how to find minterm and maxterm of 1101
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Pages in Chapter 8Introduction to Karnaugh MappingVenn Diagrams and SetsBoolean Relationships on Venn DiagramsMaking a Venn Diagram Look Like a Karnaugh MapKarnaugh Maps, Truth Tables, and Boolean ExpressionsLogic Simplification With Karnaugh MapsLarger 4-variable Karnaugh MapsMinterm vs Maxterm SolutionSum and Product NotationDon’t Care Cells in the Karnaugh MapLarger 5 & 6-variable Karnaugh Maps
Minterm vs Maxterm SolutionChapter 8 - Karnaugh Mapping PDF Version
So far we have been finding Sum-Of-Product (SOP) solutions to logic reduction problems. For each of these SOP solutions, there is also a Product-Of-Sums solution (POS), which could be more useful, depending on the application. Before working a Product-Of-Sums solution, we need to introduce some new terminology. The procedure below for mapping product terms is not new to this chapter. We just want to establish a formal procedure for minterms for comparison to the new procedure for maxterms.A 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. If a minterm has a single 1 and the remaining cells as 0s, it would appear to cover a minimum area of 1s. The illustration above left shows the minterm ABC, a single product term, as a single 1 in a map that is otherwise 0s. We have not shown the 0s in our Karnaugh maps up to this point, as it is customary to omit them unless specifically needed. Another minterm A’BC’ is shown above right. The point to review is that the address of the cell corresponds directly to the minterm being mapped. That is, the cell 111 corresponds to the minterm ABC above left. Above right we see that the minterm A’BC’ corresponds directly to the cell 010. A Boolean expression or map may have multiple minterms. Referring to the above figure, Let’s summarize the procedure for placing a minterm in a K-map:
Identify the minterm (product term) term to be mapped.Write the corresponding binary numeric value.Use binary value as an address to place a 1 in the K-mapRepeat steps for other minterms (P-terms within a Sum-Of-Products).
A Boolean expression will more often than not consist of multiple minterms corresponding to multiple cells in a Karnaugh map as shown above. The multiple minterms in this map are the individual minterms which we examined in the previous figure above. 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. By directly we mean that a 0corresponds to a complemented variable, and a 1 corresponds to a true variable. Example: 010converts directly to A’BC’. There was no reduction in this example. Though, we do have a Sum-Of-Products result from the minterms. Referring to the above figure, Let’s summarize the procedure for writing the Sum-Of-Products reduced Boolean equation from a K-map:
Form largest groups of 1s possible covering all minterms. Groups must be a power of 2.Write binary numeric value for groups.Convert binary value to a product term.Repeat steps for other groups. Each group yields a p-terms within a Sum-Of-Products.
Nothing new so far, a formal procedure has been written down for dealing with minterms. This serves as a pattern for dealing with maxterms. Next we attack the Boolean function which is 0for a single cell and 1s for all others.