# Boolean Variables

### Logical Operators

Boolean variables `true`

and `false`

are quintessential to computer programming. Let’s describe the basic boolean operations implemented in Julia:

Operator | Syntax | Description |
---|---|---|

not | !x | negation |

and | x && y | returns true if both operands are true |

or | x |

Importantly, `&&`

and `||`

are **short-circuited** (see Wiki).

This has a series of advantages. In particular, we can do

```
if a > 0 && expensive_computation(b) > 0
do_something()
end
```

In this way, we avoid performing the expensive computation if it’s not necessary (when `a>0`

returnes `false`

).

Also, you won’t get a nasty error when doing something like

```
if @isdefined(ge) && ge>0
print("ge exists and is greater than 0")
end
```

because trying to assess whether an undefined variable is greater than zero is usually not permitted in any programming language.

As for the ‘or’ operator, the fact that it is short-circuited means that it will return `true`

if the first expression is `true`

without the need to evaluate the second. This can also lead to performance gains.

```
if 3 > 2 && expensive_computation(b) > 0
do_something()
end
```

The `expensive_computation`

function won’t be called, as the first expression returnes `true`

.

### Logical to Number

In Julia, `Bool`

is a subtype of `Integer`

. `true`

equals 1, while `false`

equals zero. In particular, we can do numerical operations on `Bool`

types without the need of any type conversion.

```
true + true # 2
```