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**Exercises 1.2 (Chapter 1) Prepared by Dr. Lamiaa Elshenawy**

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

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Exercise 1 Convert the following binary numbers to octal and hexadecimal numbers ( ) 2 = (226) 8 =(96)16 ( ) 2= (624) 8 =(194)16 ( ) 2= (515) 8 =(14D)16 ( ) 2 = ( ) 8 =(9.95A)16 ( ) 2= (31.53) 8 =(19.AC)16 ( ) 2= (56.6) 8 =(2E.C)16

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

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**Which method is faster? Way (1) is faster**

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: Convert directly to binary= ( ) 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: 25,478,036 = ( ) 9’scomplement = ( ) 10’scomplement 63, 325, 600 = ( ) 9’scomplement = ( ) 10’scomplement 25,000,000 = ( ) 9’scomplement = ( ) 10’scomplement 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: ( ) 2 =( ) 1’s complement =( ) 2’s complement ( ) 2 =( ) 1’s complement =( ) 2’s complement ( ) 2 =( ) 1’s complement =( ) 2’s complement ( ) 2 =( ) 1’s complement =( ) 2’s complement ( ) 2 =( ) 1’s complement =( ) 2’s complement ( ) 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: =0001 – = – (negative number) 1001 – = – (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 (+3) + (+5)=( ) 2 +16 – (+13)=( ) 2 +8 – (– 4)=( ) 2 (– 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 BCD=( ) excess‐3 code=( ) 2421 code=( ) 8,4,-2,-1 Code= ( ) Gray Code= ( )

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**Useful website http://coderstoolbox.net/number/**

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