1. Boolean Algebra and Circuits Andrew Knoll Ted Bealin

2. Boolean Algebra George Boole Invented Boolean Algebra in 1850 Algebraic rules applied to logic Foundation of modern electronics

3. Basic Properties of Boolean Algebra Similar to Standard Algebra: – Values – Operators

4. Basic Properties of Boolean Algebra Values ⁻True or False Operators ⁻AND, OR, NOT

5. Basic Properties of Boolean Algebra Written Form: ⁻P AND Q:PQ ⁻P OR Q: P + Q ⁻NOT P P’

6. ABABA+BA’B’ TTTTFF TFFTFT FTFTTF FFFFTT Basic Properties of Boolean Algebra

7. PropertyExamples Commutativex + y = y + xxy= yx Associative(x+y) + z = x + (y + z)(xy)z = x(yz) Distributivex + (yx) = (x + y)(x + z)x(y + z) = (xy) + (xz) Identityx + 0 = xx(1) = x Complementx + x’ = 1x(x’) = 0 Basic Properties of Boolean Algebra

8. 1.abc’ + ab’c’ 2.ac’b + ac’b’Commutative Property 3.ac’(b + b’)Distributive Property 4.ac’ (1)Compliment 5.ac’Identity Basic Properties of Boolean Algebra

9. Gates and Logic Networks

10. Sum of Products Form abc + ab’c + ab’c’+ a’b’c + a’b’c’ Minimization abcf(a,b,c) 1111 1100 1011 1001 0110 0100 0011 0001

11. Sum of Products Form Minimization abcf(a,b,c) 1111 1100 1011 1001 0110 0100 0011 0000

12. Sum of Products Form abc + ab’c + ab’c’+ a’b’c Minimization abcf(a,b,c) 1111 1100 1011 1001 0110 0100 0011 0000

13. Karnaugh Map b Minimization aa’ b11 b’ abf(a,b) 111 100 011 000

14. Minimization abab’a’b’a’b c11 c’1 ab + bc

15. Minimization abab’a’b’a’b cd11 cd’11 c’d’11 c’d11 bd + b’d’