Paper 1 - Fundamentals of Boolean algebra

Simplifying Boolean Algebra

  • Boolean expressions can be simplified by applying De Morgan's law, distribution, association, commutation and double negation.
  • Equivalent expressions produce the same outputs, even when one circuit uses fewer gates.
  • This page rebuilds the theory and activities from the supplied lesson decks as interactive practice.

Visual channel

Simplifying Boolean algebra De Morgan's law Double negation Association A V (B V C) Commutation A V B = B V A Distribution factor or expand Swap AND and OR, invert each term Equivalent circuits can use fewer components
Dual coding

Verbal channel

  • De Morgan's law changes AND to OR, or OR to AND, while negating the relevant terms.
  • Double negation removes pairs of NOT operators, for example ¬(¬A) = A.
  • Association removes unnecessary brackets when the same operator continues across the expression.
  • Commutation swaps the order of two terms without changing the output.
  • Distribution can expand or factor an expression to make simplification easier.

Activity 1

Build and connect Boolean gates

Drag copies of the gates onto the canvas. Click a placed gate to select it, then click an input connector on another gate to add a flexible wire. Click any wire to delete it.

Reusable logic gate simulator

Open standalone simulator

Activity 2

Complete the truth tables

Enter only 0 or 1 into each editable cell. The tables compare pairs of equivalent expressions from the lesson and answer slides.

Activity 3

Choose the alternative expression

Use the dropdowns to choose an equivalent expression. These prompts come directly from the supplied answer activity.

Activity 4

Worked example and simplification reflection

Compare the two screenshots from the answer deck, then decide which simplified expression matches the shorter circuit and explain why the simpler circuit is preferable.

Before simplification

(¬A V ¬B) ∧ A

Logic-gate diagram for the expression open bracket not A OR not B close bracket AND A

After simplification

Equivalent shorter circuit

Simplified logic-gate diagram with fewer components

Reference

Source diagrams from the lesson decks

These screenshots from the supplied PowerPoints are included as reference examples alongside the interactive tasks.

Answer activity

De Morgan equivalent pair 1

Worked example showing equivalent logic circuits for De Morgan's law

Answer activity

De Morgan equivalent pair 2

Worked example showing a second equivalent logic-circuit pair for De Morgan's law