In digital circuit theory, combinational logic (also called combinatorial logic) is a type of logic circuit whose 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.
Combinational logic is used when 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 equivelant |
|---|---|---|---|---|
| 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:
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