1. Boolean Algebra How gates get picked

2. Boolean Arithmetic Boolean ≠ Binary – Boolean – 1/0 only, no places Boolean addition:

3. Boolean Arithmetic Boolean addition: + means OR

4. Boolean Multiplication Boolean multiplication

5. Boolean Multiplication Boolean multiplication Multiplication is AND

6. Boolean Variables

7. Identities Additive:

8. Identities Multiplicative:

9. Double Complement

10. Break …

11. Commutative Property Order of variables not important:

12. Associative Property + and · associative – Just like "normal" algebra

13. Distributive Can distribute/factor – Just like "normal" algebra

14. Theorem 1 A + AB = A

15. Theorem 2

16. Theorem 3 (A + B)(A + C) = A + BC

17. Example: A + AC + BC A(1 + C) + BC A(1) + BC A + BC

18. Example: AB + AB' A(B + B') A(1) A

19. Example: A + A'B' + B' A + B'(A' + 1) A + B'(1) A + B'

20. Example: A + B + A' (A + A') + B (1)+ B 1

21. Example: A(B +AB) + AC AB + AAB + AC AB + AB + AC AB + AC A(B + C)

22. Truth Table Truth table defines Boolean function – When in doubt, check the truth table…

23. Proof By Exhaustion ABAB 0001 0101 1001 1110 AB 00111 01101 10011 11000

24. DeMorgan's Theorems

25. DeMorgan's Break up solid bar by switching operation:

26. Samples