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Exercise 1.2 (Chapter 1) Prepared by Dr. Lamiaa Elshenawy 1 Logic Design (CE1111 )

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Exercise 1 Convert the following binary numbers to octal and hexadecimal numbers 1. (10010110) 2 2. (110010100) 2 3. (101001101) 2 4. (1001.100101011010) 2 5. (11001.101011) 2 6. (101110.110) 2

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Exercise 2 Convert the following octal and hexadecimal numbers to binary numbers 1. (234) 8 2. (4FA2) 16 3. (5B23.AD67) 16 4. (3721.421) 8

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Exercise 3 Convert the hexadecimal number 64CD to binary, and then convert it from binary to octal Convert the decimal number 431 to binary in two ways: 1. Convert directly to binary 2. Convert first to hexadecimal and then from hexadecimal to binary Which method is faster?

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Exercise 4 Find the 9’s and the 10’s complement of the following decimal numbers: 1. 25,478,036 2. 63, 325, 600 3. 25,000,000 4. 00,000,000

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Exercise 5 Obtain the 1’s and 2’s complements of the following binary numbers: 1. (00010000) 2 2. (00000000) 2 3. (11011010 ) 2 4. (10101010) 2 5. (10000101) 2 6. (11111111) 2

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Exercise 6 Perform subtraction on the given unsigned binary numbers using the 2’s complement of the subtrahend: 1. 10011 - 10010 2. 100010 – 100110 3. 1001 – 110101 4. 101000 - 10101

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Exercise 7 Perform the mathematical operations on the given signed numbers using the 2’s complement for negative numbers and subtraction operation 1. (+3) + (+5) 2. +16 – (+13) 3. +8 – (– 4) 4. (– 9) – (+5)

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Exercise 8 Represent the unsigned decimal numbers 791 and 658 in BCD Convert decimal 6,514 to both BCD and ASCII codes Represent the decimal number 6,248 in 1. BCD 2. excess ‐ 3 code 3. 2421 code 4. 8,4,-2,-1 Code 5. Gray Code

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