Digit (math)

A digit is a numeric symbol (such as "2" or "5") used in combinations (such as "25") to represent numbers (such as the number 25) in positional numeral systems. The name "digit" comes from the fact that the 10 digits (Latin digiti meaning fingers) of the hands correspond to the 10 symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective decem meaning ten) digits.

In a given numeral system, if the base is an integer, the number of digits required will always be equal to the absolute value of the base. For example, the decimal system (base 10) has ten digits (0 through to 9), whereas binary (base 2) has two digits (0 and 1).

In a basic digital system, a numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by its place value, and summing the results.

Each digit in a number system represents an integer. For example, in decimal the digit "1" represents the integer one, and in the hexadecimal system, the letter "A" represents the number ten. A positional number system must have a digit representing the integers from zero up to, but not including, the radix of the number system.

Thus in the positional decimal system, the numbers 0 to 9 can be expressed using their respective numerals '0' to '9' in the rightmost 'units' position. The number 12 can be expressed with the numeral '2' in the units position, and with the numeral '1' in the 'tens' position, to the left of the '2' while the number 312 can be expressed by three numerals: '3' in the 'hundreds' position, '1' in the 'tens' position, and '2' in the 'units' position.

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