Decimal system base value – UGC NET Question

The decimal system is the standard system used in everyday counting and arithmetic. It employs ten distinct digit symbols from 0 to 9. Because the number of symbols in a positional system equals its base, the base of the decimal system is 10. All place values are powers of 10 such as 1, 10, 100 and 1000.

Option A:
Option A suggests base 2, which is used for binary and involves only digits 0 and 1. This is not consistent with decimal, which uses more symbols. Therefore base 2 cannot be correct.

Option B:
Option B proposes base 4, which would require exactly four distinct digits, often 0 to 3. Since decimal requires ten, base 4 does not match its structure.

Option C:
Option C indicates base 8, which corresponds to the octal system with digits 0–7. It fails to accommodate the digits 8 and 9 that appear in decimal notation.

Option D:
Option D is correct because decimal uses ten symbols and is defined as a base-10 positional system. Every position represents a power of 10, confirming that 10 is its base.