Connect statements, expressions, circuits and tables
Move between all four Boolean representations and verify that each describes the same function.
Exam scope and assessment notes
This original learning sequence follows Topic 10 of Cambridge IGCSE Computer Science 0478, 2026–2028 syllabus Version 6. It covers standard symbols and functions for NOT, AND, OR, NAND, NOR and XOR/EOR, and translation among statements, expressions, circuits and truth tables. NOT has one input; other gates have at most two. Circuit practice is limited to three inputs and one output and keeps the requested design without simplification. Lessons and checks support learning but do not award an official Cambridge grade. Full timed-paper practice, practical programming in an executable workspace and human subject-teacher review remain outstanding; the separate 2029–2031 syllabus is not mapped here.
Before you begin
- Be able to read binary 0 and 1 as the two possible logic values. Each lesson introduces the gate or translation skill it uses.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which representation is a useful bridge between prose and a gate diagram?
What you will learn
- Translate words into an expression
- Draw a matching circuit
- Check a truth table against the circuit
| A | B | NOT B | A AND NOT B |
|---|---|---|---|
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
Core idea
A statement, expression, circuit and truth table can represent the same Boolean function. A reliable chain is statement → expression → circuit → truth table. At each step, the input meanings and output rule must stay unchanged.
In a logic circuit, 1 represents TRUE and 0 represents FALSE. A gate applies a defined rule to its input value or values and produces one binary output.
A reliable method
Define inputs from the statement, write the expression, map each operator to a gate, enumerate all input combinations, and evaluate the circuit. Compare a true case and false case to the statement before accepting the result.
Keep the given statement, expression, diagram or table in view while working. Check each row or connection against the rule, and preserve the stated circuit structure; the syllabus does not ask you to simplify it.
Pause and explain
What is the output sequence for Y=A AND NOT B on 00,01,10,11?
Worked example
A light turns on when A is true and B is false. Connect the four representations.
Show the worked solution
- Statement: A is true and B is false.
- Expression: Y=A AND NOT B.
- Circuit: B through NOT, then A and NOT B into AND. Table outputs on 00,01,10,11 are 0,0,1,0.
Answer The statement, expression Y=A AND NOT B, circuit and output column 0,0,1,0 agree.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Translate “Y is true when A and B are both true” into an expression and gate description.
Give me a hint
Both means AND.
Compare my reasoning
- Write Y=A AND B.
- Connect A and B to an AND gate.
- The gate output is Y.
Expression Y=A AND B; circuit A,B into AND.
Look for these in your work
- Statement captured
- Gate mapped
For Y=A XOR B, list the truth-table output sequence and explain the 11 row.
Give me a hint
XOR is true only when inputs differ.
Compare my reasoning
- For 00, inputs match: 0.
- For 01 and 10, they differ: 1.
- For 11, they match: 0.
0,1,1,0; on 11 both inputs are true so it is not exactly one.
Look for these in your work
- Four outputs
- 11 explained
A system output is true for all pairs except 00. State its statement, expression, circuit and output pattern.
Give me a hint
Use the rule that at least one input is true.
Compare my reasoning
- Statement: A or B or both are true.
- Expression: Y=A OR B.
- Circuit: A and B feed OR; outputs on 00,01,10,11 are 0,1,1,1.
Y=A OR B; circuit is a two-input OR; output pattern 0,1,1,1.
Look for these in your work
- Words
- Expression and circuit
- Table pattern
Common mistakes
- Changing what an input means midway
- Forgetting the NOT when drawing or tabulating
- Treating a consistent table as proof of the right input definitions
What can you explain now?
For Y=A AND NOT B, on which input pair is the output 1?
Compare with the explanation
A=1, B=0
Both A and NOT B must be 1.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What should remain consistent as you translate between representations?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.