Number Systems‚ Base Conversions‚ and Computer Data Representation Decimal and Binary Numbers When we write decimal (base 10) numbers‚ we use a positional notation system. Each digit is multiplied by an appropriate power of 10 depending on its position in the number: For example: 843 = 8 x 102 + 4 x 101 + 3 x 100 = 8 x 100 + 4 x 10 + 3 x 1 = 800 + 40 + 3 For whole numbers‚ the rightmost digit position is the one’s position (100 = 1). The numeral in that position indicates how many ones
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Procedure 1.Convert the decimal number 125 into binary. Use the division-by-two method shown in the following example. 125 /2 = 62 r=1 62 /2 = 31 r=0 31 /2 = 15 r=1 15 /2 = 7 r=1 7 /2 = 3 r=1 3 /2 = 1 r=1 1 /2 = 0 r=1 01111101 2.Convert your binary result back into decimal to prove your answer is correct. This is also shown in the following example. Weights = 128 64 32 16 8 4 2 1 Bits = 0 1 1 1 1 1 0 1 64 + 32 + 16 + 8 + 4 + 1 = 125 Task 2: Procedure 1.Convert the binary number 10101101
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Introduction | 3 | | 4.1 | Decimal System | 5 | | 4.2 | Binary System | 6 | | 4.3 | Hexadecimal System | 7 | | 4.4 | Octal system | 8 | 5. | Algorithms | 9 | 6. | Solved Examples | 14 | 7. | Programs | 18 | 8. | Advantages | 36 | 9. | Applications | 37 | 10. | References | 37 | | | | | TITLE: CONVERSION OF NUMBER SYSTEMS SUBTITLE: 1. Conversion of binary to decimal number system 2. Conversion of octal to decimal number system 3. Conversion
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two digits 1 and 0. Hence‚ our ordinary decimal number system consisting ten digits (0-9) do not suits the data representation of CPU. It works with simple binary system. BINARY NUMBER SYSTEM It uses two symbols or digits i.e. 0 and 1. And all the symbol‚ Arithmetic number etc. are represents in the form of 0’s and 1’s. And ordinary decimal number can be converted to its binary form in the following manner- Ques: Convert (45) 10 to its Binary equivalent 2 45 2 22 1 2 11 0 2
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representingnumbers of a given set‚ using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three‚ the decimal symbol for eleven‚ or a symbol for other numbers in different bases. Equivalent Numbers in Decimal‚ Binary and Hexadecimal Notation: Decimal Binary Hexadecimal 0 00000000 00 1 00000001 01 2 00000010 02 3 00000011 03 4 00000100 04 5 00000101 05 6 00000110 06
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25-6 (2 pts. each; 20 points total) 1. F 2. T 3. T 4. F 5. T 6. F 7. T 8. F 9. F 10. F Exercises #1 - #3‚ p.26 (10 pts. Each; 30 points total) #1. Convert the following decimal numbers to binary. 11 dec = 00001011 65 dec = 01000001 100 dec = 01100100 255 dec = 11111111 #2. Convert the following binary numbers to decimal. 1101 = 13 1000 = 8 101011 = 43 #3. What are the ASCII codes for each letter in your name? 83‚ 97‚ 109 Assignment #1 – Chapter #1 M/C
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Number Systems Base 2: The Binary Number System Base 8: The Octal Number System Base 16: The Hexadecimal Number System Learning Objectives • At the end of the lesson the student should be able to: – Identify the different number base system – Convert base ten numbers to base two‚ eight or sixteen – Convert base two‚ eight or sixteen numbers to base ten – Perform basic operations on various base numbers Number Base • What is a number base? A number base is a specific collection
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and provides programmers a detailed template for the next step of writing code in a specific programming language. I have chosen to create a pseudo code because I found that this tells the user a step by step process on how to convert decimal to binary or binary to decimal. A flow chart is a graphical or symbolic representation of a process. Each step in the process is represented by a different symbol and contains a short description of the process step. The flow chart symbols are linked together
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network connection? i. Ping – Packet Internet Groper I. The ping command uses a series of echo requests‚ and the networking device receiving the echo requests responds with a series of echo replies to test a network connection. 17. Convert the
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useful to the student of computing due to the fact that number systems other than the familiar decimal (base 10) number system are used in the computer field. Digital computers internally use the binary (base 2) number system to represent data and perform arithmetic calculations. The binary number system is very efficient for computers‚ but not for humans. Representing even relatively small numbers with the binary system requires working with long strings of ones and zeroes. The hexadecimal (base 16) number
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