Circuit Diagrams · Writing Expressions from Circuits · Simplification Rules
CSZoneCambridge IGCSE Computer Science 0478
Logic Gate Symbols
Drawing Logic Circuits
AND gate: D-shape; flat back on input side. Output is 1 only when A=1 AND B=1. OR gate: curved shield shape. Output is 1 when A=1 OR B=1. NOT gate: triangle with a circle (bubble). Single input. Inverts the signal. NAND: AND gate + bubble at output. NOR: OR gate + bubble at output. XOR: curved OR gate with extra curved line. Output 1 only when inputs DIFFER.
Cambridge 0478 uses standard IEC/IEEE gate symbols — you must recognise and draw them correctly in the exam
Reading a Logic Circuit
Expression from Circuit → Truth Table
// Example circuit: A, B are inputs // NOT A feeds into an AND gate with B // AND output feeds into OR gate with C
// Step 1: write intermediate expressions Wire 1 = NOT A Wire 2 = (NOT A) AND B
// Step 2: write final expression X = ((NOT A) AND B) OR C
// Step 3: complete truth table // (list all combos of A, B, C = 8 rows) // work left to right through the expression
Work through the circuit left to right — label each wire with its expression, then combine to get the output
Boolean Simplification Rules
De Morgan's Laws & Key Identities
De Morgan's Theorem: NOT(A AND B) = NOT A OR NOT B NOT(A OR B) = NOT A AND NOT B
Identity laws: A AND 1 = A · A OR 0 = A Annihilation: A AND 0 = 0 · A OR 1 = 1 Idempotent: A AND A = A · A OR A = A Complement: A AND NOT A = 0 · A OR NOT A = 1
De Morgan's laws are the most commonly tested — know both forms and how to apply them to simplify expressions
Exam Practice
Have a go at this question
Cambridge IGCSE 0478 style
A logic circuit has inputs A and B. The output X is: X = NOT(A OR B). (a) Complete a truth table for this circuit. (b) Using De Morgan's Law, write an equivalent expression for X without using NOT directly on the bracket.
5 marks
(a) Truth table: A=0,B=0→X=1; A=0,B=1→X=0; A=1,B=0→X=0; A=1,B=1→X=0 [2]. (b) By De Morgan's Law: NOT(A OR B) = NOT A AND NOT B [1], so X = NOT A AND NOT B [1]. This is equivalent to a NOR gate [1].
Key Takeaways
What to Remember
AND = D-shape; OR = curved shield; NOT = triangle + bubble; NAND/NOR = AND/OR + output bubble
Read circuit left to right; label each wire; combine to form final Boolean expression
De Morgan's: NOT(A AND B) = NOT A OR NOT B; NOT(A OR B) = NOT A AND NOT B
Simplification reduces circuit complexity — fewer gates needed saves cost and power