The ebook FEEE  Fundamentals of Electrical Engineering and Electronics is based on material originally written by T.R. Kuphaldt and various coauthors. For more information please read the copyright pages. 
Home Digital Karnaugh Mapping Sigma and PiNotation  
Search the VIAS Library  Index  
Sigma and PiNotationFor 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. minterm sum ΣΣ (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. f(A,B,C,D) = Σ m(1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15)
or
f(A,B,C,D) = Σ(m_{1},m_{2},m_{3},m_{4},m_{5},m_{7},m_{8},m_{9},m_{11},m_{12},m_{13},m_{15})
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. maxterm product πBelow, 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. f(A,B,C,D) = π M(2, 6, 8, 9, 10, 11, 14)
or
f(A,B,C,D) = π(M_{2}, M_{6}, M_{8}, M_{9}, M_{10}, M_{11}, M_{14})
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.


Home Digital Karnaugh Mapping Sigma and PiNotation 