UGC NET Questions (Paper – 1)

The integer part 10₂ equals 2. The fractional part .1011₂ equals 1/2 + 0/4 + 1/8 + 1/16 = 0.6875. Total = 2 + 0.6875 = 2.6875.

Option A:
Option A correctly computes fractional weights and adds them to the integer part.

Option B:
Option B (2.625) misses the 1/16 term and matches 10.101₂.

Option C:
Option C (2.75) would match 10.11₂, not 10.1011₂.

Option D:
Option D (2.5625) corresponds to a different fractional-bit pattern and is too small.

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.

To convert 101101.011₂ to decimal, we split it into integer and fractional parts. The integer 101101₂ equals 1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 1×1 = 32 + 8 + 4 + 1 = 45. The fractional .011₂ equals 0×1/2 + 1×1/4 + 1×1/8 = 0.25 + 0.125 = 0.375. Adding these gives 45.375. Hence, 45.375 is the correct decimal value.

Option A:
Option A carefully evaluates both the integer and fractional bits to obtain 45.375. It shows correct use of base-2 positional weights, including negative powers for the fractional part. Because both parts sum to 45.375, this option accurately reflects the binary input.

Option B:
Option B, 45.625, would require the fractional part to be .101₂ (0.5 + 0.125) instead of .011₂. Therefore it misinterprets which bits are set in the fractional portion. As a result, it slightly overestimates the correct value.

Option C:
Option C, 45.5, assumes the fractional part contributes only 0.5, which corresponds to .1₂, not .011₂. This ignores one of the lower-order fractional bits and therefore under-represents the actual value of the binary fraction.

Option D:
Option D, 46.375, incorrectly increases the integer part by 1, as if 101110₂ were used instead of 101101₂. This mismatch in the integer component significantly changes the total, so it does not represent the given binary number.

The bits after the binary point correspond to 1/2, 1/4, 1/8, and 1/16. In 0.1011₂, we have 1×1/2 + 0×1/4 + 1×1/8 + 1×1/16 = 0.5 + 0 + 0.125 + 0.0625 = 0.6875. Thus, the decimal value of 0.1011₂ is 0.6875.

Option A:
Option A correctly sums the contributions of the 2⁻¹, 2⁻³, and 2⁻⁴ places and omits the 2⁻² place because its bit is zero. The resulting 0.6875 accurately reflects the binary pattern.

Option B:
Option B, 0.625, equals 0.5 + 0.125 and would correspond to 0.101₂, which has only three fractional bits. It neglects the contribution of the 2⁻⁴ bit.

Option C:
Option C, 0.75, corresponds to 0.11₂ (0.5 + 0.25) and does not match the given bit arrangement.

Option D:
Option D, 0.5625, equals 0.5 + 0.0625, which would correspond to 0.1001₂. This ignores the 2⁻³ bit present in 0.1011₂.

The integer part 111₂ equals 1×4 + 1×2 + 1×1 = 7. The fractional part .001₂ equals 0×1/2 + 0×1/4 + 1×1/8 = 1/8 = 0.125. Adding these components yields 7 + 0.125 = 7.125. Therefore, the decimal equivalent of 111.001₂ is 7.125.

Option A:
Option A correctly computes both the integer and fractional contributions and combines them. It uses the appropriate negative powers of 2 for the bits after the point, giving a precise decimal value of 7.125.

Option B:
Option B, 7.25, would require the fractional part to be .01₂ (1/4) rather than .001₂. This misinterprets which bit is set in the fractional portion and hence is not correct.

Option C:
Option C, 7.5, corresponds to a fractional part of .1₂, where only the 1/2 place is set. This does not align with .001₂, which has only the 1/8 position set.

Option D:
Option D, 7.375, equals 7 + 0.375, which would correspond to fractional bits .011₂. Since the given binary has only the last fractional bit as 1, this value is inconsistent.