A digit is a type of symbol (a numeral 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 (ancient Latin digiti meaning fingers) of the hands correspond to the 10 symbols of the common base 10 number system, i.e. the decimal (ancient Latin adjective dec. meaning ten) digits.
In a given number system, if the base is an integer, the number of digits required is always 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).
Mental calculation comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper. People use mental calculation when computing tools are not available, when it is faster than other means of calculation (for example, conventional methods as taught in educational institutions), or in a competitive context. Mental calculation often involves the use of specific techniques devised for specific types of problems.
Many of these techniques take advantage of or rely on the decimal numeral system. Usually, the choice of radix determines what methods to use and also which calculations are easier to perform mentally. For example, multiplying or dividing by ten is an easy task when working in decimal (just move the decimal point), whereas multiplying or dividing by sixteen is not; however, the opposite is true when working in hexadecimal.
A telephone number is a unique sequence of digits assigned to each telephone subscriber station, telephone line, or since the advent of digital telephony to an electronic telephony device, such as a mobile telephone. The telephone number serves as the address to switch telephone calls using a system of destination routing. It is entered or dialed by the calling party on the originating telephone set which transmits it in the process of signaling to a telephone exchange which completes the call either to another locally connected subscriber or via the public switched telephone network (PSTN) to the called party.
The concept of using telephone numbers instead of subscriber names when connecting calls was developed and first used between 1879 and 1880 in Lowell, MA, for the purpose of ease of training new telephone operators.
Elementary arithmetic is the simplified portion of arithmetic which includes the operations of addition, subtraction, multiplication, and division.
Elementary arithmetic starts with the natural numbers and the written symbols (digits) which represent them. The process for combining a pair of these numbers with the four basic operations traditionally relies on memorized results for small values of numbers, including the contents of a multiplication table to assist with multiplication and division.
In mathematics, the digit sum of a given integer is the sum of all its digits, (e.g.: the digit sum of 84001 is calculated as 8+4+0+0+1 = 13). Digit sums are most often computed using the decimal representation of the given number, but they may be calculated in any other base; different bases give different digit sums, with the digit sums for binary being on average smaller than those for any other base.
Let S(r,N) be the digit sum for radix r of all non-negative integers less than N. For any 2 ≤ r1 < r2 and for sufficiently large N, S(r1,N) < S(r2,N).