List input combinations for truth tables
Enumerate every possible row for one, two or three binary inputs.
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
How many possible values does one Boolean input have?
What you will learn
- Count the possible input combinations
- List rows systematically
- Avoid omitted or repeated cases
| 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
Each input can be 0 or 1. With n inputs there are 2ⁿ possible combinations: two rows for one input, four for two, and eight for three. A three-input table must show every combination once.
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
List rows in binary counting order. For A,B,C, keep A fixed for four rows at a time, B for two, and C changes every row: 000,001,010,011,100,101,110,111. This pattern prevents gaps.
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
Which list is complete for two inputs A and B?
Worked example
How many rows are needed for inputs A, B and C, and list them in binary order.
Show the worked solution
- There are 2³ possible combinations.
- 2³=8.
- Count from binary 000 to 111.
Answer Eight rows: 000, 001, 010, 011, 100, 101, 110, 111.
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.
List the rows for one input X.
Give me a hint
Start at 0 and count in binary.
Compare my reasoning
- The input can be 0.
- The next and only other value is 1.
0, 1.
Look for these in your work
- Two rows
- Both values
List all rows for A, B in binary order.
Give me a hint
Count from binary 00 to 11.
Compare my reasoning
- Start 00.
- Increment to 01 and 10.
- Finish at 11.
00, 01, 10, 11.
Look for these in your work
- Four cases
- No repeats
A draft three-input table has seven rows. Explain the defect and give the correct row count.
Give me a hint
Calculate 2 raised to the number of inputs.
Compare my reasoning
- Each of three inputs can independently be 0 or 1.
- There are 2×2×2=8 combinations.
- One row is missing from the seven-row draft.
It is incomplete; three inputs require eight rows.
Look for these in your work
- Combination count
- Missing-row conclusion
Common mistakes
- Listing only rows where one input changes
- Counting the header as an input combination
- Using four rows for three inputs
What can you explain now?
How many input rows are needed for three Boolean inputs?
Compare with the explanation
8
Each of three inputs has two possible values, so 2×2×2=8.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What pattern helps you enumerate all rows for three inputs?
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.