Binary of decimal 53 – UGC NET Question

Converting 53 to binary involves finding powers of 2 that sum to 53. The largest power less than 53 is 32, leaving 21. The next is 16, leaving 5. Then 4 leaves 1, and finally 1 leaves 0. This corresponds to bits for 32, 16, 4 and 1, giving 110101₂.

Option A:
Option A, 110011₂, equals 32 + 16 + 2 + 1 = 51, which is smaller than 53. It lacks the 4's contribution that is present in the correct representation.

Option B:
Option B is correct because 110101₂ represents 32 + 16 + 4 + 1 = 53. All necessary powers of 2 are present to match the decimal number.

Option C:
Option C, 110111₂, equals 32 + 16 + 4 + 2 + 1 = 55, which overshoots the desired value by 2.

Option D:
Option D, 111101₂, corresponds to 32 + 16 + 8 + 4 + 1 = 61. This includes an 8's bit that should not be present when representing 53.