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Logic Gates and Boolean Algebra

De Morgan's laws

  • 3 things to know
  • AS Unit 1

Overview

Procedure for applying De Morgan's laws to an expression and most common mistake made when applying De Morgan's laws.

What you need to know

Answer each one before you reveal it.

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Key term

How is a negation covering a whole Boolean expression removed, and how would you check the result on a worked case?

Key term

State De Morgan's law for a negated AND.

Key term

State De Morgan's law for a negated OR.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State De Morgan's law for a negated AND.

    Model answer

    The complement of A·B equals ¬A + ¬B.

  2. 2

    State De Morgan's law for a negated OR.

    Model answer

    The complement of A + B equals ¬A·¬B.

  3. 3

    Describe the procedure for applying De Morgan's laws to an expression.

    Model answer

    Remove the negation that covers the whole expression, change every AND to an OR and every OR to an AND, and negate each of the individual terms.

  4. 4

    Verify that ¬(A + B) equals ¬A·¬B when A = 1 and B = 0.

    Model answer

    On the left, A + B is 1 and its complement is 0; on the right, ¬A is 0 and ¬B is 1 so their AND is 0, and the two sides agree.

  5. 5

    Substitute A = 1 and B = 0 to verify that ¬(A·B) equals ¬A + ¬B.

    Model answer

    On the left, A·B is 0 and its complement is 1; on the right, ¬A is 0 and ¬B is 1 so their OR is 1, and the two sides agree.

  6. 6

    Simplify ¬(¬A + B).

    Model answer

    Applying the law gives ¬(¬A)·¬B, and double negation makes this A·¬B.

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