Maximum unsigned with n bits – UGC NET Question

With n bits, there are 2^n distinct binary patterns ranging from all zeros to all ones. If we interpret these patterns as unsigned integers, the smallest value is 0 and the largest is when all bits are 1. This all-ones pattern corresponds to 2^n - 1. Therefore, the maximum unsigned integer with n bits is 2^n - 1.

Option A:
Option A is correct because subtracting 1 from 2^n removes the zero pattern and leaves the highest possible value. This matches the idea that counting from 0 yields 2^n different values.

Option B:
Option B, 2^n, would be one larger than the highest valid pattern and cannot be represented with n bits. It would require an additional bit.

Option C:
Option C, 2n, assumes only a linear relationship between bit count and value, which contradicts the exponential growth of binary patterns.

Option D:
Option D, 2^(n - 1), is the magnitude associated with the highest single bit, but it is not the maximum value obtainable when all bits are 1.