Hexadecimal of 999 decimal – UGC NET Question

In hexadecimal, 3E7 means 3×16² + 14×16¹ + 7×16⁰. Calculating this gives 3×256 + 14×16 + 7 = 768 + 224 + 7 = 999. This matches the target decimal value exactly. Hence 3E7 is the correct hexadecimal representation of 999.

Option A:
3D7 corresponds to 3×256 + 13×16 + 7 which equals 768 + 208 + 7 = 983. As 983 is less than 999, this option does not match the given decimal number. It shows how changing a single digit alters the decimal result.

Option B:
3E6 converts as 3×256 + 14×16 + 6 = 768 + 224 + 6 = 998. This value is very close to 999 but still one less, so it is not acceptable as the exact representation. Small differences in the least significant digit matter in conversions.

Option C:
3E7, with digits 3, E (14) and 7, expands to 768 + 224 + 7 = 999. Because this equals the required decimal, this hexadecimal code is exactly correct. Its structure shows how three hex digits can represent a three-digit decimal number just under 1000.

Option D:
3F7 stands for 3×256 + 15×16 + 7 = 768 + 240 + 7 = 1015. Since 1015 is greater than 999, the value overshoots the target. Therefore it cannot be considered the correct conversion for 999.