# unary

The term unary defines operators in Boolean ( binary ) algebra, trinary algebra, arithmetic, and set theory . Sometimes a unary operation is called a monadic operation or a singulary operation.

In Boolean algebra , there is only one unary operation, known as negation. This operation changes the value of the bit (binary digit) from 0 to 1 or from 1 to 0.

In trinary algebra, which involves three-level logic with states that can be represented by the numbers -1, 0, and 1, there are five unary operators. They are called invert, rotate-up, rotate-down, shift-up, and shift-down. The actions performed by these operators are denoted in the following table.

Input |
Invert |
Rotate-up |
Rotate-down |
Shift-up |
Shift-down |

-1 | 1 | 1 | -1 | ||

1 | -1 | 1 | -1 | ||

1 | -1 | -1 | 1 |

In common arithmetic, the unary operators are negation, the reciprocal, and the absolute value. Negation involves reversing the sign of a number. For example, the negation of 4 is -4, and the negation of -23 is 23. The reciprocal involves dividing 1 by the number. Thus, the reciprocal of 4 is 1/4, and the reciprocal of -23 is -1/23. The absolute value involves reversing the sign of a number if it is negative, and leaving the number unchanged if it is 0 or positive. Thus, the absolute value of 4 is 4, and the absolute value of -23 is 23.

In set theory, there is one unary operator, called complementation. Given a set *S* that is a subset of some universal set *U* , the complement of *S* , written *S'* , is the set containing all elements of *U* that are not in *S* .

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