Convert the following fractional binary number into decimal.
1100101.10110
Answer:
(1100101.10110) 2
= 1 x 2 6 + 1 x 2 5 + 0 x 2 4 + 0 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 + 1 x 2 -1 + 0 x 2 -2 + 1 x 2 -3 + 1 x 2 -4 + 0 x 2 -5
= 64 + 32 + 0 + 0 + 4 + 0 + 1 + 0.5 + 0 + 0.125 + 0.0625 + 0
= (101.6875) 10
Explanation:
- To obtain the decimal equivalent of a binary number, individual digits of binary number should be multiplied by powers of 2 starting with the rightmost digit multiplied by 2 0 , second last digit multiplied by 2 1 , third last digit multiplied by 2 2 and so on up to the leftmost digit.
- For digits after the decimal point, the leftmost digit should be multiplied by 2 -1 and the next digit by 2 -2 and so on up to the rightmost digit.
