Combinatorial Logic

Implement truth table

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Libraries:
Simulink / Logic and Bit Operations

Description

The Combinatorial Logic block implements a standard truth table for modeling programmable logic arrays (PLAs), logic circuits, decision tables, and other Boolean expressions. You can use this block in conjunction with Memory blocks to implement finite-state machines or flip-flops.

Examples

Two-Input AND Logic

This example builds a two-input AND function, which returns 1 when both input elements are 1, and 0 otherwise. To implement this function, specify the Truth table parameter value as [0; 0; 0; 1] The portion of the model that provides the inputs to and the output from the Combinatorial Logic block might look like this:

The following table indicates the combination of inputs that generate each output. The input signal labeled Input corresponds to the column in the table labeled Input 1. Similarly, the input signal Input 2 corresponds to the column with the same name. The combination of these values determines the row of the Output column of the table that is passed as block output. For example, if the input vector is [1 0], the input references the third row:

(2^1*1 + 1) The output value is 0.

Circuit Logic

This sample circuit has three inputs: the two bits (a and b) to be summed and a carry-in bit (c). It has two outputs: the carry-out bit (c') and the sum bit (s).

The truth table and corresponding outputs for each combination of input values for this circuit appear in the following table.

To implement this adder with the Combinatorial Logic block, you enter the 8-by-2 matrix formed by columns c' and s as the Truth table parameter. You can also implement sequential circuits (that is, circuits with states) with the Combinatorial Logic block by including an additional input for the state of the block and feeding the output of the block back into this state input.

Extended Examples

Building a Clutch Lock-Up Model

Use Simulink® to model and simulate a rotating clutch system. Although modeling a clutch system is difficult because of topological changes in the system dynamics during lockup, this example shows how enabled subsystem can easily handle such problems. We illustrate how to employ important Simulink modeling concepts in the creation of the clutch simulation. Designers can apply these concepts to many models with strong discontinuities and constraints that may change dynamically.

• Open Model

Ports

Input

Port_1 — Input signal

vector

Input signal, specified as a vector. The type of signals accepted by a Combinatorial Logic block depends on whether you selected the Boolean logic signals option (see Implement logic signals as Boolean data (vs. double)). If this option is enabled, the block accepts real signals of type Boolean or double.

Data Types: double | Boolean

Output

Port_2 — Output signal

scalar | vector

Output signal, double if the truth table contains non-Boolean values of type double; Boolean otherwise. The type of the output is the same as that of the input except that the block outputs double if the input is Boolean and the truth table contains non-Boolean values.

Data Types: double | Boolean

Parameters

Truth table — Matrix of outputs

matrix

You specify a matrix that defines all possible block outputs as the Truth table parameter. Each row of the matrix contains the output for a different combination of input elements. You must specify outputs for every combination of inputs. The number of columns is the number of block outputs.

The Truth table parameter can have Boolean values (0 or 1) of any data type, including fixed-point data types. If the table contains non-Boolean values, the data type of the table must be double.

The relationship between the number of inputs and the number of rows is:

number of rows = 2(number of inputs)

Simulink^® returns a row of the matrix by computing the row's index from the input vector elements. Simulink computes the index by building a binary number where input vector elements having zero values are 0 and elements having nonzero values are 1, then adding 1 to the result. For an input vector, u, of m elements:

row index = 1 + u(m)*2⁰ + u(m-1)*2¹ + ... + u(1)*2^m-1

Programmatic Use

Block Parameter: TruthTable

Type: character vector

Values: matrix

Default: '[0 0;0 1;0 1;1 0;0 1;1 0;1 0;1 1]'

Block Characteristics

Data Types	Boolean | double
Direct Feedthrough	yes
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

More About

Model Coverage

If you have a Simulink Coverage™ license, the Combinatorial Logic block receives decision and condition coverage. Decision coverage measures the number of time steps that the block outputs each row of the truth table.

If the block passes each row of the truth table as the output for at least one time step, decision coverage is 100%. Otherwise, decision coverage is the number of truth table values output during at least one time step, divided by the total number of truth table values. Because the Combinatorial Logic block always has at least one value in the truth table, the minimum achievable decision coverage is one divided by the total number of truth table values.

Condition coverage measures the number of time steps where each input is equal to zero, which indicates a false condition, and the number of times each input is not equal to zero, which indicates a true condition. If the input signal to the Combinatorial Logic block has a single input element, Simulink Coverage reports only decision coverage, because decision and condition coverage are equivalent.

Simulink Coverage records whether each element of the input array is true at least once and false at least once. If all block inputs are false for at least one time step and true for at least one time step, condition coverage is 100%. From a coverage perspective, the behavior is the same as a Logical Operator block that has the Operator parameter set to OR with a vector signal input.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a