Largest 10-bit unsigned value – UGC NET Question

For an n-bit unsigned integer, the maximum representable value is 2ⁿ − 1. With 10 bits, this becomes 2¹⁰ − 1 = 1024 − 1 = 1023. This value corresponds to the bit pattern of ten ones in binary, 1111111111₂. Thus, 1023 is the highest decimal number that fits in 10 unsigned bits.

Option A:
Option A follows the standard formula for unsigned range and correctly computes 2¹⁰ − 1 as 1023. It matches the idea that the all-ones pattern is the largest representable value in a fixed-width binary system. Therefore, this option is accurate.

Option B:
Option B, 1024, equals 2¹⁰ itself and would need 11 bits (1 followed by ten zeros) for representation. It lies just outside the range of 10-bit patterns, so it is not representable as a maximum with 10 bits.

Option C:
Option C, 511, is the maximum value for 9-bit unsigned representation (2⁹ − 1). Using it for 10 bits ignores the additional capacity provided by the extra bit. Thus, it underestimates the possible maximum.

Option D:
Option D, 512, is 2⁹ and would require at least 10 bits, but it is not the maximum of the 10-bit range. Higher values up to 1023 are possible, so 512 does not exhaust the 10-bit unsigned capacity.