Combinational logic
In
Combinational logic is used in
Practical design of combinational logic systems may require consideration of the finite time required for practical logical elements to react to changes in their inputs. Where an output is the result of the combination of several different paths with differing numbers of switching elements, the output may momentarily change state before settling at the final state, as the changes propagate along different paths. [2]
Representation
Combinational logic is used to build circuits that produce specified outputs from certain inputs. The construction of combinational logic is generally done using one of two methods: a sum of products, or a product of sums. Consider the following 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, all logical statements which yield true results are summed, giving the result:
Using
Logic formula minimization
Minimization (simplification) of combinational logic formulas is done using the following rules based on the laws of Boolean algebra:
With the use of minimization (sometimes called logic optimization), a simplified logical function or circuit may be arrived upon, and the logic combinational circuit becomes smaller, and easier to analyse, use, or build.
See also
- Sequential logic
- Asynchronous circuit
- Field-programmable gate array
- Formal verification
- Relay logic
- Programmable logic controller
- Ladder logic
References
- ^
Savant, C.J. Jr.; Roden, Martin; Carpenter, Gordon (1991). Electronic Design: Circuits and Systems. p. 682. ISBN 0-8053-0285-9.
- ISBN 017-771044-6.
- Predko, Michael; Predko, Myke (2004). Digital electronics demystified. McGraw-Hill. ISBN 0-07-144141-7.
External links
- Belton, D.; Bigwood, R. "Combinational Logic & Systems Tutorial Guide". Archived from the original on 2013-10-22.
