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Using De’Morgan’s

Using De’Morgan’s. On of the most useful principles in boolean algebra is De’Morgan’s Theorem, which allows one to switch between ANDs and NORs and ORs and NANDs. NOT terms or Inverted terms are represented with a line over the terms AB = A + B A + B = AB.

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Using De’Morgan’s

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  1. Using De’Morgan’s • On of the most useful principles in boolean algebra is De’Morgan’s Theorem, which allows one to switch between ANDs and NORs and ORs and NANDs. • NOT terms or Inverted terms are represented with a line over the terms • AB = A + B • A + B = AB

  2. To convert A+B into a form that can be implemented using a NAND gate follow these steps: • 1. Double Complement the term A+B = A+B • 2. Use DeMorgan’s to distribute one of the complements A+B = A B The equation is now a NAND of the complemented inputs. To convert AB into a form that can be implemented using a NOR gate follow these steps: • 1. Double Complement the term AB = AB • 2. Use DeMorgan’s to distribute one of the complements AB = A + B The equation is now a NOR of the complemented inputs.

  3. A B Output 0 0 0 0 1 1 1 0 0 Out = A B 1 1 0 DoubleC A B DeM A + B Simplify A + B

  4. Exercise 1 A B C Output 0 0 0 1 0 0 1 0 0 1 0 0 Out = A B C + A B C 0 1 1 0 DoubleC A B C + A B C 1 0 0 0 DeM (A B C) ( A B C) 1 0 1 0 1 1 0 1 1 1 1 0 1.Draw a gate diagram that implements this function in three NAND gates plus invertors. Your diagram will have two levels of NAND gates.

  5. Exercise 2 • Build a truth table for the following problem: PC power/security. A computer needs to be secured from un-authorized access in the following way: The power should only come on when A. The security key is present in the lock B. The case cover is closed C. The user presses the power-on button. • Use DeMorgan’s and boolean algebra to convert a function extracted from your truth table above, into one that can be constructed with either NANDs or NORs. • Draw a circuit diagram with gates that implements your function from step 2.

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