Binary, Hexadecimal, Decimal Conversions

Fractional Binary to Fractional Decimal

1. Assign each bit a 2 to the power of -n where n is position of bit from right of decimal point.
2. Multiply each power with its corresponding bit value.
3. Sum of all multiplication values of each bit will be final answer. Example:

$$0.11_2->0.7510_{10}$$ $$0.11=(1\times 2^{-1})+(1\times 2^{-2})=0.5+0.25=0.7510$$

Fractional Decimal to Fractional Binary

1. Multiply fractional part of decimal number by 2
2. If value is greater than 1, set the binary bit to 1 and carry the fractional part of value to next operation.
3. If value is less than 1, set binary bit to 0 and carry fractional part of value to next operation.
4. Use carry as value and start from step 1.
5. Repeat step 1-4 until carry is zero. Successively multiply fractional values by 2 until fractional value is 0. Example:

$$0.8125_{10}->0.1101_2$$

0.8125 (multiply by 2)  =  1.625  =  0.625 carry 1  (MSB) 0.625 (multiply by 2)  =  1.25  =  0.25 carry 1  (↓) 0.25 (multiply by 2)  =  0.50  =  0.5 carry 0  (↓) 0.5 (multiply by 2)  =  1.00    =  0.0 carry 1  (LSB)