Logical Operators & | ~ (MATLAB Function Reference)

Logical operations

A & B
A | B
~A

Description

The symbols &, |, and ~ are the logical operators and, or, and not. They work element-wise on arrays, with 0 representing logical false (F), and anything nonzero representing logical true (T). The & operator does a logical and, the| operator does a logical or, and ~A complements the elements of A. The function xor(A,B) implements the exclusive or operation. Truth tables for these operators and functions follow.


Inputs		and	or	xor	not
`A`	`B`	`A&B`	`A\|B`	`xor(A,B)`	`~A`
`0`	`0`	`0`	`0`	`0`	`1`
`0`	`1`	`0`	`1`	`1`	`1`
`1`	`0`	`0`	`1`	`1`	`0`
`1`	`1`	`1`	`1`	`0`	`0`

The logical operators have the lowest precedence, with arithmetic operators and relational operators being evaluated first.

The precedence for the logical operators with respect to each other is:

1.: not has the highest precedence.

2.: and and or have equal precedence, and are evaluated from left to right.

Remarks

The logical operators have M-file function equivalents, as shown:


and	`A&B`	`and(A,B)`
or	`A\|B`	`or(A,B)`
not	`~A`	`not(A)`

Examples

Here are two scalar expressions that illustrate precedence relationships for arithmetic, relational, and logical operators:

1 & 0 + 3
3 > 4 & 1

They evaluate to 1 and 0 respectively, and are equivalent to:

1 & (0 + 3)
(3 > 4) & 1

Here are two examples that illustrate the precedence of the logical operators to each other:

1 | 0 & 0 = 0
0 & 0 | 1 = 1