There are some differences now that we are dealing with something new, maxterms. If a maxterm has a single 0 and the remaining cells as 1s, it would appear to cover a maximum area of 1s. The illustration above left shows the maxterm (A+B+C), a single sum term, as a single 0 in a map that is otherwise 1s.

Next we attack the Boolean function which is 0 for a single cell and 1s for all others.Ī maxterm is a Boolean expression resulting in a 0 for the output of a single cell expression, and 1s for all other cells in the Karnaugh map, or truth table. This serves as a pattern for dealing with maxterms. Nothing new so far, a formal procedure has been written down for dealing with minterms. Each group yields a p-terms within a Sum-Of-Products.

Convert binary value to a product term.Form largest groups of 1s possible covering all minterms.Referring to the above figure, Let’s summarize the procedure for writing the Sum-Of-Products reduced Boolean equation from a K-map: Though, we do have a Sum-Of-Products result from the minterms. The point we review for reference is that the 1s come out of the K-map as a binary cell address which converts directly to one or more product terms.īy directly we mean that a 0 corresponds to a complemented variable, and a 1 corresponds to a true variable. The multiple minterms in this map are the individual minterms which we examined in the previous figure above. Repeat steps for other minterms (P-terms within a Sum-Of-Products).Ī Boolean expression will more often than not consist of multiple minterms corresponding to multiple cells in a Karnaugh map as shown above.Use binary value as an address to place a 1 in the K-map.Write the corresponding binary numeric value.Identify the minterm (product term) term to be mapped.

Referring to the above figure, Let’s summarize the procedure for placing a minterm in a K-map: A Boolean expression or map may have multiple minterms. That is, the cell 111 corresponds to the minterm ABC above left.Ībove right we see that the minterm A’BC’ corresponds directly to the cell 010. The point to review is that the address of the cell corresponds directly to the minterm being mapped. Another minterm A’BC’ is shown above right. We have not shown the 0s in our Karnaugh maps up to this point, as it is customary to omit them unless specifically needed. The illustration above left shows the minterm ABC, a single product term, as a single 1 in a map that is otherwise 0s. If a minterm has a single 1 and the remaining cells as 0s, it would appear to cover a minimum area of 1s. We just want to establish a formal procedure for minterms for comparison to the new procedure for maxterms.Ī minterm is a Boolean expression resulting in 1 for the output of a single cell, and 0s for all other cells in a Karnaugh map, or truth table. The procedure below for mapping product terms is not new to this chapter. For each of these SOP solutions, there is also a Product-Of-Sums solution (POS), which could be more useful, depending on the application.īefore working a Product-Of-Sums solution, we need to introduce some new terminology. So far we have been finding Sum-Of-Product (SOP) solutions to logic reduction problems.

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