UGC NET Questions (Paper – 1)

The decimal 0.25 equals 1/4, which is 2^-2 in terms of powers of 2. In binary, 0.01₂ means 1 in the 2^-2 place and 0 in the 2^-1 place, giving 1/4. Hence 0.01₂ correctly represents 0.25 in decimal.

Option A:
Option A, 0.1₂, represents 1×2^-1 = 1/2, which is 0.5 in decimal. This is greater than 0.25 and unsuitable as its representation.

Option B:
Option B is correct because it places a 1 in the 2^-2 position, giving exactly 1/4. No other fractional positions contribute, so the value is precisely 0.25.

Option C:
Option C, 0.11₂, gives 1/2 + 1/4 = 3/4, which is 0.75 in decimal. This is a much larger value and cannot be equal to 0.25.

Option D:
Option D, 0.001₂, equals 1×2^-3 = 1/8 or 0.125. This is smaller than 0.25 and therefore not the correct representation.

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.