Sometimes advocated due to divisibility by 2, 3, 4, and 6. Used by humans in the vast majority of cultures. The eight digits are '0'–'7' and represent 3 bits (2 3). The two digits are '0' and '1', expressed from switches displaying OFF and ON, respectively. In contrast to decimal, or radix 10, which has a ones' place, tens' place, hundreds' place, and so on, radix b would have a ones' place, then a b 1s' place, a b 2s' place, etc. More generally, in a system with radix b ( b > 1), a string of digits d 1 … d n denotes the number d 1 b n−1 + d 2 b n−2 + … + d nb 0, where 0 ≤ d i < b. In the system with radix 13, for example, a string of digits such as 398 denotes the (decimal) number 3 × 13 2 + 9 × 13 1 + 8 × 13 0 = 632. Root can be considered a synonym for base, in the arithmetical sense. For example, (100) 10 is equivalent to 100 (the decimal system is implied in the latter) and represents the number one hundred, while (100) 2 (in the binary system with base 2) represents the number four.

In any standard positional numeral system, a number is conventionally written as ( x) y with x as the string of digits and y as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9. In a positional numeral system, the radix ( pl.: radices) or base is the number of unique digits, including the digit zero, used to represent numbers.

Base of ten