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
Boolean Function Digital Logic and Computer Design by Ravinder Nath Rajotiya - September 6, 2023September 10, 20230 Boolean function A Boolean function is a Boolean algebraic equation derived generally from the word statement of the given problem or from the truth table. Such a function has two or more input variables. The function will produce a LOW or HIGH output when certain combinations of the input signal (binary value) is applied to the input variables. Two forms of Boolean functions Sum of Product Product of Sum Sum of Product: A sum of product (or SOP) equation is obtained by ORing the product or the minterms Minterm : A Minterm is also called as product term is one that produces a HIGH output when the values of the input variables are ANDed together. It is written for a ‘1’ or HIGH values in