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OCR H446 1.4.3 Two-variable Karnaugh maps
Part 5 of 11 · H446 1.4.3 · Boolean algebra
A Karnaugh map is a truth table rearranged as a grid, and students who never learn which cell holds which input state go wrong before any grouping begins. Covering OCR H446 1.4.3, this worksheet builds the two-variable map from locating a state, through placing outputs, to reading a term from a group.
Students will:
- locate the cell that represents a given input state
- transfer truth-table or expression outputs into the correct map cells
- decide whether a proposed group is valid in size and shape
- read a term from a group by asking which variables stay constant
- explain why a diagonal pair of cells cannot be treated as adjacent
Inside: 8 explanation cells, 4 multiple-choice questions, 2 fill-in-the-blanks cells and 2 written answers. 19 marks, about 40 to 50 minutes.
Series: H446 1.4.3 · Boolean algebra, part 5 of 11.
Shared by Coding PathwayVerified teacher
- 16 cells
- About 45 minutes
- CC BY-SA 4.0
- Shared 31 Aug 2026
- Updated 3 Sept 2026
Preview
The whole resource, exactly as a class sees it. Answers and marking are held back.
Two-variable Karnaugh maps
A Karnaugh map is a truth table arranged as a grid. It does not create new input combinations: each cell represents one state of the input variables, and the number placed in that cell is the output for that state.
You will first learn to locate states, then place outputs, then simplify. This order matters: grouping is much easier once the grid has meaning.
You should already know: two-input truth tables and Boolean expressions written as product terms joined by OR.
Worked model: inputs label the cell; the output goes inside it
In the map below, A chooses the column and B chooses the row.
| B / A | A=0 | A=1 |
|---|---|---|
| B=0 | state AB=00 | state AB=10 |
| B=1 | state AB=01 | state AB=11 |
For the truth-table row A=1, B=0, move to column A=1 and row B=0. The cell represents state AB=10. If the expression is true for 10, put 1 inside; otherwise put 0.
The letters A and B are variables. On one run of a circuit each variable has the state 0 or 1. They are not outputs and they are not values to add together.
Which cell represents the input state A=0, B=1?
- Arow B=0, column A=1
- Brow B=1, column A=1
- Crow B=1, column A=0
- Drow B=0, column A=0
Worked model: truth-table outputs become map entries
Consider F = (A ∧ B) ∨ (A ∧ ¬B). Split at OR and place each product term.
- A ∧ B is true only at A=1, B=1, so state 11 receives 1.
- A ∧ ¬B is true only at A=1, B=0, so state 10 receives 1.
- The other states receive 0.
| B / A | 0 | 1 |
|---|---|---|
| 0 | 0 | 1 |
| 1 | 0 | 1 |
The two 1s form one group of 2. Across the group, B changes but A stays 1. Discard B and keep A, so F = A. Grouping removes the variable whose state no longer affects the output.
| B / A | 0 | 1 |
|---|---|---|
| 0 | B 0 A 0 | B 0 A 1 |
| 1 | B 1 A 0 | B 1 A 1 |
Check the completed map
Your map should contain a vertical pair where A=0 and a horizontal pair where B=1. The bottom-left 1 belongs to both groups; overlap is allowed.
Which expression is read from those two groups?
- AA ∧ B
- B¬A ∧ B
- CA ∨ ¬B
- D¬A ∨ B
Which is a valid Karnaugh-map group?
- AA rectangle containing two 1s
- BThree adjacent 1s
- CA diagonal pair of 1s
- DA rectangle containing a 0 to make it larger
Read a group by asking what stays constant
For each variable, inspect every cell in the group:
- constant 1 → keep the variable;
- constant 0 → keep its negation;
- changes → discard it.
Terms from separate groups are joined with OR. Groups must be rectangles containing 1, 2 or 4 cells, must contain only 1s, and should be as large as possible.
Worked-to-independent example
For (¬A ∧ ¬B) ∨ (A ∧ ¬B), the map is:
| B / A | 0 | 1 |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 0 | 0 |
Do not simplify by guessing from the original expression. Read the group: A changes across the pair, while B remains 0.
What is the simplest expression represented by the group?
- AA
- B¬B
- C¬A
- DB
On paper, group the 1s in the completed map for ¬A ∨ B. State the term produced by each group and the final simplified expression.
Aim for two groups of two; overlap is permitted.
Students type their answer here.
Explain why a diagonal pair of 1s cannot be treated as adjacent in a Karnaugh map.
Refer to the number of input variables that change.
Students type their answer here.
Closed-book checkpoint
Complete the method from memory. No answer bank is provided.
Review your responses
Check every response against its command word and the supplied constraints. Strengthen unsupported answers with accurate method, mechanism, state or contextual consequence before submitting.