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

Exercise 1 Convert the following binary numbers to octal and hexadecimal numbers (10010110) 2 = (226) 8 =(96)16 (110010100) 2= (624) 8 =(194)16 (101001101) 2= (515) 8 =(14D)16 (1001.100101011010) 2 = (11.4532) 8 =(9.95A)16 (11001.101011) 2= (31.53) 8 =(19.AC)16 (101110.110) 2= (56.6) 8 =(2E.C)16

Exercise 2 Convert the following octal and hexadecimal numbers to binary numbers (234) 8 =(10011100) 2 (4FA2) 16 =(100111110100010) 2 (5B23.AD67) 16 =(101101100100011.1010110101100111) 2 (3721.421) 8 =(11111010001.100010001) 2

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 (110010011001101) 2 =(62315) 8 Convert the decimal number 431 to binary in two ways: Convert directly to binary= (110101111) 2 Convert first to hexadecimal and then from hexadecimal to binary=(1AF) 16 =(110101111) 2 Which method is faster? Way (1) is faster

Exercise 4 Find the 9’s and the 10’s complement of the following decimal numbers: 25,478,036 = (74521963) 9’scomplement = (74521964 ) 10’scomplement 63, 325, 600 = (36674399) 9’scomplement = (36674400 ) 10’scomplement 25,000,000 = (74999999) 9’scomplement = (75000000 ) 10’scomplement 00,000,000 = (99999999) 9’scomplement = (100000000 ) 10’scomplement

Exercise 5 Obtain the 1’s and 2’s complements of the following binary numbers: (00010000) 2 =(11101111) 1’s complement =(11110000) 2’s complement (00000000) 2 =(11111111) 1’s complement =(00000000) 2’s complement (11011010 ) 2 =(00100101) 1’s complement =(00100110) 2’s complement (10101010) 2 =(01010101) 1’s complement =(01010110) 2’s complement (10000101) 2 =(01111010) 1’s complement =(01111011) 2’s complement (11111111) 2 =(00000000) 1’s complement =(00000001) 2’s complement

Exercise 6 Perform subtraction on the given unsigned binary numbers using the 2’s complement of the subtrahend: 10011 - 10010 =0001 100010 – 100110= – 000100(negative number) 1001 – 110101= – 101100(negative number) 101000 – 10101=010011

Exercise 7 Perform the mathematical operations on the given signed numbers using the 2’s complement for negative numbers and subtraction operation (+3) + (+5)=(0000 1000) 2 +16 – (+13)=(0000 0011) 2 +8 – (– 4)=(00001100) 2 (– 9) – (+5)=(10001110) 2

Exercise 8 Represent the unsigned decimal numbers 791 and 658 in BCD 791=(0111 1001 0001) BCD , 658=(0110 0101 1000) BCD Convert decimal 6,514 to both BCD and ASCII codes 6,514 =(0110 0101 0001 0100) BCD =(0110110 0110101 0110001 0110100) ASCII Represent the decimal number 6,248 in BCD=(0110 0010 0100 1000) excess‐3 code=(1001 0101 0111 1011) 2421 code=(1100 0010 0100 1110) 8,4,-2,-1 Code= (1010 0110 0100 1000) Gray Code= (0101 0011 0110 1100)

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