In mathematics and computer science, the binary numeral system (or base-2 numeral system) represents numeric values using the two symbols 0 and 1. Numbers represented in this system are commonly called binary numbers. Counting in binary is similar to counting in any other number system. Beginning with a single digit, counting proceeds through each symbol, in increasing order. Decimal counting uses the symbols 0 through 9, while binary only uses the symbols 0 and 1. When the symbols for the first digit are exhausted, the next-higher digit (to the left) is incremented, and counting starts over at 0. This is known as carrying. When the result of an addition exceeds the value of a digit, the procedure is to "carry" the excess amount to the left, adding it to the next positional value. In binary, counting is the same except that only the two symbols 0 and 1 are used. Thus after a digit reaches 1 in binary, an increment resets it to 0 but also causes an increment of the next digit to the left:
0001, (rightmost digit starts over, and next digit is incremented)
0010, 0011, (rightmost two digits start over, and next digit is incremented)
0100, 0101, 0110, 0111, (rightmost three digits start over, and the next digit is incremented)
1000, 1001, ...
|Binary number ||Equivalent decimal number |
|0 ||0 |
|1 ||1 |
|10 ||2 |
|11 ||3 |
|100 ||4 |
|101 ||5 |
|110 ||6 |
|111 ||7 |
|... ||... |
Any number can be represented by any sequence of bits (binary digits)
. Because of its straightforward implementation in digital circuitry using logic gates
, the binary system is used internally by almost all modern computers and computer-based devices such as mobile phones.
All computers built by Konrad Zuse
used the binary notation for numbers.