Question

The decimal equivalent of \( (101111.1101)_2 \) is

• A. 52.6789
• B. 38.6254
• C. 47.8125
• D. 51.6328

Hint:

For converting binary to decimal, break the number into integer and fractional parts. Convert both parts separately and add them to get the final result.

Answer 1

The Correct Option is C

To convert the binary number \( 101111.1101_2 \) to decimal, we first convert the integer part and the fractional part separately: - Integer part: \( 101111_2 = 32 + 16 + 8 + 4 + 0 + 1 = 61 \) - Fractional part: \( 0.1101_2 = 0.5 + 0.25 + 0 + 0.0625 = 0.8125 \) Thus, the decimal equivalent is \( 61 + 0.8125 = 47.8125 \). Therefore, the correct answer is option (3).