Evaluate Boolean expressions row by row
Substitute input values into a logic expression and evaluate brackets and NOT correctly.
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
If B=0, what is NOT B?
What you will learn
- Substitute values for named inputs
- Apply NOT and gate rules in a clear order
- Check an expression against each row
| 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 Boolean expression describes the same operation as a logic circuit. For A AND NOT B, first find NOT B for the row, then AND the result with A. Parentheses make the intended grouping explicit.
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
Write the input values, evaluate any NOT term, then evaluate the remaining gate. Add an intermediate column when a value is reused or a mistake would be hard to spot. Do not assume a precedence rule that the expression does not state; use its brackets and structure.
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
For A=1, B=1, what is A AND NOT B?
Worked example
Evaluate Y=A AND NOT B for A=1, B=0.
Show the worked solution
- B=0, so NOT B=1.
- Substitute A=1 and NOT B=1.
- 1 AND 1 gives 1.
Answer Y=1.
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.
Evaluate Y=NOT A OR B for A=1, B=0.
Give me a hint
Calculate the NOT term first.
Compare my reasoning
- NOT A = 0.
- Substitute: 0 OR 0.
- OR of two zeros is 0.
Y=0.
Look for these in your work
- NOT term
- Final OR
Evaluate Y=(A OR B) AND C for A=0, B=1, C=1.
Give me a hint
Follow the parentheses before the final AND.
Compare my reasoning
- A OR B = 0 OR 1 = 1.
- Now calculate 1 AND C.
- C=1, so the result is 1.
Y=1.
Look for these in your work
- Bracket evaluated
- Final gate evaluated
A warning W is on when the door is open (O=1) and the alarm is armed (A=1). Write an expression and evaluate O=1, A=0.
Give me a hint
Both conditions are required.
Compare my reasoning
- Combine O and A with AND.
- Substitute 1 and 0.
- AND outputs 0 because one required condition is false.
W=O AND A; for 1,0, W=0.
Look for these in your work
- Statement converted
- Scenario evaluated
Common mistakes
- Applying AND before calculating the stated NOT term
- Changing the input values between steps
- Leaving brackets ambiguous
What can you explain now?
For A=0, B=0, find A AND NOT B.
Compare with the explanation
0
NOT B is 1, but 0 AND 1 is still 0.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Why can an intermediate column help when completing a truth table?
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.