Binary of decimal 0.75 – UGC NET Question

Decimal 0.75 is equal to 3/4. In binary, 0.11₂ represents 1/2 plus 1/4, which sums to 3/4. Therefore, the exact binary representation of 0.75 is 0.11₂.

Option A:
Option A, 0.1₂, equals 1/2 or 0.5 in decimal. This is smaller than 0.75 and does not account for the additional 1/4.

Option B:
Option B, 0.01₂, equals 1/4 or 0.25 in decimal, which is far from 0.75. It lacks the 1/2 component entirely.

Option C:
Option C, 0.101₂, equals 1/2 + 0 + 1/8 = 5/8 or 0.625 in decimal. This is closer but still not equal to 0.75.

Option D:
Option D is correct because 0.11₂ combines 1/2 and 1/4 to give exactly 3/4. This is a standard example of a terminating binary fraction.