Binary of decimal 0.375 – UGC NET Question

Decimal 0.375 equals 3/8. In binary, the fraction 1/4 is 0.01₂ and 1/8 is 0.001₂, so 3/8 is 1/4 + 1/8. The binary sum of 0.01₂ and 0.001₂ gives 0.011₂. Therefore, 0.011₂ is the exact binary representation of 0.375.

Option A:
Option A is correct because it has ones in the 2^-2 and 2^-3 positions, giving 1/4 + 1/8 = 3/8. This matches the decimal fraction exactly.

Option B:
Option B, 0.001₂, represents 1/8 or 0.125 in decimal, which is too small compared to 0.375. It lacks the 1/4 component.

Option C:
Option C, 0.01₂, equals 1/4 or 0.25 in decimal, still smaller than 0.375. It accounts for only one of the required fractional parts.

Option D:
Option D, 0.111₂, equals 1/2 + 1/4 + 1/8 = 7/8 or 0.875 in decimal, which is much larger than 0.375.