K-Map Redundant and Don’t Care Digital Logic and Computer Design by Ravinder Nath Rajotiya - September 14, 2023September 14, 20230 Introduction In Simplification using K-Map we used minterms or Maxterms to group 1's or 0's respectively to form pair, quad or octets. There may be situations where all the 1's which are part of one group are overlapped by other groups or certain input conditions may not be contributing in getting the minterms or maxterms of the output functions. In the following discussions, we will see how to account for such conditions. Redundant Groups A redundant group is one whose all the 1’s have been used or ovelapped by other groups. We can always eliminate such group. Let us take an example and understand how redundant group can be dropped thus not part of solution. Example: Simplify the SOP equation given by F(ABC) = ∑(2,3,5,7). Figure-1 There
Introduction to Karnaugh-Map STLD/Digital Electronics by Ravinder Nath Rajotiya - August 7, 2019May 10, 20210 Karnaugh Map (K-map) K-Map is a pictorial representation of the Boolean function. It is a systematic method of simplifying the Boolean expression. A K-Map is an arrangement of the adjacent cell , each cell representing the minterm or the maxterm of the SOP or the POS equations. The number of adjacent cells in a K-Map depends on the number of input variables in an equation. The number of cell equals 2N where N is the number of input variables. Let us see how the minterm or the maxterms of the SOP or POS equations are represented. Two variable K-Map Table in figure-1 on the left is a truth table for two input variables. The output is shown in column marked ‘F’. m0, m1, m2,