Decimal of binary 11001 – UGC NET Question

Binary 11001 can be converted to decimal by using positional weights 16, 8, 4, 2 and 1. The bits from left to right are 1, 1, 0, 0, 1. This gives 1×16 + 1×8 + 0×4 + 0×2 + 1×1 = 16 + 8 + 1 = 25. So the correct decimal equivalent is 25.

Option A:
Option A is correct because the sum of the active place values 16, 8 and 1 equals 25. The zeros in the 4's and 2's positions do not contribute to the total. This matches the binary pattern exactly.

Option B:
Option B gives 21, which would correspond to a different set of active bits, such as 10101₂. The given pattern 11001 has a different combination of ones and zeros, so 21 cannot be the right answer.

Option C:
Option C suggests 27, which would require additional contribution beyond 16 + 8 + 1. That would come from a nonzero 2's or 4's bit, which we do not have. Therefore 27 does not match the pattern.

Option D:
Option D gives 29, which is again larger than 25 and would require a different binary configuration. Since the 4's and 2's places are zero, extra value cannot appear in the sum.