1. Circuits, Truth Tables & Boolean Algebra

2. Expressions Can describe circuits in terms of Boolean expression

3. Expressions Write Q as a function of A, B and C

4. Expressions Write Q as a function of A, B and C

5. Expressions Write Q as a function of A, B and C

6. Expressions Write Q as a function of A, B and C

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

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

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

10. Sum Of Products Can convert any truth table to expression – Identify ways to get 1 output X = 1 if red OR green OR yellow

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

22. Simplification

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

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

25. Multiple Outputs INOUT ABXY 0001 0100 1000 1111

26. Multiple Outputs