UGC NET Questions (Paper – 1)

The decimal 4095 is equal to 2¹² − 1, which corresponds to twelve 1s in binary and three Fs in hexadecimal. FFF₁₆ means 15×16² + 15×16¹ + 15×16⁰. This expands to 3840 + 240 + 15 = 4095. Therefore FFF is the unique hexadecimal representation of 4095 among the options.

Option A:
FFE₁₆ equals 15×256 + 15×16 + 14 = 3840 + 240 + 14 = 4094. This is just one less than 4095, so it is a typical near-miss distractor. Since it does not give the exact decimal, it is not correct.

Option B:
EF0₁₆ corresponds to 14×256 + 15×16 + 0 = 3584 + 240 + 0 = 3824. This value is significantly lower than 4095, so this option cannot represent the given decimal number.

Option C:
FFF₁₆ expands to 3840 + 240 + 15 = 4095, exactly the decimal number in the question. It represents the largest value possible with three hexadecimal digits, which matches the idea of 2¹² − 1. This is why this choice is correct.

Option D:
EFFF₁₆ stands for 14×4096 + 15×256 + 15×16 + 15 which is far larger than 4095. Because it uses four hex digits with a non-maximal leading digit, it represents a different range of values. Thus this cannot be correct for 4095.