Use NAND and NOR gates
Combine AND or OR with inversion to evaluate NAND and NOR outputs.
Section 10 · Boolean logic
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
What does NAND combine?
What you will learn
- Evaluate NAND by inverting AND
- Evaluate NOR by inverting OR
- Read output bubbles correctly
Core idea
NAND means NOT AND: first find A AND B, then invert that result. NOR means NOT OR: first find A OR B, then invert it. A small circle at the output is a reminder to perform this final inversion.
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
Use the base gate before the bubble. NAND is 0 only on input 11; NOR is 1 only on input 00. These facts are useful checks, but show the base result and inversion when explaining a row.
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 NAND for inputs 1,1?
Worked example
Evaluate NAND and NOR for A=1, B=0.
Show the worked solution
- AND is 0 because both inputs are not 1; invert it for NAND.
- OR is 1 because at least one input is 1; invert it for NOR.
Answer NAND=1; NOR=0.
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.
Find NAND and NOR for inputs 0,0.
Give me a hint
Find AND and OR first, then invert.
Compare my reasoning
- AND(0,0)=0, so NAND=1.
- OR(0,0)=0, so NOR=1.
- Both outputs are inverted base-gate outputs.
NAND=1; NOR=1.
Look for these in your work
- Base results
- Both inversions
For inputs 1,1, find NAND and NOR.
Give me a hint
AND and OR are both 1 for this row.
Compare my reasoning
- AND(1,1)=1, then invert for NAND.
- OR(1,1)=1, then invert for NOR.
- Both final results are 0.
NAND=0; NOR=0.
Look for these in your work
- NAND output
- NOR output
A circuit uses a NOR gate for output Y. A=0, B=1. Explain why Y=0.
Give me a hint
Evaluate OR before considering the output bubble.
Compare my reasoning
- At least one OR input is 1, so OR=1.
- The NOR bubble inverts that result.
- NOT 1 is 0.
Y=0 because OR(0,1)=1 and NOR inverts it.
Look for these in your work
- OR evaluated
- Inversion explained
Common mistakes
- Stopping at the AND or OR result
- Treating a NAND bubble as an extra input
- Claiming NOR is true when any input is true
What can you explain now?
When is NOR output 1?
Compare with the explanation
Only when both inputs are 0
OR is 0 only on 00; NOR inverts that to 1.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What input pair makes NAND false? What pair makes NOR true?
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.