UGC NET Questions (Paper – 1)

To convert 0.625 to binary, we repeatedly multiply by 2 and record the integer parts. Multiplying 0.625 by 2 yields 1.25, giving a first bit of 1 and remainder 0.25. Multiplying 0.25 by 2 gives 0.5, with bit 0 and remainder 0.5, and multiplying 0.5 by 2 gives 1.0, with bit 1 and no remainder. Reading the bits in order, we get 0.101₂, which equals 0.625 in decimal.

Option A:
Option A, 0.11, equals 1×2^-1 + 1×2^-2 in binary. This is 0.5 + 0.25 = 0.75 in decimal. Since 0.75 is larger than 0.625, 0.11 cannot be the correct representation.

Option B:
Option B, 0.101, has bits at positions 2^-1 and 2^-3. Its value is 1×2^-1 + 0×2^-2 + 1×2^-3 = 0.5 + 0 + 0.125 = 0.625. This exactly matches the given decimal fraction, so it is the correct binary form.

Option C:
Option C, 0.001, represents 1×2^-3, which equals 0.125. This is much smaller than 0.625. Therefore, 0.001 cannot be the correct binary representation for 0.625.

Option D:
Option D, 0.01, corresponds to 1×2^-2, which is 0.25 in decimal. Because 0.25 is again different from 0.625, this option is not correct for the given fraction.