# Digital Design (4th Edition)

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Boolean Algebra Logic Gates Chapter 2

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p. 56 in Mano

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Algebraic Manipulation s Examples 1) x(x’+y) =? 2) x+x’y =? 3) (x+y)(x+y’) =? 4) xy + x’z + yz =? 5) (x + y)(x’ + z)(y + z)
Complement of a Function s Use DeMorgan’s theorem. (A + B + C)’ = (A + x) => B+C=x = A’x’ => DeMorgan (5a) =A’(B+C)’ => substitute B+C=x =A’(B’C’) => DeMorgan (5a) =A’B’C’ => associative (4b) s Generalized DeMorgan’s theorem (A+B+C+…+F)=A’B’C’…F’ (ABC…F)’=A’+B’+C’+…+F’

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Example s Find the complement of the following functions • F’=(x’yz’+x’y’z)’ • G=[x(y’z’+yz)]’

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Unformatted text preview: • Take duals • Complement each literal Minterms & Maxterms Example s f 1 =? and f 2 =? Find minterms and maxterms s f1=x’y’z’+xy’z’+xyz=m1+m4+m7 s f2=x’yz+xy’z+xyz’=m3+m5+m6+m7 s Complement of f1 • f1’=x’y’z’+x’yz’+x’yz+xy’z+xyz’ s Take the complement of f1’ to obtain f1 in maxterms • f1=(x+y+z)(x+y’+z)(x+y’+z’)(x’+y+z’)(x’+y’+z) =M0.M2.M3.M5.M6 = Π (0,2,3,5,6) • f2=? İ n maxterms Standart forms s F1=? s F2=? Three- and two-level implementation s Difference? 3-input XOR Gate...
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## This note was uploaded on 01/13/2011 for the course CENG 275 taught by Professor Suleymantosun during the Spring '10 term at Ankara Üniversitesi.

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Chapter2 - • Take duals • Complement each literal...

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