Binary equivalent of 947 decimal – UGC NET Question

To convert 947 to binary, we divide repeatedly by 2 and track the remainders or use powers of 2. The expansion 947 = 512 + 256 + 128 + 32 + 16 + 2 + 1 corresponds to bits set at those positions. Writing these powers in binary yields 1110110011₂, which is the shortest binary representation without leading zeroes. Therefore, option B correctly represents 947 in binary.

Option A:
Option A corresponds to a binary number slightly larger than 947 because it sets some higher-order bits that increase the value. When its powers-of-two expansion is computed, the sum exceeds 947. Hence, this binary string does not represent the required decimal number.

Option B:
Option C omits some of the powers of two needed to reach 947 and includes a different combination instead. Its positional value expansion produces a smaller decimal number than 947. Thus, it cannot be the correct binary representation of 947.

Option C:
Option B has ones exactly in the positions corresponding to 512, 256, 128, 32, 16, 2 and 1, whose sum is 947. No unnecessary leading zeros are present, so it is a minimum-length form. Every other combination of bits shown in the options changes this sum. Hence, 1110110011₂ is the valid minimal binary representation for 947.

Option D:
Option D rearranges the ones in a different pattern, leading to a distinct combination of powers of two. When expanded, its decimal value is less than 947, so it fails to match the given decimal number. Therefore, it is not the correct binary representation.