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

2. 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

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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= ( )

10. Useful website http://coderstoolbox.net/number/
em.htm