Hexadecimal system base value – UGC NET Question

Hexadecimal is a positional number system that uses sixteen distinct symbols, namely 0–9 and A–F. Since the base of a number system equals the count of unique digits used, the base for hexadecimal must be 16. This larger base allows compact representation of binary data in groups of four bits. Therefore, 16 is the only correct base for the hexadecimal system.

Option A:
Option A suggests a base of 8, which corresponds to the octal system, not hexadecimal. Octal uses digits 0–7 and so it cannot represent sixteen distinct values with a single digit. Thus, it does not match the properties of hexadecimal.

Option B:
Option B is correct because hexadecimal uses exactly sixteen distinct symbols and therefore has base 16. Each hex digit represents a value from 0 to 15, aligning with the base-16 structure. This is why hexadecimal is very convenient for grouping four binary bits into one hex digit.

Option C:
Option C shows base 10, which is associated with the decimal system using digits 0–9. Decimal cannot directly represent values 10–15 with a single symbol, so it does not match the hexadecimal definition. Hence 10 is not the correct base here.

Option D:
Option D gives base 2, which is used for the binary system that has only two digits 0 and 1. Hexadecimal requires sixteen distinct symbols, so a base of 2 would be entirely inconsistent with its digit set.