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Reuse Combinatorial Logic by Defining Truth Table Functions

Truth table functions implement combinatorial logic design in a concise, tabular format. Typical applications for truth tables include decision making for:

  • Fault detection and management

  • Mode switching

For example, this truth table function has the name ttable. It takes three arguments (x, y, and z) and returns one output value (r).

The function consists of this arrangement of conditions, decisions, and actions.


Decision 1

Decision 2

Decision 3

Default Decision

x == 1





y == 1





z == 1






r = 1r = 2r = 3r = 4

Each of the conditions entered in the Condition column must evaluate to true (nonzero value) or false (zero value). Outcomes for each condition are specified as T (true), F (false), or - (true or false). Each of the decision columns combines an outcome for each condition with a logical AND into a compound condition, which is referred to as a decision.

You evaluate a truth table one decision at a time, starting with Decision 1. The Default Decision covers all possible remaining decisions. If one of the decisions is true, you perform its action, and then the truth table execution is complete.

For example, if conditions x == 1 and y == 1 are false and condition z == 1 is true, then Decision 3 is true and the variable r is set equal to 3. The remaining decisions are not tested and evaluation of the truth table is finished. If the first three decisions are false, then the Default Decision is automatically true and its action (r=4) is executed. This table lists pseudocode corresponding to the evaluation of this truth table example.



if ((x == 1) & !(y == 1) & !(z == 1))
  r = 1;

If Decision 1 is true, then set r=1.

elseif (!(x == 1) & (y == 1) & !(z == 1))
  r = 2;

If Decision 2 is true, then set r=2.

elseif (!(x == 1) & !(y == 1) & (z == 1))
  r = 3;

If Decision 3 is true, then set r=3.

  r = 4;

If all other decisions are false, then Default Decision is true. Set r=4.

Define a Truth Table Function

  1. In the object palette, click the truth table function icon . Move your pointer to the location for the new truth table function in your chart.

  2. Enter the signature label for the function, as described in Declare Function Arguments and Return Values.

  3. Program the truth table function. For more information, see Program a Truth Table.

  4. In the Model Explorer, expand the chart object and select the truth table function. The arguments and return values of the function signature appear as data items that belong to your function. Arguments have the scope Input. Return values have the scope Output.

  5. In the Data properties dialog box for each argument and return value, specify the data properties, as described in Set Data Properties.

  6. Create any additional data items required by your function. For more information, see Add Data Through the Model Explorer.

    Your function can access its own data or data belonging to parent states or the chart. The data items in the function can have one of these scopes:

    • Local — Local data persists from one function call to the next function call. Valid for C charts only.

    • Constant — Constant data retains its initial value through all function calls.

    • Parameter — Parameter data retains its initial value through all function calls.

    • Temporary — Temporary data initializes at the start of every function call. Valid for C charts only.

    In charts that use MATLAB® as the action language, you do not need to define temporary function data. If you use an undefined variable, Stateflow® creates a temporary variable. The variable is available to the rest of the function. For more information, see Define Temporary Data.

    You can initialize your function data (other than arguments and return values) from the MATLAB workspace. For more information, see Initialize Data from the MATLAB Base Workspace.

Declare Function Arguments and Return Values

The function signature label specifies a name for your function and the formal names for its arguments and return values. A signature label has this syntax:

[return_val1, return_val2,...] = function_name(arg1, arg2,...)
You can specify multiple return values and multiple input arguments. Each return value and input argument can be a scalar, vector, or matrix of values. For functions with only one return value, omit the brackets in the signature label.

You can use the same variable name for both arguments and return values. For example, a function with this signature label uses the variables y1 and y2 as both inputs and outputs:

[y1, y2, y3] = f(y1, u, y2)
If you export this function to C code, y1 and y2 are passed by reference (as pointers), and u is passed by value. Passing inputs by reference reduces the number of times that the generated code copies intermediate data, resulting in more optimal code.

Call Truth Table Functions in States and Transitions

You can call truth table functions from the actions of any state or transition. You can also call truth table functions from other functions. If you export a truth table function, you can call it from any chart in the model.

The syntax for a call to a truth table function is the same as the function signature, with actual arguments replacing the formal ones specified in a signature. If the data types of an actual and formal argument differ, a function casts the actual argument to the type of the formal argument.


If the formal arguments of a function signature are scalars, verify that inputs and outputs of function calls follow the rules of scalar expansion. For more information, see How Scalar Expansion Works for Functions.

Specify Properties of Truth Table Functions

You can set general properties for your truth table function through its properties dialog box. To open the function properties dialog box, right-click the truth table function box and select Properties from the context menu.


Function name. Click the function name link to bring your function to the foreground in its native chart.

Function Inline Option

Controls the inlining of your function in generated code:

  • Auto — Determines whether to inline your function based on an internal calculation.

  • Inline — Inlines your function if you do not export it to other charts and it is not part of a recursion. (A recursion exists if your function calls itself directly or indirectly through another function call.)

  • Function — Does not inline your function.


Signature label for your function. For more information, see Declare Function Arguments and Return Values.


Controls the level of diagnostics for underspecification in your truth table function. For more information, see Correct Overspecified and Underspecified Truth Tables.


Controls the level of diagnostics for overspecification in your truth table function. For more information, see Correct Overspecified and Underspecified Truth Tables.

Action Language

Controls the action language for your Stateflow truth table function. Choose between MATLAB or C. For more information, see Language Options for Stateflow Truth Tables.


Function description. You can enter brief descriptions of functions in the hierarchy.

Document Link

Link to online documentation for the function. You can enter a web URL address or a MATLAB command that displays documentation in a suitable online format, such as an HTML file or text in the MATLAB Command Window. When you click the Document link hyperlink, Stateflow displays the documentation.

Where to Use a Truth Table

A truth table function can reside anywhere in a chart, state, or subchart. The location of a function determines its scope, that is, the set of states and transitions that can call the function. Follow these guidelines:

  • If you want to call the function only within one state or subchart and its substates, put your truth table function in that state or subchart. That function overrides any other functions of the same name in the parents and ancestors of that state or subchart.

  • If you want to call the function anywhere in that chart, put your truth table function at the chart level.

You can also add a Stateflow Truth Table block directly to your Simulink® model.

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