# How the Boolean math tools work

The Boolean math tools interpret the input cell values as Boolean values, where non-zero values are considered true and the value 0 is considered false. The input rasters are tested on a cell-by-cell basis.

There are four tools for performing boolean logical operations: Boolean And, Boolean Or, Boolean XOr and Boolean Not.

## Boolean logic conditions

### Boolean And

If both values are true, the output is 1. If one or both values are false, the output is 0.

```Input1 ≠ 0 and Input2 ≠ 0, Output = 1
Input1 ≠ 0 and Input2 = 0, Output = 0
Input1 = 0 and Input2 ≠ 0, Output = 0
Input1 = 0 and Input2 = 0, Output = 0```

### Boolean Or

If one or both values are true, the output is 1. If both values are false, the output is 0.

```Input1 ≠ 0 and Input2 ≠ 0, Output = 1
Input1 ≠ 0 and Input2 = 0, Output = 1
Input1 = 0 and Input2 ≠ 0, Output = 1
Input1 = 0 and Input2 = 0, Output = 0```

### Boolean XOr

If one value is true and one value is false, the output is 1. If both values are true or both are false, the output is 0.

```Input1 ≠ 0 and Input2 ≠ 0, Output = 0
Input1 ≠ 0 and Input2 = 0, Output = 1
Input1 = 0 and Input2 ≠ 0, Output = 1
Input1 = 0 and Input2 = 0, Output = 0```

### Boolean Not

Unlike the other boolean tools, there is only one input for Boolean Not.

If the value is true, the output is 0 (the complement of true). If the value is false, the output is 1.

```Input1 ≠ 0, Output = 0
Input1 ≠ 0, Output = 1```

## NoData handling

If any of the input cell values is NoData, the output value will be NoData.