Binary of decimal 0.5 – UGC NET Question

The decimal 0.5 equals 1/2, which is exactly one power of 2 in the denominator. In binary fractions, 0.1₂ represents 1×2^-1, which equals 1/2 or 0.5 in decimal. Therefore, the correct binary representation of 0.5 is 0.1₂.

Option A:
Option A is correct because it assigns a 1 to the 2^-1 place and zeros elsewhere, giving 1/2. This matches the decimal fraction exactly.

Option B:
Option B, 0.01₂, represents 1×2^-2 which equals 1/4 or 0.25. This is smaller than 0.5 and cannot be the correct equivalent.

Option C:
Option C, 0.11₂, equal to 1×2^-1 + 1×2^-2, gives 1/2 + 1/4 = 3/4. This is larger than 0.5 and therefore incorrect.

Option D:
Option D, 1.0₂, equals 1 in decimal and represents a whole number rather than a fraction. It does not correspond to 0.5.