1. Boolean Algebra Logic Gates
Chapter 2

15. p. 56 in Mano

26. Algebraic Manipulation
Examples
x(x’+y) =?
2) x+x’y =?
3) (x+y)(x+y’) =?
4) xy + x’z + yz =?
5) (x + y)(x’ + z)(y + z)

27. Complement of a Function
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)
Generalized DeMorgan’s theorem
(A+B+C+…+F)’=A’B’C’…F’
(ABC…F)’=A’+B’+C’+…+F’

28. Example Find the complement of the following functions Take duals
F=(x’yz’+x’y’z)
G=[x(y’z’+yz)]
Take duals
Complement each literal

32. Minterms & Maxterms

33. Example
f1=? and f2=? Find minterms and maxterms

34. f1=x’y’z+xy’z’+xyz=m1+m4+m7 f2=x’yz+xy’z+xyz’=m3+m5+m6+m7
Complement of f1
f1’=x’y’z’+x’yz’+x’yz+xy’z+xyz’
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=? in maxterms

35. Standart forms
F1=?
F2=?

36. Three- and two-level implementation
Difference?

39. 3-input XOR Gate