UGC NET Questions (Paper – 1)

Four hexadecimal digits range from 0000₁₆ to FFFF₁₆, and FFFF corresponds to 16⁴ − 1. Evaluating 16⁴ gives 65536, so subtracting 1 yields 65535. Therefore, 65535 is the largest decimal value representable with exactly four hex digits. This follows the general pattern that an n-digit base-b number has a maximum value of bⁿ − 1.

Option A:
16383 is the maximum value for 14 bits in binary, but it does not correspond to four hex digits. It is associated with the range up to 2¹⁴ − 1, not with 16⁴ − 1. Hence this option is not appropriate for four hexadecimal positions.

Option B:
32767 is the maximum value for 15 bits in binary (2¹⁵ − 1) and is often seen for signed 16-bit integers. However, it does not match the range of four hexadecimal digits, which is governed by powers of 16, not 2¹⁵.

Option C:
65534 is one less than 65535, so it would correspond to FFFE₁₆ rather than FFFF₁₆. While it is extremely close, it is not the maximum possible value for four hex digits.

Option D:
65535 equals 16⁴ − 1 and is represented as FFFF₁₆. This is the largest value achievable when all four hexadecimal positions are set to their maximum digit F, satisfying the condition of the question.