Binary to decimal conversion

  • Any binary number can be converted to its decimal equivalent using the weight assigned to each bit position .Binary number system has base 2.
    For example,
    Suppose we have a number (101.10)2 then weight assigned to each bit is ,
    shown below :

To the left of radix point power of two increases,while to the right of radix point power of two decreases.

  • In the binary system,
    Going to the left of  radix point each digit represents an increasing power of 2, with the right most digit representing 20, the next representing 21, then 22, and so on.
    And going to the right of radix point,each digit represent an decreasing power of 2 , with left most digit representing 2-1,the next representing 2-2,then 2-3 ,then 2-4 and so on.
    The equivalent decimal representation of a binary number is the sum of the powers of  2 ,which each digit represents.

    The binary numbers is converted to decimal number as follows:
  • Example 1:

( 1101 )= (   ?  )10

=[ 1 × 2] + [ 1× 2] + [ 0 × 2]+[ 1 × 2]
=[ 8 ]+[ 4 ]+[ 0 ]+[ 1 ]
=( 13 )10

  • Example 2:

( 0000 )= (   ?  )10

=[ 0 ×  23 ] + [ 0  × 2] + [ 0  × 2]  + [ 0  × 20]
=[ 0 ]+[ 0 ]+[ 0 ]+[ 0 ]
=( 0 )10

  • Example 3:

( 111111 )2 = (   ?   )10

=[ 1 × 2] +[ 1 × 24 ] + [ 1 × 2] + [ 1 × 2] +[ 1 × 2]+ [ 1 × 2]
=[ 32 ]+[ 16 ]+[ 8 ]+[ 4 ]+[ 2 ]+[ 1 ]
=( 63 )10

  • Example 4:
(101101.11)2 = (  ?  )10
= [  1  × 25 ] + [  0  × 24 ] + [  1  × 23 ] + [  1  × 22 ] + [  0  × 21 ] + [  1  × 20 ] +
[ 1 × 2-1 ] + [ 1  × 2-2 ]
= [ 1 × 32 ] + [ 0 × 16 ] + [ 1 × 8 ] + [ 1 × 4 ] + [ 0 × 2 ] + [ 1 × 1 ] + [ 1 ×0.5] +[ 1 × 0.25 ]
= [ 32 ]+ [ 0 ] + [ 8 ] + [ 4 ] + [ 0 ] + [ 1  ]+ [ 0.5 ] + [ 0.25 ]
= ( 45.75 )10
  • Example 5:

    ( 0.101010 )= (  ?  )10

    =[ 0 × 2] +[ 1 × 2-1 ] + [ 0 × 2-2 ] + [ 1 × 2-3 ] + [ 0 × 2-4  ] +[ 1 × 2-5 ] + [ 0×2-6 ]
    =[ 0 ]+[ 0.5 ]+[ 0 ]+[ 0.125 ]+[ 0 ]+[ 0.03125 ]+[ 0 ]
    =( 0.65625 )10                                                               back to DIGITAL ELCTRONICS