   in mathematical numeral systems, the radix or base is the number of unique digits, including zero, used to represent numbers in a positional numeral system. 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 any positional numeral system (except unary, where the radix is 1), the number x and its base y are conventionally written as (x)_y, although for base ten the subscript is usually assumed and not written, as it is the most common way to express value. for example, (100)_{10} (in the decimal system) represents the number one hundred, whilst (100)_2 (in the binary system with base 2) represents the number four. == etymology == radix is a latin word for "root". root can be considered a synonym for base in the arithmetical sense. == in numeral systems == in the system with radix 13, for example, a string of digits such as 398 denotes the decimal number 3 \times 13^2 + 9 \times 13^1 + 8 \times 13^0. more generally, in a system with radix b (b > 1), a string of digits d_1 \ldots d_n denotes the decimal number d_1 b^{n-1} + d_2 b^{n-2} + \cdots + d_n b^0, where 0\leq d_i < b . commonly used numeral systems include: {| class="wikitable sortable" ! base/radix ! name ! description |- | 10 | decimal system | the most used system of numbers in the world, is used in arithmetic. its ten digits are "0â9". used in most mechanical counters. |- | 12 | duodecimal (dozenal) system | is often used due to divisibility by 2, 3, 4 and 6. it was traditionally used as part of quantities expressed in dozens and grosses. |- | 2 | binary numeral system | used internally by nearly all computers, is base two. the two digits are "0" and "1", expressed from switches displaying off and on respectively. used in most electric counters. |- | 16 | hexadecimal system | is often used in computing. the sixteen digits are "0â9" followed by "aâf". |- | 8 | octal system | is occasionally used in computing. the eight digits are "0â7". |- | 60 | sexagesimal system | originated in ancient sumeria and passed to the babylonians. used nowadays as the basis of our modern circular coordinate system (degrees, minutes, and seconds) and time measuring (hours, minutes, and seconds). |- | 64 | mime base64 | is also used in computing, using as digits "aâz", "aâz", "0â9&
Elementary_mathematics Numeral_systems