Canonical forms for logic circuits

Insights into Mathematics

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A key problem in circuit analysis is to associate to a logical circuit, typically made of logic gates such as AND, OR, NOT, XOR, NAND and NOR, an algebraic expression that captures the effect of that circuit on all possible inputs. Such an effect is called a Boolean function, and it acts on the space of possible 0/1 values that can be assigned to the input values. For example if we have three inputs A,B and C then there are 23=8 different possible values of 0's and 1's that can be assigned to these three, and so then there are 28 Boolean functions representing all possible circuits with these inputs.

Such a Boolean function has a geometric interpretation, and in this video we show how to get an algebraic version, both using the technology of Boolean algebra and the alternate, more powerful technology of the original Algebra of Boole. The advantages of the latter start becoming pretty obvious, once you start doing the computations.

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