Binary of decimal 73 – UGC NET Question

To convert 73 to binary, we repeatedly divide by 2 or find powers of 2. The decomposition is 73 = 64 + 8 + 1, corresponding to bits in positions 6, 3, and 0. Writing ones in these positions and zeros elsewhere gives 1001001₂. Therefore, 1001001₂ is the binary representation of 73.

Option A:
Option A correctly places ones in the 2⁶, 2³, and 2⁰ positions, which sum to 64 + 8 + 1 = 73. This matches the value of the original decimal number.

Option B:
Option B, 1000101₂, corresponds to 64 + 4 + 1 = 69, which is less than 73. It misplaces the 1 at the 2³ position.

Option C:
Option C, 1010010₂, equals 64 + 8 + 2 = 74, which is greater than 73 and therefore not equal to it.

Option D:
Option D, 1101001₂, represents 64 + 32 + 8 + 1 = 105, which is far larger than 73 and clearly incorrect.