Boolean minimization, step by step.
Short lessons and interactive tools for turning truth tables into the smallest circuits — built for students of digital logic.
What “minimizing” means
The same function, three ways. Every method on this site is a careful way of getting from the first to the last.
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1 Start from the truth table
The rows where F is 1 are the minterms: here 0, 4, 5 and 7.
# A B C F 0 0 0 0 1 1 0 0 1 0 2 0 1 0 0 3 0 1 1 0 4 1 0 0 1 5 1 0 1 1 6 1 1 0 0 7 1 1 1 1 -
2 Find the prime implicants
Combine minterms that differ in one bit until nothing more combines. Three groups survive:
-00covers 0, 4BC10-covers 4, 5AB1-1covers 5, 7AC
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3 Choose the smallest cover
Minterm 0 needs BC and minterm 7 needs AC. Together they already cover 4 and 5, so AB is not needed.
F = AC + BC
Two AND gates and one OR gate, instead of four 3-input ANDs.
Tools
Seven tools, all running in your browser or on this site, and each one shows its work.
Scheinman tree method
Minimize single- and multiple-output functions and see every step of the tree, then the prime implicant chart.
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Scheinman tree, step by step
Every node of the tree drawn as you would write it by hand: the split, the matches, the check marks, then the chart.
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K-map solver
Click the cells of a 2–5 variable Karnaugh map and watch the groups and the minimal expression appear.
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Quine–McCluskey steps
The tabular method, one merge at a time, ending in the prime implicant chart.
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Truth table converter
From an expression to its truth table, minterms and canonical forms — and back again.
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Gate circuit viewer
Draw any minimized result as a network of AND, OR and NOT gates, with shared gates highlighted.
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Espresso
The classic heuristic minimizer, for comparing against exact methods on larger functions.
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Lessons
Eight short lessons, one idea each, with worked examples and self-check questions.