Solved examples of binary to decimal number conversion
Problem 1: Convert ( 10110 )2= ( ? )10
= 1 0 1 1 0
↑ ↑
MSB LSB
= 1 x 24 + 0 x 23 + 1 x 22 + 1 x 21 + 0 x 20
= 1 x 16 + 0 x 8 + 1 x 4 + 1 x 2 + 0 x 1
= 16 + 0 + 4 + 2 + 0
= 22
Therefore ( 1 0 1 1 0 )2 = ( 22 )10
Problem 2: Convert ( 111000 )2= ( ? )10
= 1 1 1 0 0 0
↑ ↑
MSB LSB
= 1 1 1 0 0 0
↑ ↑
MSB LSB
= 1 x 25 + 1 x 24 + 1 x 23 + 0 x 22 + 0 x 21+ 0 x 20
= 1 x 32 + 1 x 16 + 1 x 8 + 0 x 4 + 0 x 2 + 0 x 1
= 32 + 16 + 8 + 0 + 0 + 0
= 56
Therefore ( 1 1 1 0 0 0 )2 = ( 56 )10
Problem 3: Convert ( 010101 )2= ( ? )10
= 0 1 0 1 0 1
↑ ↑
MSB LSB
= 0 x 25 + 1 x 24 + 0 x 23 + 1 x 22 + 0 x 21+ 1 x 20
= 0 x 32 + 1 x 16 + 0 x 8 + 1 x 4 + 0 x 2 + 1 x 1
= 0 + 16 + 0 + 4 + 0 + 1
= 21
Therefore ( 0 1 0 1 0 1 )2 = ( 21 )10
Problem 4: Convert ( 101 )2= ( ? )10
= 1 0 1
↑ ↑
MSB LSB
= 1 x 22 + 0 x 21+ 1 x 20
= 1 x 4 + 0 x 2 + 1 x 1
= 4 + 0 + 1
= 5
Therefore ( 1 0 1 )2 = ( 5 )10
Problem 5: Convert ( 01111 )2= ( ? )10
= 0 1 1 1 1
↑ ↑
MSB LSB
Here, zero at the beginning does not make any sense and we can safely eliminate the zero at the MSB position.
= 1 1 1 1
↑ ↑
MSB LSB
= 1 x 23 + 1 x 22 + 1 x 21+ 1 x 20
= 1 x 16 + 1 x 8 + 1 x 4 + 1 x 2 + 1 x 1
= 8 + 4 + 2 + 1
= 15
Therefore ( 1 1 1 1 )2 = ( 15 )10