BinaryFractions

Binary Fractions

Just as we use decimal point for representing fractional decimal numbers, binary point is used to represent a fraction in binary numbers. The positional values in this case are 2^-1,2^-2,2^-3,….. for successive positions starting from binary point to its right.

For example,

(0.111)2 = 1 x 2^-1 + 1 x 2^-2 + 1 x 2^-3
                  = 1 x 0.5 + 1 x 0.25 + 1 x 0.125
                  = (0.875)10

To convert decimal fraction to binary fraction, following rules are used:

Multiply decimal fraction repeatedly by 2. The whole number part of the result gives the first bit of the binary fraction. The above procedure is repeated with fractional part of the result and so on.

Example: Convert (0.375)10 to binary fraction

0.375 x 2 = 0.750 ——– 0
0.750 x 2 = 1.50   ——– 1
0.50 x 2 = 1.00  ——— 1

Hence (0.375) 10  = (0.011)2