logicex

# logicex - CS2204 DIGITAL LOGIC STATE MACHINE DESIGN FALL...

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Polytechnic Institute of NYU Page 1 of 2 Handout No : 7 October 1, 2009 Function f(A, B, C, D) in Different Representations CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN FALL 2009 f(A, B, C, D) M(0,2,4,6,8,10,11,12,14) = The maxterm list : f(A,B,C,D) A A B B C C D D Digital Circuit Black Box : Double-rail Inputs f(A,B,C,D) A B C D Digital Circuit Double-rail Inputs Black Box : A B C D f(A, B, C, D) 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Truth Table : f (A, B, C, D) = A B C D + A B C D + A B C D + A B C D + A B C D + A B C D + A B C D The canonical SOP expression : f(A, B, C, D) =(A+B+C+D)(A+B+ C+D)(A+ B+C+D)(A+ B+ C+D)( A+B+C+D)( A+B+ C+D)( A+B+ C+ D)( A+ B+C+D)( A+ B+ C+D) The canonical POS expression : f(A, B, C, D) m(1,3,5,7,9,13,15) = The minterm list : f(A, B, C, D) = D(AB + C) + ABCD + A B D A nonminimal expression for function f = ABD + CD + AD( B + BC) k(m + s) = km + ks = ABD + CD + AD( B + C) k + km = k + m = ABD + CD + A B D + ACD k(m + s) = km + ks = ABD + A B D + D( C + C A) k(m + s) = km + ks = ABD + A B D + CD + AD k + km = k + m & k(m + s) = km + ks = ABD + CD + AD(1 + B)

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