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De Morgans Law

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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

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

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

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

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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

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

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

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

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Flip-Flops The circuit that implements memory

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Simple J-K Flip Flop

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