Inautomata theory,combinational logic(also referred to astime-independent logic[1]) is a type ofdigital logicthat is implemented byBoolean circuits,where the output is apure functionof the present input only. This is in contrast tosequential 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 hasmemorywhile combinational logic does not.
Combinational logic is used incomputercircuits to performBoolean algebraon input signals and on stored data. Practical computer circuits normally contain a mixture of combinational and sequential logic. For example, the part of anarithmetic logic unit,or ALU, that does mathematical calculations is constructed using combinational logic. Other circuits used in computers, such ashalf adders,full adders,half subtractors,full subtractors,multiplexers,demultiplexers,encodersanddecodersare also made by using combinational logic.
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
editCombinational 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 followingtruth 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:
UsingBoolean algebra,the result simplifies to the following equivalent of the truth table:
Logic formula minimization
editMinimization (simplification) of combinational logic formulas is done using the following rules based on thelaws of Boolean algebra:
With the use of minimization (sometimes calledlogic optimization), a simplified logical function or circuit may be arrived upon, and the logiccombinational circuitbecomes smaller, and easier to analyse, use, or build.
See also
editReferences
edit- ^ Savant, C.J. Jr.; Roden, Martin; Carpenter, Gordon (1991).Electronic Design: Circuits and Systems.Benjamin/Cummings Publishing Company. p. 682.ISBN0-8053-0285-9.
- ^Lewin, Douglas (1974).Logical Design of Switching Circuits(2nd ed.). Thomas Nelson and Sons. pp. 162–3.ISBN017-771044-6.
- Predko, Michael; Predko, Myke (2004).Digital electronics demystified.McGraw-Hill.ISBN0-07-144141-7.
External links
edit- Belton, D.; Bigwood, R."Combinational Logic & Systems Tutorial Guide".Archived fromthe originalon 2013-10-22.