In digital circuit theory, combinational logic (sometimes incorrectly referred to as combinatorial logic) is a type of digital logic which is implemented by boolean circuits, where the output is a pure function of the present input only. This is in contrast to sequential logic, in which the output depends not only on the present input but also on the history of the input. In other words, sequential logic has memory while combinational logic does not.
Combinational logic is used in computer circuits to do Boolean algebra on input signals and on stored data. Practical computer circuits normally contain a mixture of combinational and sequential logic. For example, the part of an Arithmetic Logic Unit, or ALU, that does mathematical calculations is constructed using combinational logic.
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Representation
Combinational logic is used for building circuits where certain outputs are desired, given certain inputs. The construction of combinational logic is generally done using one of two methods: a sum of products, or a product of sums. A sum of products can be easily visualized by looking at a truth table:
| A | B | C | Result | Logical equivalent |
|---|---|---|---|---|
| F | F | F | F |  |
| F | F | T | F |  |
| F | T | F | F |  |
| F | T | T | F |  |
| T | F | F | T |  |
| T | F | T | F |  |
| T | T | F | F |  |
| T | T | T | T |  |
Using sum of products, we take the sum of all logical statements which yield true results. Thus, our result would be:
It could then be simplified using Boolean algebra to:
Logic formulas minimization
Minimization (simplification) of combinational logic formulas is produced on the basis of the following rules:
Owing to minimization logical function is simplified, and combinational circuit becomes more compact and convenient for realization.
See also
References
- Combinational Logic & Systems Tutorial Guide by D. Belton, R. Bigwood.
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