Distinct values with n bits – UGC NET Question

Each bit in a binary pattern can independently take one of two values, 0 or 1. With n bits, there are 2 choices for each bit and the total number of combinations is 2×2×…×2 (n times), which equals 2^n. Therefore, n bits can represent 2^n distinct values.

Option A:
Option A, n, would suggest only a linear relationship between bit count and values represented. This contradicts the exponential growth observed in binary combinations.

Option B:
Option B, 2n, also implies a linear relationship and fails to capture how adding a single bit doubles the number of representable values.

Option C:
Option C, n^2, suggests a quadratic relationship, which does not match the binary combinatorial count. The correct growth is exponential, not quadratic.

Option D:
Option D is correct because each additional bit doubles the possible combinations, leading to 2^n distinct patterns. This is a fundamental property used in designing memory and address spaces.