Learn
Eight short lessons that take you from a truth table to a minimal multiple-output circuit. One idea each, a worked example, and questions to check yourself.
- Bits, truth tables, minterms and maxterms
How a truth table defines a function, and how to name its rows: minterm and maxterm numbers, and the Σm and ΠM shorthand.
- SOP, POS and canonical forms
Writing a function as a sum of products or a product of sums, straight from the truth table — and why the canonical form is the starting point, not the answer.
- The Boolean algebra identities you actually use
A short list of identities, and the one that powers every minimization method: XY + XY′ = X.
- Karnaugh maps
Minimizing by eye: Gray-code ordering, grouping 1s in powers of two, wrap-around groups and don’t-cares.
- Quine–McCluskey, by hand
The tabular method: group by number of 1s, merge, check off, repeat — a procedure that finds every prime implicant.
- Prime implicants, essentials and the cover chart
Choosing which prime implicants to keep: essential rows, dominated rows, cyclic charts and Petrick’s method.
- The Scheinman tree method
Finding prime implicants with decimal minterm numbers: split the list on one variable at a time, match equal numbers, and read each term from its path in the tree.
- Multiple outputs and shared gates
Minimizing several functions of the same inputs at once: output tags, the intersection rule, and choosing a cover that lets outputs share AND gates.
When you have worked through them, try your own functions in the Scheinman tool and compare its steps with yours.