Cambridge Syllabus Notes

Boolean Logic for IGCSE Computer Science 0478

Exam Tip: Remember that every logic gate can be expressed in terms of AND, OR and NOT. If you can write the expression first, the circuit follows automatically.

What is Boolean Logic?

Boolean logic deals with two truth values: TRUE (1) and FALSE (0). Think of it as a light switch – it’s either on or off.

Common Logic Gates

?? AND – outputs 1 only if both inputs are 1. A ∧ B
?? OR – outputs 1 if any input is 1. A ∨ B
?? NOT – flips the value. ¬A
?? XOR – outputs 1 if the inputs are different. A ⊕ B
?? NAND – NOT of AND. ¬(A ∧ B)
?? NOR – NOT of OR. ¬(A ∨ B)

From Problem Statement to Logic Expression

🔍 Example Problem: “Create a circuit that outputs TRUE when exactly two of the three inputs A, B, C are TRUE.”

Identify the condition: exactly two TRUEs.
Write the Boolean expression: $$ (A ∧ B ∧ ¬C) ∨ (A ∧ ¬B ∧ C) ∨ (¬A ∧ B ∧ C) $$
Use only AND, OR, NOT gates to build the circuit.

From Truth Table to Logic Expression

🔍 Example Truth Table:

A	B	C	Output
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	0

From the table you can read the rows where Output = 1 and write the expression:

$$ (¬A ∧ B ∧ C) ∨ (A ∧ ¬B ∧ C) ∨ (A ∧ B ∧ ¬C) $$

Building the Circuit

Use the following steps:

Group each product term (AND of literals) with an AND gate.
Feed all AND outputs into a single OR gate.
Use NOT gates to invert any input that needs ¬.

🛠️ Tip: Sketch the circuit on paper first – label each gate and wire to avoid confusion.

Exam Practice Question

Write a logic expression and draw the circuit for a system that outputs TRUE when at least two of the four inputs A, B, C, D are TRUE.

🔍 Hint: Think of it as “not fewer than two” – you can use combinations of AND, OR, and NOT.

Exam Tip: When you’re given a truth table, list all rows with output 1, then write the product terms. Combine them with OR. Simplify if possible using De Morgan’s laws or consensus theorem.

Analogy: The Party Invitation

Imagine a party where you only want to invite guests if at least two friends are coming. Each friend’s RSVP is a gate:

AND gate = “Both friends must say yes.”
OR gate = “At least one friend says yes.”
NOT gate = “Friend says no.”

By combining these gates you decide who gets the invitation card – just like building a logic circuit.

Key Takeaways

Write the Boolean expression first – it’s the blueprint.
Use only AND, OR, NOT to build any circuit.
Practice converting between problem statements, expressions, truth tables, and circuits.
Check your work by verifying the truth table of your final circuit.

Use logic gates to create logic circuits from a problem statement, logic expression or truth table