PAPER 1•BOOLEAN ALGEBRA
Boolean Algebra Laws
- Boolean expressions can be shown to be equivalent by comparing truth tables and logic gate circuits.
- Association, distribution, commutation and De Morgan's law help simplify expressions without changing the final output.
- Work through each activity in order: choose equivalent expressions, build the paired circuits, complete the truth tables, and explain what the results show.
Visual channel
Dual coding
Verbal channel
- De Morgan's law swaps AND and OR while negating the relevant terms.
- Double negation removes a pair of NOT operators, for example
¬(¬A) = A. - Association shows that regrouping the same operator does not change the output.
- Distribution can turn one expression into an equivalent expanded or simplified form.
- Commutation changes the order of terms without changing the truth table results.
Activity 1
De Morgan’s Law
- De Morgan’s law lets you rewrite a negated expression by swapping AND and OR, then negating the relevant terms.
- Using De Morgan’s law, choose an alternative expression for each prompt.
Activity 2
Association
- Association shows that when you group OR or AND operations differently, the final output stays the same.
- Use this activity to compare the grouped and simplified versions of the same expression.
Draw both circuits in the same simulator
A ∨ B ∨ C and A ∨ (B ∨ C)
Association simplification
Choose the simplified expression
Activity 3
Distribution
- Distribution lets you rewrite one Boolean expression into an equivalent expanded or simplified form.
- Each simulator below should contain the two circuits for that distribution example in the same workspace.
- Use the truth tables and comprehension questions to show why the shorter equivalent circuit is better.
Distribution pair 1
¬A ∨ (A ∧ B) and ¬A ∨ B
TRUTH TABLE: ¬A ∨ (A ∧ B) and ¬A ∨ B
Distribution pair 2
(A ∨ B) ∧ (A ∨ C) and A ∨ (B ∧ C)
TRUTH TABLE: (A ∨ B) ∧ (A ∨ C) and A ∨ (B ∧ C)
Activity 4
Commutation
- Commutation lets you change the order of terms in a Boolean expression without changing the output.
- Choose an equivalent expression for each commutation example.