Editing Combinational logic (section)

==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]]:

{| class="wikitable" style="margin: 1em auto 1em auto; text-align:center;"
|-
! {{nobold|{{mvar|A}}}} || {{nobold|{{mvar|B}}}} || {{nobold|{{mvar|C}}}} || Result || [[logical equivalence|Logical equivalent]]
|-
| {{no|F}} || {{no|F}} || {{no|F}} || {{no|F}} || <math>\neg A \wedge \neg B \wedge \neg C</math>
|-
| {{no|F}} || {{no|F}} || {{yes|T}} || {{no|F}} || <math>\neg A \wedge \neg B \wedge C</math>
|-
| {{no|F}} || {{yes|T}} || {{no|F}} || {{no|F}} || <math>\neg A \wedge B \wedge \neg C</math>
|-
| {{no|F}} || {{yes|T}} || {{yes|T}} || {{no|F}} || <math>\neg A \wedge B \wedge C</math>
|-
| {{yes|T}} || {{no|F}} || {{no|F}} || {{yes|T}} || <math>A \wedge \neg B \wedge \neg C</math>
|-
| {{yes|T}} || {{no|F}} || {{yes|T}} || {{no|F}} || <math>A \wedge \neg B \wedge C</math>
|-
| {{yes|T}} || {{yes|T}} || {{no|F}} || {{no|F}} || <math>A \wedge B \wedge \neg C</math>
|-
| {{yes|T}} || {{yes|T}} || {{yes|T}} || {{yes|T}} || <math>A \wedge B \wedge C</math>
|}


Using sum of products, all logical statements which yield true results are summed, giving the result:

: <math>(A \wedge \neg B \wedge \neg C) \vee (A \wedge B \wedge C) \,</math>

Using [[Boolean algebra]], the result simplifies to the following equivalent of the truth table:

: <math>A \wedge ((\neg B \wedge \neg C) \vee (B \wedge C)) \,</math>