Hexadecimal to decimal conversion

  • Any hexadecimal number can be converted to its decimal equivalent using the weight assigned to each bit position .Hexadecimal number system has base 16. It uses sixteen distinct symbols, most often the symbols 09 to represent values zero to nine, and AF (or alternatively af) to represent values ten to fifteen.
    For example,
    Suppose we have a number (768.15)16 then weight assigned to each bit is ,
    shown below :

To the left of radix point power of 16 increases,while to the right of radix point power of 16 decreases.

  • In hexadecimal number system,
    Going to the left of  radix point each digit represents an increasing power of 16, with the right most digit representing 160, the next representing 161, then 162, and so on.
    And going to the right of radix point,each digit represent an decreasing power of 16 , with left most digit representing 16-1,the next representing 16-2,then 16-3 ,then 16-4 and so on.
    The equivalent decimal representation of a octal number is the sum of the powers of  16 ,which each digit represents.

    The hexadecimal is converted to decimal number as follows:
  • Example 1:
    ( 567 )16 = (   ?  )10
    =[ 5× 16] + [ 6 × 16]+ [ 7 × 16]
    =[ 1280 ]+[ 96 ]+[ 7 ]

    =( 1383  )10
  • Example 2:
    ( 0000 )16 = (   ?  )10
    =[ 0 ×  163 ] + [ 0  × 16] + [ 0  × 16]  + [ 0  × 160]
    =[ 0 ]+[ 0 ]+[ 0 ]+[ 0 ]

    =( 0 )10
  • Example 3:
    ( 0 .5 A )16= (  ?  )
    10
    =[ 0 × 16] +[ 5 × 16-1 ] + [ A × 16-2 ]
    =[ 0 ]+[ 0.3125 ]+[ 0.0390625 ]
    =( 0.3515625 )10
  • Example 4:
    (7 3 F.56 )16 = (  ?  )10
    = [  7  × 162 ] + [  3  × 161 ] + [  F  × 160 ] + [  5  × 16-1 ] +[  6  × 16-2 ]
    = [ 1792 ] + [ 48 ] + [ 15 ] + [ 0.3125 ] + [ 0.0234375 ]
    = ( 1855.3359375 )10
  • Example 5:( 777 )16 = (   ?   )10
    = [ 7× 16] +[ 7 × 16]+ [ 7 × 16]
    =[ 1792 ]+[ 112 ]+[ 7 ]
    =( 1911 )10 

 

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