The binary system has the radix of ________

The radix (or base) of a number system is the count of distinct digit symbols it uses, and it also tells you what each place value in the number is a power of.

The binary number system uses only two digit symbols, \(0\) and \(1\), so its radix is \(2\). Each position in a binary number represents a power of \(2\) (units, twos, fours, eights, and so on), for example the binary number \(1011\) is evaluated as \(1 \times 2^{3} + 0 \times 2^{2} + 1 \times 2^{1} + 1 \times 2^{0} = 11\) in decimal.

This is directly linked to the fact that a bit has only two possible values, it is precisely because there are two digit symbols available that the radix of the system is \(2\), not \(0\), \(1\), or a fraction such as \(\frac{1}{2}\).

Exam tip: the radix of any number system equals the number of distinct digits it uses, decimal has \(10\) digits so its radix is \(10\), binary has \(2\) digits so its radix is \(2\).