Boolean AND/OR/NOT
- Joa Oris
Symbol
Usage & working
The boolean operators apply common boolean operations to their input values.
Boolean operator | Input type | Functionality |
|---|---|---|
AND | Multiple inputs | Logical conjunction: A ∧ B ∧ … True when all inputs are true |
OR | Multiple inputs | Logical disjunction: A ∨ B ∨ … True when at least one input is true |
NOT | Single input | Logical negation: ¬A True when the input is false |
In contrast to most components, the boolean operators use boolean values (true/false) instead of scalar values. To achieve interoperability with other control components a conversion to and from boolean values is done in the way described below.
Converting scalar values to boolean
Inputs for control components can in general be any real number. For the purpose of applying boolean operators we convert input values to boolean values in the way described by the table below. In short, input values of 0.5 or greater will be considered “true”.
Input value | Boolean value |
|---|---|
(-∞, 0.5) | false |
[0.5, +∞) | true |
Converting boolean values to scalars
The boolean values are converted back to scalars after performing the boolean operations.
Boolean value | Output value |
|---|---|
true | 1.0 |
false | 0.0 |
Examples
The output of the boolean “AND” operation is true when all inputs true. In terms of scalars, the output will be 1.0 if all inputs are at least 0.5. The output will be 0.0 otherwise.
The output of the boolean “OR” operation is true when at least one of the inputs is true.
The output of the boolean “NOT” operation is true when the single input is false.