Hexadecimal of 2047 decimal – UGC NET Question

The decimal number 2047 is equal to 2¹¹ − 1, which is the largest number representable with eleven binary bits. In hexadecimal, this boundary value appears as 7FF. 7FF₁₆ expands to 7×16² + 15×16¹ + 15×16⁰ = 1792 + 240 + 15 = 2047. Therefore 7FF is the correct hexadecimal representation.

Option A:
7EF₁₆ equals 7×256 + 14×16 + 15 = 1792 + 224 + 15 = 2031. This value is slightly less than 2047, so it cannot be the correct representation.

Option B:
7FF₁₆ gives 1792 + 240 + 15 = 2047, matching the decimal in the question exactly. It highlights the pattern that just before a power of sixteen, all lower hex digits become F.

Option C:
8FF₁₆ stands for 8×256 + 15×16 + 15 = 2048 + 240 + 15 = 2303. Since this is larger than 2047, it overshoots the target and is not correct.

Option D:
6FF₁₆ represents 6×256 + 15×16 + 15 = 1536 + 240 + 15 = 1791. This is much smaller than 2047, so it cannot match the required decimal number.