Which number system uses only the two digits 0 and 1?

Concept

A positional number system is defined by its radix, or base.

A base-r system uses r distinct digit symbols, and each position has a place value that is a power of r.

Application

Using only 0 and 1 gives two digit symbols, so the radix is 2. A base-2 number system is called binary; therefore the required system is Binary.

Cross-check and contrast

• Decimal has base 10 and uses the digits 0 through 9.

• Binary has base 2 and uses exactly the digits 0 and 1.

• Octal has base 8 and uses the digits 0 through 7.

• Hexadecimal has base 16 and uses the digits 0 through 9 together with A through F.

Thus, Binary is the answer.