1. De Morgans Law

2. Some expressions dont simplify easily For example ABC + A + C De Morgans laws can help with expressions of this kind. It comes in two flavours, both of which are useful. A.B = A+B A+B = A.B

3. Proving De Morgans Law Exercise Using Digital Works, make a circuit that shows De Morgans law

4. Proving De Morgans Law InputsOutputs ABABA.B A+B 00 01 10 11

5. Proving De Morgans Law InputsOutputs ABABA+B A.B 00 01 10 11

6. Using De Morgans Law 1.Change all AND expressions to OR, or vice versa 2.Complement the individual terms that were ANDed or ORed 3.Complement the whole expression

7. Example Apply to A+B Change or to ANDA.B Complement each termA.B Complement the whole thingA.B

8. Law of Double Negative I am not saying something not true A = A

9. Simplify these A.B A+B+C (A.B).(B.C).(C.D).(A.C)

10. Flip-Flops The circuit that implements memory

11. Simple J-K Flip Flop

12. Counter