Find the decimal equivalent of the binary number 110.101.
6.5
6.625
6.5
6.25
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2020
Integer part (110): $1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 1 \times 4 + 1 \times 2 + 0 \times 1 = 4 + 2 + 0 = 6$.
Fractional part (.101): $1 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} = 1 \times 0.5 + 0 \times 0.25 + 1 \times 0.125 = 0.5 + 0 + 0.125 = 0.625$.
The decimal equivalent is the sum of the integer and fractional parts: $6 + 0.625 = 6.625$.
– Digits to the left of the decimal point have positive powers ($2^0, 2^1, …$).
– Digits to the right of the decimal point have negative powers ($2^{-1}, 2^{-2}, …$).