Hexadecimal of 65535 decimal – UGC NET Question

Four hexadecimal digits can represent values from 0000₁₆ to FFFF₁₆, and FFFF is the largest of these. FFFF₁₆ means 15×16³ + 15×16² + 15×16¹ + 15×16⁰. Calculating this gives 61440 + 3840 + 240 + 15 = 65535. Therefore FFFF is the exact hexadecimal representation of 65535. None of the other options expand to this decimal value.

Option A:
FFFF₁₆ expands directly to 65535 because each F contributes 15 times the appropriate power of 16. This makes it the maximum value for four hex digits and matches the decimal given. Therefore this choice is correct.

Option B:
FFFE₁₆ gives 65534 since it differs from FFFF only in the last digit being 14 instead of 15. This is one less than 65535, so it is a near miss but not correct.

Option C:
FFF0₁₆ calculates as 15×4096 + 15×256 + 15×16 + 0, which is 61440 + 3840 + 240 + 0 = 65520. This is slightly smaller than 65535, so it cannot be the correct answer.

Option D:
F0FF₁₆ corresponds to 15×4096 + 0×256 + 15×16 + 15, yielding 61440 + 0 + 240 + 15 = 61695. Because 61695 differs from 65535, this hexadecimal string does not represent the required decimal value.