EEM16_F13_L03 (1) (1) - EEM16/CSM51A Logic Design of...

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EEM16/CSM51A: Logic Design of Digital Systems Lecture #3 Design of Combinational Systems Prof. Danijela Cabric Fall 2015
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Set representation of Switching Functions 2
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Normal Form Sum of Products (SoP) Form 3
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Minterm 4 For a Boolean function of n variables x1, …, xn, a product term in which each of the n variables appears once (either complemented, or uncomplemented) is called a minterm There are 2 n minterms of n variables Example:
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5 Indexing Minterms Minterm m j indexed by integer j=Σ i=0,…,n-1 x i 2 i 5
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6 Minterm Functions 6
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7 Example: E(x2, x1, x0) = m1+m2+m6 = Σm(1,2,6)
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(c) 2005-2012 W. J. Dally Truth Table F(d,c,b,a) is true if input d,c,b,a is prime No dcba q 0 0000 0 1 0001 1 2 0010 1 3 0011 1 4 0100 0 5 0101 1 6 0110 0 7 0111 1 8 1000 0 9 1001 0 10 1010 0 11 1011 1 12 1100 0 13 1101 1 14 1110 0 15 1111 0
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(c) 2005-2012 W. J. Dally F(d,c,b,a) is true if input d,c,b,a is prime No dcba q 0 0000 0 1 0001 1 2 0010 1 3 0011 1 4 0100 0 5 0101 1 6 0110 0 7 0111 1 8 1000 0 9 1001 0 10 1010 0 11 1011 1 12 1100 0 13 1101 1 14 1110 0 15 1111 0 dcba m f ) 13 , 11 , 7 , 5 , 3 , 2 , 1 ( Equation
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Example: Table → Sum of Products (Minterms)– Normal Form 10
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11 Dual: Product of Sums (PoS) Form
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12 Maxterms For a boolean function of
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