Hexadecimal of 678 decimal – UGC NET Question

In hexadecimal, each digit represents a power of 16, so 2A6 means 2×16² + 10×16¹ + 6×16⁰. This evaluates to 512 + 160 + 6, which equals 678 in decimal. Therefore 2A6 is the correct hexadecimal representation of 678. None of the other options expand to 678 when converted back to decimal.

Option A:
2A6 correctly uses the hexadecimal digits 2, A (10) and 6 in their proper positional values. When expanded as 2×256 + 10×16 + 6, it yields exactly 678. This shows that A is the correct conversion from decimal 678 to base 16.

Option B:
2B6 would be interpreted as 2×256 + 11×16 + 6 which equals 694. Since 694 is different from 678, this cannot be the correct hexadecimal form. It demonstrates how even a small change in a middle digit changes the entire value.

Option C:
2A5 corresponds to 2×256 + 10×16 + 5, which equals 677. This is very close to 678 but is still one less, so it is numerically incorrect for the given decimal. Such near values test precision in conversion.

Option D:
3A6 means 3×256 + 10×16 + 6 which totals 934, much larger than 678. Because it gives a different decimal value, it cannot represent 678 in hexadecimal. It shows the effect of changing the most significant digit in positional systems.