Decimal of binary 100110.101 – UGC NET Question

The integer part 100110₂ equals 1×32 + 0×16 + 0×8 + 1×4 + 1×2 + 0×1 = 32 + 4 + 2 = 38. The fractional part .101₂ equals 1/2 + 0/4 + 1/8 = 0.5 + 0.125 = 0.625. Adding both parts yields 38.625. Thus, the decimal equivalent is 38.625.

Option A:
Option A correctly interprets the integer and fractional bits and uses appropriate weights for each bit. The sum 38 + 0.625 = 38.625 is consistent with the structure of the binary number.

Option B:
Option B, 38.75, would require the fractional part to be .11₂ (0.75), which has both first and second fractional bits set. That does not match .101₂.

Option C:
Option C, 38.5, corresponds to a fractional part of .1₂ (0.5), ignoring the contribution of the 2⁻³ bit. This underestimates the true value.

Option D:
Option D, 39.125, suggests both an incorrect integer or fractional part, as 39.125 cannot be obtained from the given combination of bits without changing the pattern.