### Convert binary to decimal number

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 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