Binary of decimal eighteen – UGC NET Question

To convert decimal 18 into binary, we decompose it into powers of 2. Here 18 = 16 + 2, which correspond to 2^4 and 2^1. This gives a 1 in the 16's place and a 1 in the 2's place, with zeros elsewhere, forming 10010₂. Therefore, 10010 is the correct binary representation.

Option A:
Option A, 10001₂, equals 16 + 1 = 17 in decimal. This is one less than 18 and therefore not the correct equivalent.

Option B:
Option B is correct because it uses ones in the 16's and 2's positions and zeros in the others. The resulting sum 16 + 2 equals 18, matching the decimal number.

Option C:
Option C, 10011₂, equals 16 + 2 + 1 = 19. This overshoots the target value and so cannot represent 18.

Option D:
Option D, 10100₂, equals 16 + 4 = 20. It uses a different distribution of active bits that produces a larger value than desired.