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Exercises 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. ( ) 2 = (226) 8 =(96) ( ) 2 = (624) 8 =(194) ( ) 2 = (515) 8 =(14D) ( ) 2 = ( ) 8 =(9.95A) ( ) 2 = (31.53) 8 =(19.AC) ( ) 2 = (56.6) 8 =(2E.C) 16

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

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Exercise 3 Convert the hexadecimal number 64CD to binary, and then convert it from binary to octal ( ) 2 =(62315) 8 Convert the decimal number 431 to binary in two ways: 1. Convert directly to binary= ( ) 2 2. Convert first to hexadecimal and then from hexadecimal to binary=(1AF) 16 =( ) 2 Which method is faster? Way (1) 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 = ( ) 9’scomplement = ( ) 10’scomplement 2. 63, 325, 600 = ( ) 9’scomplement = ( ) 10’scomplement 3. 25,000,000 = ( ) 9’scomplement = ( ) 10’scomplement 4. 00,000,000 = ( ) 9’scomplement = ( ) 10’scomplement

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Exercise 5 Obtain the 1’s and 2’s complements of the following binary numbers: 1. ( ) 2 =( ) 1’s complement =( ) 2’s complement 1. ( ) 2 =( ) 1’s complement =( ) 2’s complement 1. ( ) 2 =( ) 1’s complement =( ) 2’s complement 1. ( ) 2 =( ) 1’s complement =( ) 2’s complement 1. ( ) 2 =( ) 1’s complement =( ) 2’s complement 1. ( ) 2 =( ) 1’s complement =( ) 2’s complement

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Exercise 6 Perform subtraction on the given unsigned binary numbers using the 2’s complement of the subtrahend: = – = – (negative number) – = – (negative number) – 10101=010011

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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)=( ) – (+13)=( ) – (– 4)=( ) 2 4. (– 9) – (+5)=( ) 2

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

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