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De Morgan’s Law

De Morgan’s Law. Some expressions don’t simplify easily. For example ABC + A + C De Morgan’s 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. Proving De Morgan’s Law. Exercise

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De Morgan’s Law

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  1. De Morgan’s Law

  2. Some expressions don’t simplify easily • For example ABC + A + C • De Morgan’s 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 Morgan’s Law • Exercise • Using Digital Works, make a circuit that shows De Morgan’s law

  4. Proving De Morgan’s Law

  5. Proving De Morgan’s Law

  6. Using De Morgan’s Law • Change all AND expressions to OR, or vice versa • Complement the individual terms that were ANDed or ORed • Complement the whole expression

  7. Example • Apply to A+B • Change or to AND A.B • Complement each term A.B • Complement the whole thing A.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

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