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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 15 Sept 2026

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The whole resource, exactly as a class sees it. Answers and marking are held back.

Two-variable Karnaugh maps

A Karnaugh map rearranges the output column of a truth table into a grid. The row and column headings give the input values; each box contains only the resulting output, 0 or 1.

You will place outputs, group neighbouring 1s and read a simpler expression from each group.

You should already know: two-input truth tables and Boolean expressions written as product terms joined by OR.

Worked model: follow the headings

In the map below, A selects a column and B selects a row.

B ↓ / A →01
0output for A=0, B=0output for A=1, B=0
1output for A=0, B=1output for A=1, B=1

For A=1 and B=0, use column 1 and row 0. Evaluate the expression for those inputs and write only its output, 0 or 1, in that box.

The headings are inputs. The value written inside a box is the output.

Multiple choice1 mark

Which box receives the output when A=0 and 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 the expression at OR and place each product term.

  • A ∧ B is true when A=1 and B=1, so that box receives 1.
  • A ∧ ¬B is true when A=1 and B=0, so that box also receives 1.
  • The other two boxes receive 0.
B ↓ / A →01
001
101

The two 1s form one group of 2. Across the group, B changes but A remains 1. Discard B and keep A, so F = A. Grouping removes a variable when changing it does not affect the output.

Fill in the blanks4 marks
Complete the map for ¬A ∨ B.
B ↓ / A →01
0B 0 A 0B 0 A 1
1B 1 A 0B 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.

Multiple choice1 mark

Which expression is read from those two groups?

  • AA ∧ B
  • B¬A ∧ B
  • CA ∨ ¬B
  • D¬A ∨ B
Multiple choice1 mark

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 →01
011
100

Do not simplify by guessing from the original expression. Read the group: A changes across the pair, while B remains 0.

Multiple choice1 mark

What is the simplest expression represented by the group?

  • AA
  • B¬B
  • C¬A
  • DB
Written answer5 marks

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.

Written answer2 marks

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.

Fill in the blanks4 marks
A Karnaugh group contains a power of entry 1 cells and no entry 2. A variable that changes inside a group is entry 3. Terms obtained from separate groups are joined using entry 4.

Review your work

For each group, identify what remains constant and explain why the changing variable is removed.