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Definitions of binary number system:

A counting system used in computers consisting of only 1's and 0's (zeros).
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In our everyday lives we use a decimal numbering system containing 10 digits, 0 through 9. Computers use a binary numbering system which contains only 2 numbers, 0 and 1, called binary digits or bits.
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A two-state system of numbers; contains binary digits 0 and 1.
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binary numeration system: a positional system of numeration that uses binary digits and a radix of two
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The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. Typically, the symbols 0 and 1 are used to represent binary numbers. Owing to its relatively straightforward implementation in electronic circuitry, the binary system is used internally by virtually all modern computers.
en.wikipedia.org/wiki/Binary_number_system