1. Circuit Simplification Truth Table  Minimized Logic Gates

2. Where We Are… Can represent a circuit's output with Boolean expression: AB + AC

3. Where We Are… We can simplify boolean expressions AB + AC A(B + C)

4. Where We Are… Thus we can simplify circuits AB + AC A(B + C)

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

6. Proof By Exhaustion AB 001 011 101 110 AB 001 011 101 110

7. DeMorgan's Theorems

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

9. Samples

11. Sum Of Products

12. Multiple Inputs

13. SOP Circuit

14. Implication 1 Can build circuit from SOP expression: Any circuit can be build with NOT, AND & OR

15. And… Can make NOT, AND & OR with only NAND NOT ANDOR

16. Implication 2 Any circuit can be build with NAND gates only…

17. Implication 2 Replace NOT with NAND

18. Implication 2 Put inversion bubbles out of AND & into OR – 2 negations cancel out

19. Implication 2

20. SOP Circuit Can build circuit from SOP expression… … but can often do better…

21. Simplification

22. Multiple Outputs Multiple outputs – Each output separate function/circuit INOUT ABXY 0001 0100 1000 1111

23. Multiple Outputs Multiple outputs – Each output separate function/circuit X = AB INOUT ABXY 0001 0100 1000 1111

24. Multiple Outputs INOUT ABXY 0001 0100 1000 1111

25. Logisim Build simplified circuit from truth table… – Window  Combinational Analysis Build truth table for circuit… – Project  Analyze Circuit