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I have a boolean expression and I need to get to the canonical forms of it (sum of minterms and product of maxterms).

In order to get an expression for the first canonical form, I need to multiply every term by (x + ~x), where x is the missing variable. Is there a similar algorithm to get to the second canonical form?

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Look here, page 7: sop-pos-conversion

You can also derive them separately from the truth table. It might be easier than converting from one to the other, depending on how large the expression is.

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