K1 SOP and POS Forms

# K1 SOP and POS Forms - Deriving sum-of-products (SOP) and...

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Deriving sum-of-products (SOP) and product-of-sums (POS) forms Every group you make on a Karnaugh map is a product term. When the product terms are unified, you've formed a sum-of-products expression. What makes the various SOP expressions different is if they're formed by grouping ones on a map – that is, if they're prime implicants – or if they're formed by grouping zeros on a map – that is, if they're prime implicates . If you group ones on a map, you've obtained an SOP expression for the uncomplemented form of a function. Let's call the function f . With f determined in SOP form, the story is basically over. We can implement the SOP form of f with a set of first-level AND gates unified by a second-level OR gate. Using bubble propagation, all of the AND gates and OR gates can be turned into NAND gates. If you group zeros on a map, you've implemented an SOP expression for the complemented form of f . We'll call this form f '. We seldom care about f '. We could implement f ' in SOP form using AND gates on the first level and a unifying OR gate on the second level, but then we'd have to invert the output to obtain

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## This note was uploaded on 01/17/2011 for the course ECE 3504 at Virginia Tech.

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K1 SOP and POS Forms - Deriving sum-of-products (SOP) and...

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