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

# Tag: POS

# Simplification using K-Map

K-Map A K-Map is a pictorial representation of the Boolean expression. By entering the values of the minterm or Maxterm an SOP or POS equation can be very easily simplified. It is very easy tool for simplifying up to 5-variable Boolean equation, but as the variable increases, solution become tedious. To begin, we will learn how to draw a 2, 3 and 4 variable K-Map. Draw 2-Variable K-Map Draw 3-Variable K-Map Draw 4-Variable K-Map Simplification Using K-Map Simplifying 2-Variable SOP equation Ex-1: Simplifying F= A'B + AB Ex-2: Simplify A'B + AB + AB' Simplifying 3-Variable SOP equation Ex-3: Ex-4 Simplifying 4-Variable SOP Equation Ex-5 Simplify F(ABCD)=∑(m1, m3, m5, m7, m9, m10,m13, m15) Ans: D Practice Problem: Simplify F= A'B'+A'B+AB' Simplify F(WXY)=∑m(1,2,3,5,7) Simplify F(ABC)=∑m(2,3,4,5 ) Simplify F(ABC)=∑m(2,3,7) + d(1,5) Simplify F(ABCD)=∑m(2,3,5,7,10,15)+d(0, 4,9,13)

# Boolean Function

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

# Introduction to Karnaugh-Map

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,

# Boolean Function

Boolean Functions The following steps are generally followed while designing the logic circuits using Boolean functions. Analysis of the given statement of the problem to find the number of variables Writing the truth table from the given statement Conversion of the truth table into a logic function/ Boolean expression using standard product of sums(SOP) or product of sums (POS) Simplify the Boolean expression Create the logic circuit using logic gates SOP and POS equations Sum of Product (SOP) equation The SOP equations are formed by ORing the product or the min-terms. Formation of Minterm and Maxterm A B C Minterm(mi) Maxterms(Mi) 0 0 0 A’B’C’ =m0 A+B+C =M0 0 0 1 A’B’C =m1 A+B+C’ =M1 0 1 0 A’BC’ =m2 A+B’+C =M2 0 1 1 A’BC =m3 A+B’+C’ =M3 1 0 0 AB’C’ =m4 A’+B+C =M4 1 0 1 AB’C =m5 A’+B+C’ =M5 1 1 0 ABC’ = m6 A’+B’+C =M6 1 1 1 ABC = m7 A’+B’+C’ =M7 Min terms The input combinations for which the output equals ‘1’ is called