computer’s language is binary 0s and 1s. The computer cannot understand typed or written instructions or data. Whenever data or instructions or input to the computer it is first converted to 0s and 1s‚ these are called binary digits (bits). There are a number of methods that are used to represent data in computer system‚ namely: 1. Binary Representation 2. ASCII - American Standard Code for Information Interchange 3. EDCDIC - Extended Binary Coded Decimal Interchange Code
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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. Ideally‚ a number system will: * Represent a useful set of numbers (e.g. all integers‚ or rational numbers) * Give every number represented a unique representation (or at least a standard representation) * Reflect the algebraic and arithmetic structure of the numbers. For example‚ the usual decimal representation of whole numbers gives every
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Written Assignment #2 Review Questions: 1.Convert each of the binary numbers to decimal numbers: A. 2 B. 4 C. 7 D. 11 E. 12 F. 18 G. 21 H. 31 I. 205 J. 227 2.Convert each of the decimal numbers to binary: A. 111 B. 10011 C. 11100 D. 101110 E. 111001 F. 1010110 G. 1011110 H. 1110000 I. 10010100 J. 11100110 3.Convert each of the octal numbers to decimal numbers: A. 30 B. 68 C. 80 D. 142 E. 240 F. 846 4.Convert each of the octal numbers to binary numbers: A. 111100 B. 1011000 C. 10101000 D
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(Task 1) Convert decimal number (125) into binary. 125 /2 = 62 remainder5 1(lsd) 62 /2 = 31 remainder0 o 31 /2 = 15 remainder5 1 15 /2 = 7 remainder5 1 7 /2 = 3 remainder5 1 3 /2 = 1 remainder 5 1 1 /2 = .5 remainder 0 1 .5 /2 = 0 remainder 0 0 Convert your answer back to decimal to prove your answer. 0 1 1 1 1 1 0 1 0+64+32+16+8+4+2+1=125 (task 2) Convert the binary number(10101101) into decimal.
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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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