Question

3. Find the byte-length 2's complement representation of each of the following decimal numbers (a) 23 (b) 111 (c) -100 (d) -55 (e) 99 (f) -15

Answer 1

Byte length means 8 bit representation

2's complement representation:

for positive numbers:

we dont need to convert to 2's complement form because the 2's complement representation is same as general binary notation

for negative numbers:

first convert given decimal to its binary form

then obtain its 1's complement form by inverting 1's to 0's and 0's to 1's of obtained binary number

then add 1 to obtained 1's complement number to get 2's complement number.

a)

23 = 00010111

b)

111 = 01101111

c)

-100

100 = 01100100

1's complement of 100 = 10011011

2's complement of 100 = 1's complement + 1

= 10011011 + 1

= 10011100

-100 = 10011100

d)

-55

55 = 00110111

1's complement of 55 = 11001000

2's complement of 55 = 1's complement + 1

= 11001000 + 1

= 11001001

-55 = 11001001

e)

99 = 01100011

f)

-15

15 = 00001111

1's complement of 15 = 11110000

2's complement of 15 = 1's complement + 1

= 11110000 + 1

= 11110001

-15 = 11110001