Graphical technique to minimise logic functions.
A K-map arranges truth-table cells in Gray code so adjacent cells differ in one variable. Group 1s in powers of two (1,2,4,8) as large as possible to get minimal sum-of-products. Don't-care cells help. Practical up to about 5 variables; Quine-McCluskey for more.
A 3-variable function simplified from 6 minterms to 2 product terms.
Karnaugh maps give a visual way to minimise logic expressions with up to about four or five variables.
Graphical technique to minimise logic functions.
Karnaugh maps give a visual way to minimise logic expressions with up to about four or five variables.
Group adjacent cells of ones in powers of two, including wrapped edges, and each group gives one product term with the variables that stay constant.
Beyond about five or six variables the map becomes hard to read, so software minimisation tools are used instead.
Typical applications include minimising the logic for a four-input safety interlock, finding the simplest expression for a seven-segment display decoder and reducing the gates needed for a controller state output.
Study "Boolean algebra" first (topic 38 of 104 in Electronics & Embedded). It covers the groundwork this topic builds on.
Wrap-around adjacency. Prime implicants. Hazard-free covers.
A 3-variable function simplified from 6 minterms to 2 product terms.
The next topic is "Combinational circuits", which builds directly on this one.
It is classed as Intermediate in Electronics & Embedded (topic 39 of 104). It is an intermediate topic. Work through the beginner topics in Electronics & Embedded first.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.