Exercise on Binary Number System
1. How many distinct values can we represent with
a) 4 bits - 16 b)5 bits - 32
2. Add the following unsigned binary numbers
a) 1110 + 111 b) 11011 + 11011
1110
0111
10101
11011
11011
110110
3. What is the largest positive number one can represent in 5-bit 2โs complement code?
25-1 -1 = 15
4. Convert the following from 2โs complement to Decimal
1010
This is a negative number as the most significant bit is 1. Find out its positive
counter by flipping all bits and then adding 1.
0101 + 1 = 0110
= 0 x 23 + 1 x 22 + 1 x 21 + 0 x 20
= 4 + 2 = 6
Hence the number is -6.
5. Convert the following decimal to 8-bit 2โs complement binary numbers.
a) 11 Division Method
11/2 โ remainder 1
5/2 - remainder 1
2/2 -- remainder 0
1/2 โ remainder 1
00001011
b) -128
Subtracting Powers of 2 Method
128 โ 128 = 0 bit 7 should be 1 as 27 = 128
10000000 = 128
Now take 2โs complete to get -128
01111111 + 1 = 10000000
