On you. Add one. Here. Tu minus one. It's one. Here. We can't. We add two and one here. Three minus two. It's one same thing here. Same thing here. Zero minus one. Can't one. Same thing here. One minus 101 minus one. It 00 minus one we can. So we had to. And we have with one here. One one minus two. Same thing we can't tu minus two. It's zero zero minus. Won't we can't. Tu minus one. It's 11 minus one. It zero and one minus one. It's zero, and we got the results. Now we will do the same thing with fractional numbers. We will do the same thing. Would just add the point like we did. In addition, one minus one. It's so we do the point here. Zero minus one. We can't. So I had to and one here to minus one. It's one here we can. So at two Tu minus one, it's 11 minus one. It's zero. So we have here 4.5 minus 1.5. It equals 23 second example. We have 110.1 minus 11.1 one minus nothing. We have one here. We can't. So we add two under. Add one. Here. One. We do the point in the same position. Here. We can't tu minus two. It's zero one minus two. We can't. So at two and one here, three minus two, it's one and the one minus one. It zero the example. We have 110.1 minus 101.111 months. 10 Here we can't so and one The point can sort add one tu minus 201 minus one minus 101 minus one. So it means six. Moment 25. One is five 0.75 equals 2055 Like we got in there in the results. But on Lee invited last example, We have 1.1101 minus 1.1011 and we have zero. Here. We have to add tu minus one. It's 11 minus 101 minus 10 We do the point in the in the same position on the one minus one . It zero see you in the next videos to do the subtraction with two's complement 29. Binary subtraction with two's complement: Hello, everyone. In this video, we will see the second method to do binary subtraction. This time it will use two's complement. First, we will convert both numbers that we want to do subtraction between them into two's complement and how to get the two's complement representation off a number. First stop, we convert the number two binary. If it is in the symbol or another system, then write the Sinead Magnitude representation off the number. It means who write the sign bit. One if it's negative and zero. If it's positive and will write the continued number in on bits, then if the number is negative, we do these steps on Lee. If the never is negative, we get the ones complete mint representation by flipping every bit how to get the ones complete mint, for example. If we have 10110 will flip every bit and it becomes 010 zero one. If it's want, it becomes zero. If zero it becomes one, then last step. We add one to the result to get to his complement representation, for example, we had this number. We converted it to wants complement, and when we add one, it becomes 01010 We added one to this number, which is the once complement, and it becomes the two's complement. Now we will see an example First. Example, we will treat 20 to minus 17. We know that we will have 5 22 in binary is 10 112 on inside monitor representation will have 0101100 here because the number is positive and this is the sign bit. But because this number is positive, we don't have to do other steps. And we already have the two's complement representation Now, second number and binary is minus 10001 inside monitored representation. We have one because of the number is negative. 10001 Now we'll have the first. Now will have the ones compliment. We just flipped a bit, but we don't flip the sign bit. So we have won the sign bit and we flip others. 01110 We get first compliment and together two's complement. We just add 1101111 We added one to this number and we got the tools compliment. And now lost step would do the addition between the two's complement off both numbers. Yes, the addition of the subtraction. And we will get the result. 010110 +101111 we get here, we get 10 here. Zero carry one one one plus one is zero. And you have one here. Same thing here and same thing here. But we ignore the carry in addition of two's complement and we get our binary number, which is plus five. We know that 20 to minus 17 is last five. A little trick to get the tools. Compliment quickly. You just flip all the bits until you arrive to the last bit where we have one. For example, we have 10110 You stop at this one, you don't rip it. It becomes so 1010 You stop here because this is the last bit where we have one. So you directly get the two's complement going from the binary number. Second example, we have 18 minus five 18 in binary is 100 10 Signed Magnet ID 010010 and minus five is in binary minus on 01 And inside magnet ID signed magnitude must have the same number off bits like the 1st 1 So we must represented and six pit. We have the first bit for the sign bit, which is one because the number is negative who have the binary number. We write it at the end and we feel other bits by zeros Two represented also in six bit like the 1st 1 And now we'll go in directly to two's complement the flip bits until we're after this one because this is the last bit where we have one becomes 111011 We stop here on now we do the addition, this number plus zero on 001 This one here we have one have zero and one has a carry 110 and one has a carry. And here we have 10 But we ignore this one, and we have our number in binary, which is 1101 It means 13 and 18. Minus five is 13 last example. We have minus six minus three. So we know that we will get minus nine minus six in binary is minus. Want one zero and side mine. It'd It's 1110 and in twos complement its one. So 10 Because this is the sign bit we don't touch it. And you stop at the last bit. One, we have zero. It's this one. Same thing for three. We have minus 11 inside money to have to represent it in four bids like this 110 Want Juan and in twos complement with flip. Until we arrive here, it becomes Swan 101 And now we do the addition. 1010 plus want 101 and we have one here. We have one here we have one. And here we have 01 We ignore the carry, but our number is wrong because we have one plus one is equal to zero. It's weird. So when we have one plus one and it gives us zero here or zero plus zero and it gives us one, we stopped because we have what we call and buffer overflow so we can to have the result because we got and buffer overflow on last thing. If you had here a negative number. For example, if in the result you got 10 01 you have to get the two's complement off this number to get the real result. The two's complement of this number is 1111 So when you're converted to Byner, it's minus seven. See you in the next video. 30. Binary multiplication: Hello, everyone. In this video we will see how to do the multiplication between two binary numbers. First example, we have 10 multiplied by one in a binary multiplication between two members. We start from here in the second number and we check each bit. If it's one, we'll write this number. If it zero will write nothing on in each digit, we put an additional point. We'll see that in examples. In this example, we have only one bit and it's one. So we ride the number. The first number. Second example. We have 10 multiplied by zero. Here we have there also right? Nothing means it's zero third example have 101 multiplied by 11 We start from here. We have one, so we write the number, and each time we will add a new additional point a point. Men zero on. Now we also have one. So we write the number 101 and second step would do the addition. We have one plus zero. It's one. They're blessed. One. It's 11 plus zero. It's one and zero plus one. It's one, and we have 1111 which is 15 and here we have five multiplied by three. It's 15 fourth example We have 11101 multiplied by 1011 We start from here. We have one. So we write the number 10 111 here with the the first point. We also have 110111 Now we do two points. Here we have zero. So it just fried zero. Now have three points and here we have one. So we're right. The number 10 111 And now we do the addition off all these numbers. One plus zero plus zero plus zero. It's one zero plus one plus zero plus zero. It's one want plus zero plus zero. Brazil. It's one one plus one plus one. It's one and we have one as they carry one plus one plus one plus zero, we have one on one of the carry. Same thing here. One plus one, it's zero on. Do you have one? As a carry on one plus one? It's 01 and we get our number. This example have 111 multiplied by 101 We start from here. We have one So we write the number. If we had zero with just ride zero here. Now we do a point. We have zero, right? Only zero now. Two points. We have one. So we write the number, allow second step. We add one plus zero plus zero. It's one same thing here. Here we have zero. Add one as a carry. Same thing here on here. We have 01 last example who have 1010 multiplied by 111 Here we have one. So we ride the number a point. Same thing here. We have one. So we write the number two points and here we write the number because we have one 01 01 And we add these numbers. Hey, we have zero Have 11 zero on one as a carry zero on one as I carry and zero on. And we got the number. And here we will see more examples. We have zero here. So we just ride zero. We do a point. We have one. So we write the number 010010 two points. You have zero here. Three points. We have one. So we write the number So one 0014 points now and we have one. So we ride the number on we do the addition off all these numbers we have here only zeros. A point is considered as a zero. Same thing here. Zeros. Hey, will have one there. We have zero here. We have one here. We have zero and one has a carry. Here we have 111 on a got the result. Now we will do a fractional number. We will do the multiplication like it wasn't a fractional number. Then we will at the point here we will consider that there is no point. So we have 1101 multiplied by 1011 We have once override the numbers. So rather than number no one, no one to a point. I have one here. 101 one two points. You have zero three points and we write the number again because we have one on. Now we act here We have 1111 and one as a carry 01 as a carry 01 as a carry on 01 And now we have to do the poem. We just count the number off bits in the fractional part of the first number, plus the number of bits in the fractional part off the second number and we count from here . And we had the point. For example, here we have one here, only one and only one here. So one plus one is two. So we count 12 and we put the point. Last example have 110.1 multiplied by 11.101 We do their multiplication normally. Here we have one. So 10011 do the point. We have zero two points and we write it again because we have 110011 from here on three points. Same thing on four points and we write it again. And now we add We have one here. Zero one zero and one as a carry one plus one plus one. Here we have one on one as a carry zero and one as a carry. We have one and one of the carry here. One plus one plus one. We have one on the one as a carry here on one plus one, it's 10 and now we'll count to put the binary point. Here we have two bits. After the point on here we have three, These three So two plus three is five and we count 12345 And we put it here and we get the result off this multiplication. See you in the next videos. 31. Binary division: Hello, everyone. In this video we'll see how to do the division between two binary numbers. First example would have won 10 divided by 10 1st we take the same number off bids from here. Here we have to. We have these two we take to from here. If it was in further than this number would add one more. 11 is greater than 10 So we put one and we minus 10 from it. I get one on Now we take the zero, the next bit 10 divided by 10 It's one time on Dwan minus 10 It's zero and we finished the division. So 110 divided by 10 It's 11 six. Divided by two is three second example. We have two bits here, so we have to take to one here on the one was Subtract. We have zero and we take the 2nd 1 zero is smaller than 10 So we put zero zero is smaller than 10 So we also put zero and we have eight divided by two. It's for, for example, we have 11001 You have to take three bits because we have three. So we take this free and 110 is superior than 101 So we have one here and we do the subtraction and we get one, and we take the The 2nd 1 10 is smaller than 101 So it's zero here and get the 2nd 1 Once there one, it is equals to 101 So it put one here and we finished the division. We'll have 25 divided by five on we get five fourth example have won 1010 divided bond 100 well through bits here and would take three. We have one here. When we do the subtraction, we get 10 and you take the next bit once. I don't want a superior than the 100 So we put one and we do the subtraction. We'll have one take the next 110 It's more than 100 So we put zero and we get 10 here. But we didn't end the division because we have to get zero here. But now we have 10 So we do the binary point here and we add a zero on 100 is equal to 100 So we put one here and when we do this obstruction, we get zero. So we stopped the division on. We get the result. Fourth example, we have 100001 divided by 100 We take three bits one and when we destruction we'll have zero. 2nd 1 is zero smaller. 00 is smaller than 100 So I put zero Same thing here on same thing here. But we can't stop the division because well, we have one here and when we must have zero. So we do the point on we add zero here. It's still smaller than this one. So it's zero. We add a zero on the 100 is equal to one's. There is also a put one and one was subtract. You get zero on we stop the division. Last example we have 1010 divided by 11 We take to bits, but 10 is smaller than 11 So we take an additional bit. We have one subjection. We get 10 We'll take the next bits. We have one here, minus 11 It's one. But we can stop the division because we must have zero here. So we do the point. Andi, as zero still smaller. So it put zero and we add zero 100 is greater than 11 So we put one on one with minus. We have one. You can see that the division is infinite because if we continue here, we have 0101010101 So we can decide to stop here after, for example, two or four bits like you want. So now we will do the division between fractional numbers would take first, we will do the division like it wasn't a fractional Numbers like there wasn't point. We take three bits from here. We have one on the one. We do the subtraction. We have zero and we take this second bit. Zero is smaller than 101 So I put zero. And now we end the division because we have no more bits here and we have zero. So now we have to put the point first, let's name and the number off bits off this fractional part off the second number. And, um, the number off bids in the fractional part off this number. Hey, we have zero. And here we have one. First, the point is here, and we will move it by an positions to the right. Then we will move it by am. Positions to the left. And here is one. Because we have one here and, um zero. First we move it by one to the right. So we had zero and we put it here and we move it by am. Positions to the left. But here is zero. So we let it here on our number is one zeros, which is for now. We will see the second example 1011 divided by 101 We will do the division. Normally have three bits through bits. One, we do the subtraction. Get zero on who have one here. One is smaller than 101 So we put zero here and now we can stop the division. So we put the point here and add zero. It's still smaller, so it put zero. And as you're here, it's still smaller because once there is a small than 101 So we put zero on the ad zero here, but now it's bigger. So we put one on. We do the subtraction and we get one one. But 11 is smaller than 101 So it put zero here and we'll add zero 110 is bigger. So add one and we do the subtraction on to have one here. But we will have the same problem because we had one here and it will be an infinite division. So we'll have their 1010 they want until infinity on. Now we have to move the point we have on our number and is one hair like in the previous example. We have one here and here we have zero. So we move it by and by and positions to the right. Then remove it by AM positions to the left here and is one So which in the positions and it becomes here and, um zero. So we don't move it. And we have 100.101 last example. Have 1000.1. Divided by 10 We take to bits one. And here we have zero under. Say the 2nd 1 zero is smaller than ones that also have zero. Same thing here you take one still smaller. We do the point on at zero here. 10 is equals to 10 So we put one and we have there. So we stopped the division. Now we will move the point by and positions to the right. But here and zero. Then we will move it by am. Positions to the left is one here Because we have wanted but having them. We have a bit here in the fractional part, off the first number. So we move it by one positions to the left on it becomes 100.0 long See you in the next videos. 32. Conclusion: Congratulations. You've just finished the course. I hope that you understood all the things we've seen in this course. If you didn't just what? The videos again and practice till you understand. And now try to solve more exercises to become fast. Well, converting or calculating. And don't forget to read the course and to give your opinion about it. Goodbye.