Binary of decimal twenty nine – UGC NET Question

Decimal 29 can be decomposed into powers of 2 as 16 + 8 + 4 + 1. In binary, this means we place ones in the positions for 2^4, 2^3, 2^2 and 2^0, and a zero in the 2^1 position. This yields the pattern 11101₂. Therefore, 11101 is the correct binary representation of 29.

Option A:
Option A, 11100₂, equals 16 + 8 + 4 = 28 in decimal. It omits the 1's place contribution and is therefore one less than the required value.

Option B:
Option B, 11110₂, equals 16 + 8 + 4 + 2 = 30, which is greater than 29. Here, the extra 2's bit makes the value too large.

Option C:
Option C is correct because 11101₂ equals 16 + 8 + 4 + 0 + 1 = 29. This pattern exactly matches the sum needed to represent the decimal number.

Option D:
Option D, 11011₂, equals 16 + 8 + 0 + 2 + 1 = 27, which is smaller than 29. The 4's place is missing while the 2's place is unnecessarily set.