Bits for zero to seven – UGC NET Question

To represent numbers from 0 to 7 inclusive, we need 8 distinct binary patterns. Each additional bit doubles the number of representable patterns, so 1 bit gives 2 values, 2 bits give 4 values and 3 bits give 8 values. Therefore, 3 bits are enough to represent 0 through 7.

Option A:
Option A, 2 bits, can represent only 2^2 = 4 distinct values, namely 0 to 3. This is insufficient for covering the full range 0 to 7.

Option B:
Option B, 4 bits, can represent 16 distinct values, which is more than required. While 4 bits would work, it is not the minimum needed, so it does not answer the question correctly.

Option C:
Option C is correct because 3 bits give exactly 2^3 = 8 different patterns, matching the eight numbers in the range 0 to 7. This makes 3 the minimum bit length required.

Option D:
Option D, 5 bits, provides 32 combinations, which is unnecessarily large for representing only eight values. It does not satisfy the requirement of minimum number of bits.