Combinational logic gates
In digital circuit theory, combinational logic sometimes also combinational logic gates to as time-independent logic  is a type of digital logic which is implemented by Boolean circuitswhere the output is a pure function of the present input only. This is in contrast to sequential logicin which the output depends not only on the present combinational logic gates 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 perform 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 unitor ALU, that does mathematical calculations is constructed using combinational logic.
Other circuits used in computers, such as half addersfull addershalf subtractorsfull subtractorsmultiplexersdemultiplexersencoders and decoders are also made by using combinational logic. An alternate term is combinatorial logic though this combinational logic gates may be considered controversial. 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: Consider the combinational logic gates truth table:.
Using sum of products, all logical statements which yield combinational logic gates results are summed, giving the result:. Using Boolean algebrathe result simplifies to the following equivalent of the truth table:. 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 optimizationa simplified logical function or circuit may be arrived upon, and the logic combinational circuit becomes smaller, and easier to analyse, use, or build.
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