Convert hexadecimal fraction to decimal fraction

Solved examples of Hexadecimal fractions to decimal fraction conversion

Problem 1: Convert ( E F . B 1 )₁₆= ( ? )₁₀

_{= E F . B 1}
↑ ↑
MSD LSD

= E x 16¹ + F x 16⁰ . B x 16^-1 + 1 x 16^-2

= 14 x 16 + 15 x 1 . 11 x ( 1 / 16 ) + 1 x ( 1 / 256 )

= 224 + 15 . ( 0. 6 8 7 5 ) + ( 0 . 0 0 3 9 0 6 2 5 )

= 239 + 0. 6914

= 239 . 691406

Therefore ( E F . B 1 )₁₆ = ( 2 3 9 . 6 9 1 4 0 6 )₁₀

Problem 2: Convert ( 0.9D9 )₁₆= ( ? )₁₀

_{= 0 . 9 D 9}
↑ ↑
MSD LSD

= 0 x 16⁰ . 9 x 16^-1 + D x 16^-2 + 9 x 16^-3

= 0 x 1 . 9 x ( 1 / 16 ) + 13 x ( 1 / 256 ) + 9 x ( 1 / 4096 )

= 0 . (0. 5625) + (0 . 050781 ) + ( 0. 0021972 )

= 0 . ( 0 . 6154782 )

= 0 . 6154782

Therefore ( 0 . 9 D 9 )₁₆ = ( 0 . 6 1 5 4 7 8 2 )₁₀

Problem 3: Convert ( BCC.1 0 )₁₆= ( ? )₁₀

_{= B C C . 1 0}
↑ ↑

MSD LSD

= B x 16²+ C x 16¹+ C x 16⁰ . 1 x 16^-1+ 0 x 16^-2

= 11 x 256+ 12 x 16+ 12 x 1 . 1 x ( 1 / 16 )+ 1 x ( 1 / 256 )

= 2816 + 192 + 12 . ( 0 . 0625 )+ ( 0 )

= 3020 . ( 0. 0625 )

= 3020 . 0625

Therefore ( B C C . 1 0 )₁₆ = ( 3 0 2 0 . 0 6 2 5 )₁₀