Question

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1. Using binary numbers of 8 bits each, convert to binary and solve the following arithmetic operations using two’s complement representation: (10 points)

                  a) (48)₁₀ - (13)₁₀

          b) (-18)₁₀ + (-13)₁₀  

Answer 1

solution:

a) :

(48)₁₀ - (13)₁₀

Step 1:- First convert both the values in binary

48 = 00110000

13 = 00001101

Step 2:- convert negative number to 1's complement

00001101 = 11110010

Step 3:- convert 1's complement into 2's complement

11110010 + 1 = 11110011

Note: 2's complement of positive number will be same as binary number

48 - 13

48 +(-13) = 00110000+11110011 = 00100011

b):

(-18)₁₀ - (13)₁₀

Step 1:- First convert both the values in binary

18 =    00010010

13 = 00001101

Step 2:- convert negative number to 1's complement

00010010=11101101

00001101 = 11110010

Step 3:- convert 1's complement into 2's complement

11101101 + 1= 11101110

11110010 + 1 =11110011

Note: negative number represented by their 2's complement...

(-18)+ ( - 13)

(-18) +(-13) = 11101110 + 11110011 = 11100001