Karnaugh Maps — for OCR A-Level Computer Science

5 min readDec 1, 2023

Simplifying boolean expressions
Making electronic circuits more simple
How to create karnaugh maps
How to interpret Karnaugh maps

Video Explanation of how to derive the boolean algebra term from a Karnaugh map: https://youtu.be/dQ9lyk3bmCw

Video how to fill in a karnaugh map from an expression: https://youtu.be/sUgxPT009qs

Karnaugh maps, often abbreviated as K-maps, are a method used in digital electronics and Boolean algebra to simplify Boolean expressions. They provide a visual way of representing truth tables and minimize logical expressions without using algebraic methods like Boolean algebra. The purpose of Karnaugh maps is to simplify logic functions used in computer circuits and digital systems.

Purpose:

Simplify Boolean expressions.
Minimize the number of logical operations needed in digital circuits.
Provide a more intuitive and visual method compared to algebraic techniques.

Karnaugh maps rules:

Boxes can be 1, 2, 4 ,8 , 16 etc
Boxes can be across or down NOT diagonal
When the output changes you drop that letter
Use OR ∨ between boxes
Use AND ∧ inside the box
Not ¬

How can we use a Karnaugh Map to Simplify this complicated logic circuit?

If we build a 2D truth table with the inputs A and B, then put a 1 in the boxes where A, B and not B are true we get this:

Following the rules of Karnaugh maps if we get rid of the inputs the change, i.e B and not B we are left with just A

More complicated examples:

Example 1: From the Karnaugh map below write out a boolean expression

To derive the Boolean expression from the given Karnaugh map, follow these steps:

Identify the Groups:

Look for groups of ‘1’s that can be made into rectangles. The rectangles can contain 1, 2, 4, 8, etc., cells (must be a power of two).
Remember that the map wraps around, so you can group cells at the edges with each other.

2. Make the Groups as Large as Possible:

Combine adjacent ‘1’s to create the largest possible groups because larger groups will simplify to simpler expressions.

3. Write Down the Expression for Each Group:

For each group, identify which variables are the same within the group. A variable that doesn’t change (stays at 1 or 0) within a group will be part of the expression.

4. Combine the Expressions:

Combine expressions within groups with an AND operation.
Combine the expressions between groups with an OR operation

Make 2 boxes one with 2 ones and the other with 8 ones.

The bigger box with 8 ones in it (this follows the box rule size) is D. because A and B change over the columns, and C changes, D is the only one that stays the same
The smaller box is C and not A and B
Answer: B ∧ ¬ A ∧ C ∨ D