Max value 12-bit unsigned binary – UGC NET Question

In an unsigned binary system, all bit patterns represent non-negative numbers. With 12 bits, there are 2¹² distinct patterns ranging from 0 to 2¹² - 1. This gives a maximum representable value of 4095. Therefore, 4095 is the highest decimal integer that can be stored using 12 unsigned bits, making option A correct.

Option A:
Option A correctly applies the formula 2ⁿ - 1 for the maximum value of an n-bit unsigned integer. Substituting n = 12 gives 2¹² - 1 = 4095, so this option precisely captures the upper limit.

Option B:
Option B, 2047, is the maximum value for an 11-bit unsigned or for a 12-bit two's complement positive range, but not for a full 12-bit unsigned system. Hence, it underestimates the available range.

Option C:
Option C, 4096, is one greater than the maximum unsigned value and would require 13 bits to represent as the maximum range endpoint. Since we only have 12 bits, this cannot be the maximum.

Option D:
Option D, 2048, is not the maximum in the 12-bit unsigned range; it is simply a representable value well below 4095.