Computer Science - Number System Conversion and mathematical operation behind Programming | Luis Carlos | Skillshare

# Computer Science - Number System Conversion and mathematical operation behind Programming

#### Luis Carlos, Engineer, Web Developer and Instructor

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• ### 27. Addition and subtraction using all bases

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## About This Class Learn to convert and make arithmetic operations with  decimal, binary, octal and hexadecimal numbers.

This is an introductory course on digital systems and computer science area.

There are no pre-requisities for this course. If you are looking to get acquainted with the concept of number systems that are use for computer language, this is the right course for you.

Just need a computer and i will explain step by step, from the simple concept even the most complex operations.

At the end of this course, you should be comfortable making:

• Conversion between different system numbers using integer numbers

• Conversion between different system numbers using fractional numbers

• Making addition and subtraction with different bases(binary, decimal, octal and hexadecimal).

What are the requirements?

• Pleasure to learn and motivation

• Leave the rest with me

What is the target audience
?

• Students in the area of computer science with little or no notions of number systems.

• This course is also suitable for students/people with more advanced skills who want to deepen their knowledge.

Good Luck!!

## Meet Your Teacher

#### Luis Carlos

Engineer, Web Developer and Instructor

Teacher

Currently, I am an exciting Engineer and Trainer , who loves to learn and share knowledge and new experiences.

As Trainer participated in many projects directed to student in the areas of math, computer science, new technologies and web development . Several years of training helped me developed many skills that contribute to the personal development of each people.

You can follow some of my articles in my website where i share some tutorials in the area of new technologies.

Follow me on Skillshare!

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1. Presentation and course preview: welcome to the number system Curse. My name is which Carlos and I could only work s telecommunication engineer. I have seven years of experience as trainer in the areas of maths and computer science, and my main goals are increasing our knowledge in this area. Healthier personal development and success number system are using different areas off computer science such as the system, network, security and programming. At the end of the course, you'll be able to identify different number systems, cover numbers two different sizes and do it Matic operation with different number systems. Vickers is divided into models, beginner and advanced in the beginner part, you will learn demanded, used to covert in T shirt numbers and the advanced part. You will learn methods to conversion, affection all members and made addition and subtraction using different place members. The ideal students for discourse are those who study in computer science or just people want to increase their knowledge. The only requirement is the pleasure to learn, and I will make the rest to help you feel free to watch our preview video If you within five. We discussed giants 2. Course overview: My name is Wish Carlos and I'm from Particle. I will be your instructor in the next 90 minutes where you're gonna learn out to convert numbers. Using different buys is let's start with the curse of review in the introduction part, the main point side, What are the numbering systems? The different areas of use and out to represent different by his numbers. The main focus off discourse is the conversion between different numbering systems using Inti jher and fractional numbers. After making discovers Asians, you're gonna learn out to make additions and subtractions. Using the different buys is 3. Introduction: hello. In this first chapter, I'm going to talk about the importance off numbers in computer science. You use symbols in all moments off our lives. And sometimes symbols express value numbers in our days. The decimal number system is the more used. We used decimal liberation in different moments. Like when you do math exercises in school when you go shopping and see the prices on when you go to a football game and you see the number off goals in a scar. Barth. There are other different number systems, and the main difference between them is the number off symbols that are used. They are important in such areas like the computer science Elektronik or microprocessors. These different number systems are using these areas because it's more easy to computers to understand the information in a specific format. A modern computer operates on the principle off two states on and off state. This two states responds to their either being any lettering, no current present or not being present. The on state is a segment with the value one if the electrical current is present and the off state is a stagnant with the value zero. If the electrical current is not present. That's why we go binary, because as two states, two different states, each binary digit orbit is just a single zero or one which directly corresponds to a single switch in a circuit U F here this switch, and if he's in position, I corresponds to zero. The switch is open, and if this which is close position beak response to visit one. If you wear many switches together, you can't represent more numbers, more zeros and ones. So instead of one digit you went up with groups off eight that corresponds to bites. Went bike response to eight single digits. You can see another example. Two switches. And if they are in position, I and position see they are open That corresponds to value zero. If they are in position. B in position D, They are closed and corresponds to value one. A computer. Use millions off switches. The only trick is when you use that input given by images, sound or other kinds of files. You just f to convert that file's two zeros and went to the computer understands that kind of information 4. Types of number system: Hello. This is the chapter off the different types of number systems. The number systems is any system that we used to represent different numbers. We have four main types. The decimal that is the most used, the binary, the octo end, the exit decimal. These less tree are more used in some areas off the computer science I'll do. I represent the different types of number systems did decimal with by Stan I. F. 10 different values to represent one digit in this Bice did binary number system. I have two different values to represent a legit in this Bice Bice to the article number system by sight, I have eight different values to represent one digit and finally, the exit decimal. By 16 I have 16 different values to represent one digit 10 numbers from zero to nine and six letters from A to F. How do I am going to make the representation off the different number systems in the next life between Berlanti is I'm going to write device off the number in the guys off the decimal numbers. I will writes 10. Do binary to the Octel numbers eight and exit decimal numbers. 16. Why do. I use auto and exit decimal and just not do binary numbers just because when you are talking about information in a computer? U F many beats and bites to represent information many zeros and ones. The Octel and exit decimal system are just a short way, a friendly way to make the representation off binary number. Why? Because in the auto number system, with one digit, you can represent three binary bits. What makes the number more charts and in the exit decimal system, with one digit I can represent for binary bids, let's see just two examples where I have one first one binary number with nine bits 0110101 zero while and with the local number system, I used just three digits to represent this information. Finally, this second example with eight bits 01110101 I use just two digits to represent these eight bids 5. Decimal system: Hello, Industries. You I'm going to show you some properties off the decimal system. This system is the most using our lives. So why do we call the simple system? Just because that to represent a digit in a decimal number, you can use then different values from 0 to 9, it's dish. It s different place values that can be represented by by stand with positive and negative exponents. If you are talking about the interior part, do exponents are positive? And for diffraction all part the exponents are negative now, making Justin example where I'm going to the compose a number the number 156. This number s street digits and three different whites in disguise. Positive just because I f a seizure in number with no fractional parts Now I'm going to the compose the number in the different whites different place values and multiply each right. So the bites with the correspondent exponents by the correspondent digit And in defining I will some all the values So 156 is equal to 10 explode into multiplied by the correspondent Digit one ended with 10 exponents when multiplied by five edit with 10 exponents, zero multiplied by six. This will give me 100 multiplied by one ended with. Then we'll deployed by five added with one multiplied by six. The final result, as we expected, is 156. 6. Conversion from decimal to binary: I in the strip that I'm going to covert decimal numbers to binary numbers. The technique that I'm going to use is the division method where I going to make multiple divisions by two off the decimal number that I want to convert. In this first example, I'm going to covert 252 binary. The first step is the division by two off the original number and I getting the division to quotient and a reminder off that number. 250. Divide by two. I get a question off 125 and the remainder off zero. In the next situation, I'm going to use the previous question. 125. Divide by two. I get a question off 62 a remainder off one. I stopped the situation when I get zero. Indyk Oceans definer result in binary is given me by the remainder. The last reminder that I get it's the most significant bit off the binary number and the first remainder that I get is the least significant bits. So the final result to an end and 50 in decimal is one 11 11010 The next example. I'm going to make the conversion off 78 to Binary 78. Divide by two. Give us a question off 39 the remainder off. Zero. The previous quotient is used for the next situation. 39. Divide by two. I get a question off 19 and the remainder of one when I get zero. Indyk, Ocean I stopped detour ation and I get the final number in my reminder. 1001110 In the final example, I'm going to convert 177 to binary. Let's make the first situation. 177. Divide by two. Give me a question off 88 the remainder ever won. The previous question is used in the next Division 88. Divide by to give me a portion off 44 and the remainder of zero. This process stops when the question is zero and I get the final number. In my remainder. 10110001 You can see it right? The final results. Things 7. Conversion from decimal to octal: in this feel you? I'm going to show you how to convert decimal to octo numbers. The first Met that I'm going to use is the division methods that used in the previous chapter. When you convert decimal to binary numbers instead of used division by two. To get binary numbers, you will divide by eight. To get Octel numbers, you can see the first example 250 division by eight. You get er cautioned 31 a reminder off to In the second division, you gonna make the division with the previous portion by eight and gets caution of tree and remainder seven in the final. Itaru a shin. You're going to make the division division off three by eight and get a question of zero and remainder three You will yet the final number 372 in Octel given by the team. Either second method that I use is their conversion from decimal to binary in the first step and in the second step, a conversion from binary to Octel. Using this matching table, first step decimal to binary. What you learn from the previous chapter to wonder than 50 in decimal is given by 11111010 in binary. After you have the binary number, you wanna make groups off three bass with the original binary number and used the matching table to see the corresponding Otto number you can see over here. 0111 when 1010 notes that you edit at left 10 to make these three groups off three bits to use this table. In the second example, I'm gonna convert 78 to auto using the first matters 78. Divide by eight. Give me a caution of nine and Reminder six in the second Division nine. Divide by eight. Give me a question of one and reminder one and in the final Division one, divide by eighth. Give me a caution of zero and remainder. One final Octel number 116 Using the second methods, I'm going to covert 70 18 decimal to binary 1001110 And now I'm going to make groups off tributes. 001 that corresponds to one in octo 0011 in octo and 110 six in uncle. Final example conversion off 177 to auto first met its the division by eight off the decimal number. 177. Divide by eight Gift as 22 off quotient and remainder off. One 22. Divide by hate quotient of two and remainder off six and in the last division to divide by eight cautions zero and remainder two. Final result to 61 in Octel. Using the second method, I'm going to make the conversion from decimal to binary. 177 is 10110001 Make groups off three beats you get 010110001 That gives do 61 using the matching table between the binary numbers and the Octel numbers. 8. Conversion from decimal to hexadecimal: Hello. In this chapter, I'm going to make the conversion from decimal to exit decimal numbers. First met that I'm going to use is the division methods I'm going to divide by 16 decimal number until I get my final exit decimal number first. Example 250. Divide by 16 quotient off 15 and remainder off, then letter a second iteration. 15. Divide by 16 quotient of zero and remainder off. 15 Letter f Don't forget that to make the representation off digit inaccessible U F 16 different values from zero to F final results 250 in decimal is F A in exas Immel. Second method used is the conversion from destined to binary in the first step and in the second step, binary to exit decimal. I just used this matters because in the previous chapter, I make this calculation decimal to binary. I just have this result in binary. If you think it's more easy to have the result in one step, just making the division by 16 you can use the first method now make the calculation. 250 is equal to 11111010 in binary, making two groups off four bits. I get 1111 is letter f and 1010 is letter. A second example. Conversion from 78 in decimal to exit decimal 78. Divide by 16. Give me a question toe four and a reminder off. 14 Letter e far Divide by 16. Give me a coast of zero and remainder off. Four. Final results. 70 18 Decimal is for E in exit decimal using the second matters first Govert from decimal to binary 78 in decimal is 1001110 in binary making. Two groups of forbids I get 0100 It's the number four and 1110 It's letter find results for a in the final example conversion off 177 to exit decimal. First the division method one under than 77 division by 16 quotient of 11 and remainder off when 11 divide by 16. Give me a caution to zero and remainder off. 11. Letter B Final result 177 in decimal is B one in exit decimal using the second method first , the conversion from decimal to binary. 177. Intestinal is 1011 0001 making two groups. I get 1011 Letter B and 0001 Number one. 9. Conversion from binary to decimal: Hello. In the previous chapters, they learned how to convert from decimal to binary Octel and exit decimal numbers. In the next chapters do wheeler out to cover binary numbers to the other treat bases. Let's start with the conversion from binary to decimal numbers by their system used the base to and like idea the tree basis each digit as different weights. To get the decimal numbers from a binary number, you have to make the multiplication off each value each digit value and the correspondent white in the final. You some all the values. Let's see the first example. 11011 This is a number off five digits and five different weights that you can see in the stable at the right off this life. Now I'm going to make the multiplication off each value Digit and the correspondent wait 11011 is equal to to explain and far multiplied by when ended with to expunge entry multiplied by one edit with to expand into multiply by zero. This is zero always U F a bit with value zero, the final result is zero, and that we to explain it went multiplied by one added weight to expand zero multiplied by one, you get the final result off. 16 ended with eight headed wits to edit with one, you get 27 in decimal. In the second example that I show you conversion off 10011 in binary to their symbol is equal to do, explained for multiplied by one at the wit to explain entry multiplied by zero. This is zero edit with zero again and we to explain it when multiplied by one and finally added, we do expanded zero multiplied by one, you get 16 ended. We do edit with one in decimal, you get the results off 19 and in the final example, conversion off. 101010 in Binah B two decimal do exponents five multiplied by one ended with zero with two exponents tree multiplied by one ended with zero again edit with to explain it, one multiplied by one with zero again, you get the final result off 32 ad with eight edit with 2 42 in decimal 10. Conversion from binary to octal: In this chapter, you will learn how to cover binary to auto numbers. This is not totally new for you, because when you learn how to convert decimal total numbers, you use dis methods. First. Example. I have a binary number off nine digits and I'm going to make the conversion from binary to octo. The first step is split the binary numbers in groups off three bids, you will get 010 that corresponds to two in Octel, 111 response to seven in Octel and 100 response too far in octo. The final number to 174. Next example conversion off 10101 from binary to octo. Let's make display. Eating off the number 010 that responds to in ah total and 1015 in Octel. Final number 25 in Octel. The last example conversion off when 10111 from binary to octo splitting the number 110 six in uncle and 1117 in Octel. Final number 67 11. Conversion from binary to hexadecimal: by Mary to exit decimal conversion. This is the last chapter off conversion from binary numbers to the other basis. Like in the previous chapter, when I uncovered binary to total numbers. I f. The original number and F splits the number in groups of four bids for this case. I have the original number 01010101100 Now I'm going to make this pleat off fart bit. 0101 In the stable, you can see it's the number 501 dear one Number five again and 1100 is letter c. My final number is 55 c in exit decimal. Second number conversion off 111101 to exit decimal. I'm going to make again groups of four beats. I put to the result left toe air forbids in this second group 0011 It's street in exit decimal and 1101 It's latter D in exile. Decimal Final results three d. Second example Conversion off. 1010110 To exit decimal splitting in groups of four beats, I get 0101 it's five and 0110 it's number six. Final results 56 in exit decimal 12. Conversion from octal to binary : Let's make now the conversion from auto to binary in numbers. To make this conversion, I have to convert each Octel digit in groups off three binary digits. First example, The number to 141 in octo Digit two in Octel is represented by the tree visiting binary 010 for in Octel 100 and one in nuttall. 001 Final number 010100001 In binary. Second example. Conversion off. 123 from octo to binary. Converting the first digit one in until I get 001 2nd visit in Arkle 010 answered. Digital knocked 011 My final number in binary is 001010011 in binary and in the final example, conversion off. 315 to binary First Digital Street. I get 011 2nd digit is one. I get 001 and third digit is five. I get cereal 10 My final number is 011001101 13. Conversion from octal to decimal : I'm going to start now with the octo numbers conversion. The first cases Octel two decimal conversion Octel system as base it and like in the other bases, each digit as different whites. To get the final decimal number, you have to multiply each value digit and the correspondent white and in the final son all the values first. Example. Number 34 34 as two digits and two different weights at exponents one and exponents zero. Making do multiplication. I get three multiplied by eight exponents. One ended with four multiplied by eight exponents. Zero final result is the addition off 24 week for give me a result off pretty eight in decimal. Second example Converse enough when under then 27 2 decimal 127 is one multiplied by eight exponents too. Added, we do multiplied by eight exponents. One ended with seven multiplied by eight exponents. Zero you get 64 added with 16 with seven. Final result in decimal is 87. In the final conversion, 531 in octo is equal to five multiplied by eight exponents to edit with tree multiplied by eight exponents. One at that, we'd want multiplied by eight exponents. Zero you get 320 edit with 24 7 with one. Final result in decimal is 345. 14. Conversion from octal to hexadecimal: upto two eggs, a decimal numbers conversion to make these kind off conversion. First, I have to convert each octel digits to a binary number off three bits. In the first example, I have the number 71 in Octel and I get from this number. The digits seven is 111 in binary and digital is 001 in binary. Joining this number, I'm going to make two groups of four beats and I get 0011 and 1001 My final number is giving by these two groups is street from this first group and nine from these second group 39 in exit decimal. Use my final number second number conversion off 104 from Octo to exit decimal, making the group's off three beats. I get 001 000 and 100 joining debates and making two groups of far beats. I get 0010 It's still in exit and 0100 It's for in exit. My final number 24 in exit decimal. Finally, my last example. Conversion off 237 from Octo to exit decimal converting the first digit two is equal to 010 Tree in article is 011 and seven in October is 111 making the group's off for bits. I get 1001 It's number nine in exit and 1111 It's F in eggs. A final number is nine F in exit decimal. 15. Conversion from hexadecimal to binary : After making the conversion from exit decimal two decimal numbers, I'm going to make the conversion to binary numbers. To make this kind off conversion, I have to convert each exit decimal digit into groups of four binary digits. Like you can see in the first example, Number two I in NZ decimal is equal to 0010 from the digit to and 1010 from the digit a Joining the two groups. I get my final by their number 00101010 in by now is the final number. Second example. Conversion off 45 in exit decimal to Biden Mary making the groups of four beats. I get 0100 from the digit for and 0101 from the digit five. Joining the two groups I get 01000101 and in the final example, conversion off. 34 B from eggs accessible to binary. Now I f. Three groups of four bits 0011 from the digit tree in X a decimal 0100 from the digit for and 1011 from the digits be in exit decimal. My final binary number is given by 0011 01001011 16. Conversion from hexadecimal to decimal : exit decimal numbers conversion. First, I'm going to talk about the conversion from exit decimal numbers. Two decimal numbers exact symbol system as Bice 16 and, like the other bases each digit as different whites. To get my final decimal number, I make the multiplication off each value Digit and the correspondent white and in the final Sam All the values first. Example. The number 23 in exit decimal, this number as two digits and two different whites. 16 exponents one and 16 exponents zero making de multiplication. I get two multiplied by 16 exponents when added with stream multiplied by 16 exponents. Zero is equal toe 32 ended with street 35. In decimal is my final number, making the second conversion Govert F one in exit decimal two. Decimal making dim multiplication 15 multiplied by 16 exponents. One ended with one multiplied by 16 exponents. Zero. My final result is the addition off 240 with one toe. 141 is my final result in their civil. Finally, the conversion from e a tree from exit decimal two decimal making the multiplication. I get 14 multiplied by 16 exponents, too added with Dan multiplied by 16. Explain it. One ended with tree multiplied by 16 exponents. Zero. My final result is 3747 in decimal. 17. Conversion from hexadecimal to octal : exit decimal talkto numbers conversion Dutra assortment Exit decimal number two A natural number. I have to make it into two steps. First, the compression from exact symbol to binary number, using groups off four bits and in second step through sort do binary number into a knocked the lumber using groups of three beats into binary number first. Example. Number six in exit decimal. Making the split off the number in groups of four bits, I get 01 10 from the digit six and 1010 from the digit. Now I'm going to split the visionary number in groups of three beats and I get 001 101 010 That corresponds to the actual number. 152 second example. Courage enough. Three A from X, A decimal to octo making do two groups of four beats. I get 0011 from the digital tree and 1010 from the digit making two groups off three beats . I get 111 that response to seven in octo and 010 that corresponds to two in auto. This is my final number. Do lest example, conversion off tree would be from exit decimal to AKEL, making the three groups of four beats. I get 0011 from the digital tree 0001 from digit one and one zoo 11 from the digit be making the group's off three bits I get 001 100 011011 and my final number is 1433 in awful . 18. Conversion from decimal to binary using fractional numbers: Hello. In this next videos, I'm going to show you out to make the conversion with numbers with fractional parts. First, I'm going to start with the conversion from decimal to binary numbers. You know that decimal numbers can f two parts and in teacher part and the fractional parts that can be separated by coma, you can see in this example you have the integer part for 57 and diffraction all part 375 converting the integer part you know, from the previous chapters that you have to divide the number by two. And with the reminder you have the result in by Derry of the conversion from decimal to binary, starting with this first example and the conversion off the Inti jher. Barth, I'm going to make the division by two. I get my cautions and my reminder in the next division I'm gonna use the previous caution in there and get again And new caution and a new reminder. These alteration stops when I get a caution off zero and the remainder will give me the result in binary of the interior parts off the number de final result is equal to 111 001 001 To get my fractional parts, I have to multiply the fractional part by two. I get this result and in the next it ration, I will use the fractional part off the multiplication and multiply again by two and get again the new result this multiplication by two. Well, stop when I get zero in the multiplication by two, or I will get a periodic number. The result in binary is given by the into seizure part off the multiplication in disguise is 0110 that you can see in the last row. So the result off the fractional part is this four bit 0110 and the final result is the interior park. 111 001001 coma and the fractional part 0110 Now making another example, converting this number with the intention part 351 and the fractional part 59375 I'm going to start with the in teacher part, so I'm gonna make the division by two and get quotient and remainder in the next division. I'm gonna use the previous caution and get again a new coaltion and a new reminder. This will stop when I get zero Indyk Ocean and the remainder will give me the result in binary. So my in Tischer part is equal to 101011 one one one. Now making the conversion off the fractional part. I will multiply by two and I get this result. And in the next role, I will use diffraction all part and I will multiply again by two and get and you result again. I will stop this situation where I get zero or a periodic number. The interior part off the multiplication will give me the final result in binary 10011 zero is my final results. And the interior part with fractional part of is 101 011111 Goldman and my fractional part 10011 And in the next and last example conversion from decimal to binary Off the number 71 coma 10 starting with the in Tischer part in making the division by two. I get my Kocian and Reminder and I will use the question to the next division by two and get a nuke ocean and reminder. This will stop when I get zero in the caution and the remainder will give me the final result in binary 1000 11 when and finally diffraction ALS Part zero Goma 10. Multiple life by to I get this result and I will stop the multiplication when I get zero or a periodic number. In this case, I will get not zero but a periodic number. You can see that in the second row and in the less rule you have this same result. So this 0011 will repeat again. Starting in this lest column in this zero, this will repeat again 0011 So my final number, the fractional part is 00011 and do for final bits will repeat again, buddy. Ethically, the final number is drink Fisher part with the fractional part. The teacher part is given by 1000111 coma and the fractional part is 00 01 When with these four final beats repeatedly 19. Conversion from binary to decimal using fractional numbers: binary to decimal numbers conversion. In the first lessons, you learn out to convert in teacher numbers from binary to decimal. In this chapter, you will learn how to convert numbers with into Asia, part in fractional part from binary two decimal. What is the main difference between this? These two different parts off the number, the integer part? We'll use positive exponents, and the fractional part will use negative exponents. If you see in this table the values off, the negative exponents with by stew will give you values bigger than zero and smaller, then one. The first example. I'm going to make the conversion off this number to They're simple, from binary to decimal, and in the final you will get this results, starting with the anti jher part with positive exponents. If you remember to convert from binary to decimal, you have to multiply each value digit by the correspondent white, with base to and positive exponents starting and going to get one multiplied by two exponents. Zero ended with one multiplied by to explain. Entry ended with one multiplied by two exponents. Six ended with one multiplied by to explain and seven added, with one multiplied by two exponents AIDS. The final result, as you expected, is 457 in decimal now converting the fractional part off the number. The different is that you have negative exponents and you will make the calculation weren't multiplied by two exponents minus two Editor one multiplied by two exponents minus stream. The final result is 0.355 and response to this fractional part of second example converting Divide every number 10 1110.11011 two decimal from binary to decimal starting with Indonesia part What 01110 is equal to two exponents five multiplied by one editor. It's too explained for multiplied by zero added with two exponents tree multiplied by one edit with to explain and to multiply by. One ended with two exponents, one multiplied by one and finally Edwards two exponents zero multiplied by zero. My final result is the same of 32 with eight with four with two 46 in their symbol. De fractional parts is 11011 And making the calculation with negative exponents, I will have two exponents minus when multiplied by one added with two exponents minus two multiplied by one head with two exponents minus street multiplied by zero ended with two exponents minus four multiplied by one ended with two exponents minus five multiplied by one, and this will give 0.8437 five Final results 46.84375 in their symbol. 20. Decimal to other bases conversion using fractional numbers: decimal to other basis conversion. This kind of conversion is very similar, Like the conversion from decimal to binary. This is my first example the number 78 coma to 50 in decimal. And if I want to convert this number into other base theme Tischer parts, I have to divide the number by the base that I want the remainder off the division. Give me the final result off the interior part in the new Bice, making this practical example first converting doing teacher part off the number into buys right? I have to divide the number by eight. I get a caution and the reminder when the cautions is zero. The reminder. Give me the final result for the integer part. 78 in decimal is equal to 116 in octo using devices 16 converting from decimal to 16. The integral part. I made the division by 16. I get a quotient and the reminder when I get zero in the oceans, The reminder Give me the final result. 70 18 Decimal is equal to four e in Bice 16 to convert diffraction ALS part First I have to multiply Defection a LPA parts by the base value that's I want take the fractional part as the value to multiply in the next step the fractional parts that I get dessert column I will use in the next multiplication and I will stop when I get zero or I get the periodic number. The final result of the conversion is given by this Fort Collins. The teaser part of the multiplication in disguise for the base right for the conversion from by stand to buy it zero coma to 50 in decimal is equal to zero coma to zero in Bice, right? And the final result is the integer part and the fractional part u F 116 coma to zero in octo as final results to the exit decimal conversion, I have to multiply diffraction apart by 16. And when I get zero or a periodic number in the multiplication, the anti jher part, give me the final result. Zero coma to 50 in decimal is equal to zero coma for zero in vice 16 and the final result is the interior part with the fractional part integer part for E in fractional part for zero. If I want to covert at that simple number. Two other buys different off eight and 16. First, the interior parts in this example I want to cover to buy 20 and I'm going to make the division by 20 to get the Indian jher parts. I get the quotient in the reminder and I will stop when I get zero on the Kocian. The reminder. Give me the final results. In device 20 you have 20 different values to make the representation off. A digit in death buys the numbers from 0 to 9 and letters from A to G 876 in their symbol is equal to two tree G in Bice. 20. The fractional part. I have to multiply by 20 and when I get zero or the periodic number in disguise zero. The in teacher part off these two multiplication will give me the final results in Bice 20 zero Coma. Eight In base 10 is equal to zero coma G in Bice 20. So the final result is to treat G for the interior barks and G for the fractional part 21. Binary to other bases conversion using fractional numbers: binary to other basis conversion. You learn in the previous videos debt. To make the conversion from a binary number two Octel or exit decimal number, you have to split the visionary number in groups of three beats to get ductile Digit. The correspondent Octel Digit and Split in four beats Divine every number to get to correspondent exas Immel. Digits in disguise. I'm going to show you out to convert the number 11011 coma. 011 In binary cover ting to Octel, I may display eat in groups of three beats and I get 011011011 These three groups of three beats are the same f the same value the same digit. It's stream tree tree, Coleman Tree. It's the number in octo to cover to to exit decimal ice pleat. This number in groups of far beats and I get 0001 Corresponds to the digit 110 11 response to this should be an 0110 response to the digit six. My final number is one B. Goldman, six in exit decimal, making another example. The number 1110 Coma 1111 Making this split off the numbering groups off three beats. To get my Octel number, I get 001 Want went zero one went one 100 1674 in octo converting to exit decimal split the number in groups of four bids 1110 Goma 1111 The two digits are e an in fractional part. If my final number is E if now if I want to convert two other by different of powers of two are different then the conversion is not direct. First, I have to convert from binary to decimal and in the second step, I have to convert from decimal to device that I want to cover it in the second step from decimal to device that I want I use the division method to get the interior part In the final Bice and the fractional part I used the multiplication matters. I should hear a dia gram and I have a binary number the original binary number first covert to decimal. Then I have my decimal number and I'm going to convert in disguise in this example to device. Seven to get the number in by seven. The interior part I will divide by seven and the reminder. Give me the final result in by seven and deflection apart, I will multiply by seven and interior part of the multiplication. Give me the fractional part off the results in base seven now making an example. Conversion off went 101 Goma 0112 by seven. First the conversion from binary to decimal. So I will multiply each digit by the correspondent white that f base to one multiplied by two exponents tree other than one multiplied by two exponents too ended with one multiplied by two exponents. Zero I get certain in decimal for the interior parts diffraction ALS parts is one multiplied by two exponents minus two ended with one multiplied by to explain in my industry it give me the number zero comma 375 in decimal. So my final number in the symbol is one tree The integer part coma 375 in decimal. This is the first step off the conversion now making the second step, converting from decimal to Dubai's seven I f. Here the symbol number now I'm going to convert the into Asia part using the division methods. I'm going to make the division by seven. I get a quotient and a reminder. When the Coche int is zero, the reminder will give me the final result in base seven. So the result is 16 in base seven. To get the fractional part, I real multiply deflection a LPA part off the decimal number by seven. And when I get zero in the multiplication on a periodic number, the interior part off the multiplication give me the final result in disguise. You can see that in the first row, and in this aero you have the same results. So this is a periodic number. These numbers will repeat again, so the final number in by seven is zero coma. 2424 Periodic final results is 16 for the teacher part and two for periodic. For the fractional parts 22. Binary addition: Mary Addition. Divine Eri addition is very similar with decimal addition, but instead of you, Stan values to represent one digit used to values to represent one digit. So with values it's possible for different combinations. A showing disabled the possible combinations if beat 10 and 20 sum is zero and carry it. Zero between is zero and beat two is one some one and carry it. Zero beat one is one and B two is zero. Sum is one and carry with zero. And finally, if beat one is one and beat two is one some zero and carry it one. If you don't understand how I do this, Sam, it's difficult to you. You may The storm did binary Sam into a decimal Sam and you'll see at the final Divine Eri results in this less row you get to that one in binary blues. One in binary is equal to one in decimal plus one intestinal. The number one in binary is equal to one in decimal, so I can make this this change from binary to decimal one in decimal plus one, industrial is equal to intestinal interest. Forming to binary again is equal to a 10 in binary. This zero is the same result, and this one is carrying a bit. When we used the decimal system, we have the carrier beat, too, when the result exceeds nine. In this example, five Blues nine is equal to four carry it, one that gives the result off. 14. I'm going to show you now. Three more examples. Addition off the two numbers went zero Went 1010 with 011101 and making the calculation. Zero blues one is 11 Blue zero is one zero plus one is when? When Blues. When is this last row? So it's zero. Carry it. When? When. Blues When Blues one is one with Carrier one when Blue zero plus zero is when and when. Blues zero is one and I f You Peter. My final results. 1110111 In binary. Next example addition off 11100101 with When When? 010111 And the first calculation is one. Lose one is zero. Carry a 11 plus zero plus one is zero carrier. When now I F tree once again when Poland Poland is one. Kerry is when 10 p. Zero It's one zero plus one is when when blue zero is one. When pulls went zero carrying one and again tree ones, it's when carry it one that goes to do less results. So my final memories when when zero went one when 100 and finally the final example. 110101 ended with 1010 went one starting the calculation when blues When is zero carried one when plus zero plus one is zero. Carrier went when blues went zero is zero carrying one and again when Blues zero pulls Went zero carried one one plus one plus zero is zero carrier one. Now I f tree one cities one with carry it one. So my final result is went when 00000 in binary 23. Binary subtraction: in this video, I'm going to show you out to subtract two binary numbers using the two's complement Demet that I'm going to use is the conversion off a subtraction. I'm going to reform a subtraction into a new addition with negative numbers using the two's complement in the table, you can see the difference between inside Gnant numbers and two's complement numbers. In stagnant numbers, you just f positive numbers. And with the two's complement, you can transform positive into negative numbers. What distinguished this to type of numbers, positives and negatives is the most significant bit. If you are talking about positive numbers, the most significant bit is zero. And to the negative numbers, the most significant bit is one like you can see in the table toke. Avert positives. Two negatives. You just used the two's complement like you can see an example over here. Seven. Positive 0111 Like I said, the first beat that left is zero and minus seven starts with one because its a negative number and the rest of the beats are 000 How do I make the calculation to to give a negative number to get thick the negative number. It's easy starting from the right to the left. Off the number when you find the 1st 1 You changed all the bits, zeros, toe one and once two zeros and you get the negative number. In this example, I have positive number 20 and I get minus 20 with this technique. 1st 1 this tree bits are going to change inverted and you get minus 20 is 101100 Second example from the number 18 I will get minus fighting with two's complement, the number starting from the right to the left. I get the 1st 1 and I will revert these four beats at left and I will get 10111 zero with the beats on the left one because it's a negative number. Now I'm going to make the subtraction off. Two numbers. 16 minus nine. I'm going transform to an addition with the positive number and the negative number 16 send with minus nine. So I get the two's complement off nine to get my minus nine nine in decimal. Positive is 01001 This is my 1st 1 so I'm going to invert the forbids that left and I get 10111 minus night in decimal. Making the calculation 16 minus nine is equal to this calculation. If I made a subtraction, but I'm going to transform into an addition off 16 with minus nine with the Deuce Complement and I get this number 000111 The carry wheat is ignore, so my my beats on left zero. So it's a positive number. This number in decimal is 7 16 headed with minus nine is seven in decimal. My second example. Nine. Subtracting with 17 is equal to nine. Edit with minus 17 so I get the tooth's compliment off. 17 17 010001 This is my 1st 1 So I'm going to invert these five beats on the left and I get 101111 Now making the calculation. Don't forget to put zeros on the left because this is a positive number. If you have one on the left, this means that is a negative number. Okay, making the two's complement off 17. I get 001001 ended with 101111 This Give me a result off 111000 The bit on the left is Gary Bit. You will in our this bit now to know this result this is a negative beats If you make again the two's complement you go. You will going toe to give You're going to have the absolute number off this negative number. I make the two's complement and I will get 001000 This is eight in decimal. So this number is minus eight nine minus 17 is minus eight in decimal. 24. Introduction to arithmetic operations with different bases: Hello. In this final section, you're going to join the conversion and the enigmatic operations that you learn from the previous chapters. In Section two, you learn how to make conversion. Using different buys is by stew 8 10 and 16. And in the section for you learn out to my Edit Matic operations, addition and subtraction using device to now you're going to join these two sections and you're gonna learn out to make enigmatic operations using the four main Bisys. 25. Hexadecimal and octal addition: Octel and exit decimal numbers addition. In the next videos, I'm going to use negative and positive numbers to make addition and subtraction. I'll do I distinguish between them. If the most significant bits is equal to zero. I'm talking about positive numbers. You can add zero that left off the number. Death. Don't change the value off that's number. And if the most significant, it is equal to one. I'm talking about negative numbers, ones that left off the number. Don't change that value in a negative number. First. Example. Tree in decimal is equal to 011 in binary. This zero at left means that the number is positive now to change to minus tree. I have to make the juice compliment so minus tree in decimal is equal to 101 in binary. To change this binary number from three beats to eight beats. I have one that left and I get 1111 when when 01 in binary. This number don't change in exit decimal number is equal to F D. Now, making our first example of an addition with Octel numbers, the number 37 added with 25 in octo first step The conversion from Otto to binary Making two groups off. Three beats. I get 011 from digit three and 111 from the digits. Seven 010 Front digit two and 101 from the digit five. Making the addition off these two numbers. Using the stable I get 000110100 I had three beats that left 30 beats just to force that this number is positive because the last bit waas one if I don't add the street beats so I get zero from this tree First groups six from these 2nd 2 groups And for for these last groups of tree 064 in Octel is my final number now making the second edition 15 in total for three in Octel The addition off these two numbers First, the conversion from by 82 ways to and I get 001 from digit one and 101 from digit five 100 front digit for and 011 from digit three. I added again 30 That left just to force this number to be positive now making the addition I get 000110000 and my final number in Octel is 060 Finally, the example with exit decimal numbers. The addition off one I with to tree conversion from by 16 to buys two and I get 0001 from digit one and 1010 from digit I 0010 front digit to and 0011 from digits. Three. Making the addition I get 00111101 making two groups off four bits and I get my final exit . Decimal number is equal to tree the 26. Hexadecimal and octal subtraction: I industry, do you? I'm gonna make the subtraction using auto and exit decimal numbers by sight. And by 16 1st I'm going to start with Octel numbers I f two numbers 14 and 37 in octo. First, I'm going to make the conversion to binary numbers. 14 in Octel is equal to 001 from the digit one and 100 from the digit for In this number three, give me 011 and digits seven. Give me one. Went one. Now I'm going to make the transformation from a subtraction into an addition. So I have to make the deuce compliment off this number and I get 10000 When? Now I can make the addition with these two numbers and I get the final binary number off 111 01 When 01 you can see that the most significant beat is one. So this is a negative number. I just add one that left off the number to make groups of three and four beats to transform the number from binary to auto and exit decibel converting from binary to Otto. I make these three groups off three beats and I get 755 in octo converting to eggs a decimal i f two groups of four beats and I get the number A D and converting from binary to decimal. You know that this is a negative number. And if I make the two's complement, I'm going to convert this negative number into its positive number with positive signal. And this number is this positive number is 19. So the final result in decimal is minus 19. Now, using exit decimal numbers, I f two numbers tree for in exit decimal and 71 in by 16 making first the conversion to binary. I get 0011 from the digit tree 0100 from the digit for. And from this number, I get 0111 from the digits seven and 0001 from the digit one now making the deuce compliment off this number. I get 10001111 Now, I can make the addition with these two numbers, and the result is 1100 0011 in binary. This is that negative number because off the most significant bit with value one now transforming this binary number into a nocturnal number. I get 703 and transforming into an exit decimal number I get. See tree. Finally, this negative number. If I used the Deuce compliment, I'm gonna know the number, but with positive value. Positive signal. So this number is minus 61 in decimal. 27. Addition and subtraction using all bases: Hello. This video I will show you out of my condition and subtraction using different based on numbers, you can make addition with the combination off the different best numbers that you learn. The only trick is when you use Bice 8 16 and decimal, you must convert to binary to make the A vision. After you make the addition in binary, you will have the resulting binary so you can make again the conversion to device that you want in the final. Let's make the first example. I want to make the addition off 12 in exit decimal and 21 in BIST 10. The first step is to convert two bites, too 12 in answer decimal two Bass two is equal to 0001 from the digit one and 0010 from the digit to to cover 21 in decimal to base to you F to use division methods. Now that you have the two numbers, let's make the addition. So you get this final number in binary. You can convert this number into octo and can convert to exit decimal de final number inartfully 047 in exit decimal to seven and in decimal 39 39. Now, when I want to make subtraction, it's the same matters. First, I want to convert by this 8 16 intent to binary, then the second number. I have to make the juice compliment to get the Deuce compliment off the second number. If you ever positive number, the number will be negative. After the Deuce compliment, I make the addition off a positive number and the negative number, and I will get the final number in Binary de final buys debt. I want I messed to convert the binary number two debt buys, making one example 37 in Octel subtracting with one A in exit decimal 37 is 011 one. Want one? This first street beats from the digit tree and the second tree beats from the digits. Seven 0001 is digit one from this number in exit decimal, and 1010 is a from this number the first digit. Now I'm going to make the two's complement off this number. This number waas positive, and now it's a negative because the most significant bit making the addition I get this number Positive number Carry bit is ignored. Now I can transform into the Octel number 05 in Octel 05 in exit decimal and 05 in decimal number. Now making the second example 12 in Octel Subtraction. Weeds 20 in decimal. 12 is equal to 001 010 in binary and 20. Using the division method, I get in binary 010100 Making the twos Compliments. This number. Use it to complement off these. The most significant beat basis from 0 to 1. And making the addition I get 110110 This number is negative now, making the conversion to octo. I get 66 converting to exit decimal. I get F six and now making the deuce compliment off this final result. I get the number, but with positive signal. This number with positive signal is then. So this number in binary ese minus 10