## Modelica.Blocks.MathBoolean

Library of Boolean mathematical functions as input/output blocks

### Information

This package contains basic mathematical operations on Boolean signals.

The new features are:

• If useful, blocks may have an arbitrary number of inputs (e.g., "And" block with 2,3,4,... Boolean inputs). This is based on the "connectorSizing" annotation which allows a tool to conveniently handle vectors of connectors.
• The blocks are smaller in size, so that the diagram area is better utilized for trivial blocks such as "And" or "Or".

Extends from Modelica.Icons.Package (Icon for standard packages).

### Package Content

Name Description
MultiSwitch Set Boolean expression that is associated with the first active input signal
And Logical 'and': y = u[1] and u[2] and ... and u[nu]
Or Logical 'or': y = u[1] or u[2] or ... or u[nu]
Xor Logical 'xor': y = oneTrue(u) (y is true, if exactly one element of u is true, otherwise it is false)
Nand Logical 'nand': y = not ( u[1] and u[2] and ... and u[nu] )
Nor Logical 'nor': y = not ( u[1] or u[2] or ... or u[nu] )
Not Logical 'not': y = not u
RisingEdge Output y is true, if the input u has a rising edge, otherwise it is false (y = edge(u))
FallingEdge Output y is true, if the input u has a falling edge, otherwise it is false (y = edge(not u))
ChangingEdge Output y is true, if the input u has either a rising or a falling edge and otherwise it is false (y=change(u))
OnDelay Delay a rising edge of the input, but do not delay a falling edge.

## Modelica.Blocks.MathBoolean.MultiSwitch

Set Boolean expression that is associated with the first active input signal

### Information

The block has a vector of Boolean input signals u[nu] and a vector of (time varying) Boolean expressions expr[:]. The output signal y is set to expr[i], if i is the first element in the input vector u that is true. If all input signals are false, y is set to parameter "y_default" or the previous value of y is kept if parameter use_pre_as_default = true:

```// Conceptual equation (not valid Modelica)
i = 'first element of u[:] that is true';
y = if i==0 then (if use_pre_as_default then pre(y)
else y_default)
else expr[i];
```

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

### Parameters

NameDescription
expr[nu]Sets y = if u[i] then expr[i] else y_default (time varying)
use_pre_as_defaultSet true to hold last value as default (y_default = pre(y))
y_defaultDefault value of output y if all u[i] = false

### Connectors

NameDescription
u[nu]Set y = expr[i], if u[i] = true
yOutput depending on expression

## Modelica.Blocks.MathBoolean.And

Logical 'and': y = u[1] and u[2] and ... and u[nu]

### Information

The output is true if all inputs are true, otherwise the output is false.

The input connector is a vector of Boolean input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to true: y=true.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

### Connectors

NameDescription
u[nu]Vector of Boolean input signals
yBoolean output signal

## Modelica.Blocks.MathBoolean.Or

Logical 'or': y = u[1] or u[2] or ... or u[nu]

### Information

The output is true if at least one input is true, otherwise the output is false.

The input connector is a vector of Boolean input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

### Connectors

NameDescription
u[nu]Vector of Boolean input signals
yBoolean output signal

## Modelica.Blocks.MathBoolean.Xor

Logical 'xor': y = oneTrue(u) (y is true, if exactly one element of u is true, otherwise it is false)

### Information

The output is true if exactly one input is true, otherwise the output is false.

The input connector is a vector of Boolean input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

### Connectors

NameDescription
u[nu]Vector of Boolean input signals
yBoolean output signal

## Modelica.Blocks.MathBoolean.Nand

Logical 'nand': y = not ( u[1] and u[2] and ... and u[nu] )

### Information

The output is true if at least one input is false, otherwise the output is false.

The input connector is a vector of Boolean input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

### Connectors

NameDescription
u[nu]Vector of Boolean input signals
yBoolean output signal

## Modelica.Blocks.MathBoolean.Nor

Logical 'nor': y = not ( u[1] or u[2] or ... or u[nu] )

### Information

The output is false if at least one input is true, otherwise the output is true.

The input connector is a vector of Boolean input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

If no connection to the input connector "u" is present, the output is set to false: y=false.

Extends from Modelica.Blocks.Interfaces.PartialBooleanMISO (Partial block with a BooleanVectorInput and a BooleanOutput signal).

### Connectors

NameDescription
u[nu]Vector of Boolean input signals
yBoolean output signal

## Modelica.Blocks.MathBoolean.Not

Logical 'not': y = not u

### Information

The output is false if at least one input is true, otherwise the output is true.

The input connector is a vector of Boolean input signals. When a connection line is drawn, the dimension of the input vector is enlarged by one and the connection is automatically connected to this new free index (thanks to the connectorSizing annotation).

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

### Connectors

NameDescription
uBoolean input signal
yBoolean output signal

## Modelica.Blocks.MathBoolean.RisingEdge

Output y is true, if the input u has a rising edge, otherwise it is false (y = edge(u))

### Information

A rising edge of the Boolean input u results in y = true at this time instant. At all other time instants, y = false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

### Parameters

NameDescription
pre_u_startValue of pre(u) at initial time

### Connectors

NameDescription
uBoolean input signal
yBoolean output signal

## Modelica.Blocks.MathBoolean.FallingEdge

Output y is true, if the input u has a falling edge, otherwise it is false (y = edge(not u))

### Information

A falling edge of the Boolean input u results in y = true at this time instant. At all other time instants, y = false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

### Parameters

NameDescription
pre_u_startValue of pre(u) at initial time

### Connectors

NameDescription
uBoolean input signal
yBoolean output signal

## Modelica.Blocks.MathBoolean.ChangingEdge

Output y is true, if the input u has either a rising or a falling edge and otherwise it is false (y=change(u))

### Information

A changing edge, i.e., either rising or falling, of the Boolean input u results in y = true at this time instant. At all other time instants, y = false.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

### Parameters

NameDescription
pre_u_startValue of pre(u) at initial time

### Connectors

NameDescription
uBoolean input signal
yBoolean output signal

## Modelica.Blocks.MathBoolean.OnDelay

Delay a rising edge of the input, but do not delay a falling edge.

### Information

A rising edge of the Boolean input u gives a delayed output. A falling edge of the input is immediately given to the output.

Simulation results of a typical example with a delay time of 0.1 s is shown in the next figure.

The usage is demonstrated, e.g., in example Modelica.Blocks.Examples.BooleanNetwork1.

Extends from Modelica.Blocks.Interfaces.PartialBooleanSISO_small (Partial block with a BooleanInput and a BooleanOutput signal and a small block icon).

### Parameters

NameDescription
delayTimeDelay time [s]

### Connectors

NameDescription
uBoolean input signal
yBoolean output signal
Automatically generated Thu Oct 1 16:07:34 2020.