UGC NET Questions (Paper – 1)

To convert 13.625 to binary, we separately convert the integer part 13 and the fractional part 0.625. The integer 13 becomes 1101₂, and 0.625 corresponds to 0.101₂ because 0.625 = 1/2 + 0/4 + 1/8. Combining them gives 1101.101₂. Therefore, 1101.101 is the correct binary representation of 13.625.

Option A:
1101.101₂ has an integer part 1101₂ (13) and fractional part .101₂ which equals 1/2 + 0/4 + 1/8 = 0.625. Adding these yields 13.625, exactly matching the decimal given. This confirms that this option is the correct binary fraction.

Option B:
1101.011₂ has the same integer part 13 but the fractional part .011₂ equals 0/2 + 1/4 + 1/8 = 0.375. Thus the total value is 13.375, which is lower than 13.625, making this option incorrect.

Option C:
1100.111₂ represents an integer part of 12 with fractional part .111₂ = 0.875, giving 12.875. Because the integer part itself is different, this cannot equal 13.625.

Option D:
1101.11₂ has integer part 13 and fractional part .11₂ = 1/2 + 1/4 = 0.75, giving 13.75. This is higher than the target decimal, so it is not the correct binary representation.