k map simplification

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  • Simplification of Boolean functions by Karnaugh Map and Tabulation Method

    Presented ByC.RameshAssistant Professor/ECEKIT-kalaignarkarunanidhi Institute Of Technology,Ciombatore.

  • IntroductionAlthough the truth table representation of a function is unique, when expressed algebraically, it can appear in many different form.Boolean functions may be simplified by algebraic means.How ever, this procedure of minimization is difficult because it takes specific rules to predict each succeeding step in the manipulative process.The map method provides a simple straight forward procedure for minimizing Boolean functions.

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  • Karnaugh Map (K-Map)A K-Map is a graphical representation of a truth table that can be used to reduce a logic circuit to its simplest terms.The Karnaugh map uses a rectangle divided into rows and columns.Any product term in the expression to be simplified can be represented as the intersection of a row and a column.The rows and columns are labeled with each term in the expression and its complement. The labels must be arranged so that each horizontal or vertical move changes the state of one and only one variable.

  • Two variable K-Mapxy0011xy0011

    xyxy

    xyxy

    m0m1

    m2m3

  • Three variable K-Mapxxyzyz0101

    xyzxyzxyzxyzxyzxy'zxyzxyz

    m0m1m3m2m4m5m7m6

    00011110

    00011110

  • Four variable K-Mapwx yz

    m0m1m3m2m4m5m7m6m12m13m15m14m8m9m11m10

    00011110

    00011110

  • Four variable K-Mapwx yz

    wxyzwxyzwxyzwxyzwxyzwxyzwxyzwxyzwxyzwxyzwxyzwxyzwx yzwx yzwxyzwxyz

    00011110

    00011110

  • Simplification Using the K-MapLook for adjacent squares.Adjacent squares are those squares where only one variable changes as one moves from a square to another.Group adjacent squares in powers of two, i.e. pairs, quads, groups of eight, groups of 16, etc.Principle 1. The more, the merrier. Hence, a quad is better than a pair.Principle 2. Share group elements only when necessary to form another or bigger group.

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  • f(A,B) = m(1,2,3) f(A,B) = m(0,1)

  • f(x1,x2,x3) = m(0,1,2,3,6) f(x1,x2,x3) = m(2,3,4,6)

  • f(x1,x2,x3,x4,x5) = m(6,7,8,9,12,13,18,22,23,24,25,28,29)

  • f(a,b,c,d,e) = m(0,2,6,8,9,10,11,18,22,26,24,25,27,30)

  • POS SimplificationSimplify the function f(A,B,C,D)=(0,1,2,5,8,9,10) in sum of products and product of sums.

    00011110001101010100110000101101

    00011110001110111110111

  • POS Simplificationf(A,B,C,D)=(A+B)(C+D)(B+D)f(A,B,C,D)=AB+CD+BD

    0001111000001000110000100

  • Minimize the following Boolean functions by K-Map

  • THANK YOU

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