Binary of decimal 101 – UGC NET Question

Decimal 101 can be expressed as 64 + 32 + 4 + 1, corresponding to 2^6, 2^5, 2^2 and 2^0. This means that in binary the bits for these positions are 1 while others are 0. Writing them in order gives 1100101₂. Thus, 1100101 is the correct binary representation of 101.

Option A:
Option A, 1100011₂, equals 64 + 32 + 2 + 1 = 99 in decimal, which is smaller than 101 and lacks the 4's place contribution.

Option B:
Option B, 1100100₂, equals 64 + 32 + 4 = 100 in decimal and is one less than 101. It misses the 1's bit.

Option C:
Option C is correct because 1100101₂ equals 64 + 32 + 4 + 1 = 101, matching the required decimal value exactly.

Option D:
Option D, 1100111₂, equals 64 + 32 + 4 + 2 + 1 = 103, which overshoots the target. It has an extra 2's bit set.