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Boolean Logic and Simplification

De Morgan's laws

  • 3 things to know
  • Component 1

Overview

De Morgan's first law, de Morgan's second law and procedure for applying De Morgan's laws.

What you need to know

Answer each one before you reveal it.

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Key term

State De Morgan's first law.

Key term

State De Morgan's second law.

Process

Describe the procedure for applying De Morgan's laws.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State De Morgan's first law.

    Model answer

    The inverse of A AND B equals NOT A OR NOT B. The bar is broken and the operator beneath it changes.

  2. 2

    State De Morgan's second law.

    Model answer

    The inverse of A OR B equals NOT A AND NOT B. The bar is broken and the operator beneath it changes.

  3. 3

    Describe the procedure for applying De Morgan's laws.

    Model answer

    The bar over the whole expression is broken and every variable is inverted. An AND then becomes an OR, and an OR becomes an AND.

  4. 4

    Apply De Morgan's law to NOT (A AND NOT B).

    Model answer

    The expression becomes NOT A OR B. The inverse of NOT B is simply B.

  5. 5

    Apply De Morgan's law to NOT (NOT A OR NOT B).

    Model answer

    The expression becomes A AND B. Each inverted variable returns to its original form.

  6. 6

    Why are De Morgan's laws useful in circuit design?

    Model answer

    De Morgan's laws convert an expression into a form using only NAND or only NOR operations. A circuit can then be built from one type of gate.

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