Binary of decimal nine – UGC NET Question

To convert decimal 9 to binary, we look for powers of 2 that sum to 9. Here 9 = 8 + 1, which corresponds to 2^3 and 2^0. This gives a binary pattern with ones in the 8's and 1's places and zeros in the 4's and 2's places, namely 1001₂. Hence 1001 is the correct binary representation.

Option A:
Option A, 1000₂, equals 8 in decimal because it has a 1 only in the 8's place. It does not include the additional 1 needed to sum to 9. Therefore it is too small.

Option B:
Option B, 1010₂, corresponds to 8 + 2 = 10 in decimal. This overshoots the required value of 9 and cannot be the correct representation.

Option C:
Option C is correct because it places ones in the 8's and 1's positions, giving 8 + 1 = 9. Zeros in the 4's and 2's positions indicate there is no contribution from those powers of 2. This matches the decimal value exactly.

Option D:
Option D, 1100₂, equals 8 + 4 = 12, which is greater than 9. The presence of a 1 in the 4's place adds extra value that does not belong to the decimal number 9.