8.9. Σ (sum) and Π (product) notationFor reference, this section introduces the terminology used in some texts to describe the minterms and maxterms assigned to a Karnaugh map. Otherwise, there is no new material here. Σ (sigma) indicates sum and lower case "m" indicates minterms. Σm indicates sum of minterms. The following example is revisited to illustrate our point. Instead of a Boolean equation description of unsimplified logic, we list the minterms.
The numbers indicate cell location, or address, within a Karnaugh map as shown below right. This is certainly a compact means of describing a list of minterms or cells in a Kmap.
The SumOfProducts solution is not affected by the new terminology. The minterms, 1s, in the map have been grouped as usual and a SumOFProducts solution written. Below, we show the terminology for describing a list of maxterms. Product is indicated by the Greek Π (pi), and upper case "M" indicates maxterms. ΠM indicates product of maxterms. The same example illustrates our point. The Boolean equation description of unsimplified logic, is replaced by a list of maxterms.
Once again, the numbers indicate Kmap cell address locations. For maxterms this is the location of 0s, as shown below. A ProductOFSums solution is completed in the usual manner.
