UGC NET Questions (Paper – 1)

The decimal number 1023 is equal to 2¹⁰ − 1, which corresponds to ten 1s in binary and 3FF in hexadecimal. 3FF₁₆ means 3×16² + 15×16¹ + 15×16⁰. This equals 768 + 240 + 15 = 1023. Therefore, 3FF is the correct hexadecimal representation among the options.

Option A:
2FF₁₆ evaluates as 2×256 + 15×16 + 15 = 512 + 240 + 15 = 767. This is well below 1023, so it is clearly not the correct representation.

Option B:
3EF₁₆ corresponds to 3×256 + 14×16 + 15 = 768 + 224 + 15 = 1007. Although close to 1023, it is still 16 less, hence not exact.

Option C:
3FF₁₆ expands to 768 + 240 + 15 = 1023, exactly matching the decimal value given. It also represents the largest value that can be stored with ten binary bits, reflecting the relation between binary and hexadecimal groupings.

Option D:
4FF₁₆ stands for 4×256 + 15×16 + 15 = 1024 + 240 + 15 = 1279. Since 1279 is greater than 1023, this hexadecimal number overshoots the value in the question.