1. Objective / Мета роботи
Gain fluency in minimizing Boolean functions — writing their canonical forms and reducing them to minimal DNF/CNF both algebraically and with a Karnaugh map.
By the end of the class the student should be able to:
- read a function’s canonical forms from its truth table — the canonical DNF (the sum of full minterms over the -rows) and the canonical CNF (the product of full maxterms over the -rows);
- minimize algebraically by equivalent transformations — eliminating implications, applying De Morgan, and simplifying with distributivity, combining, absorption, and the complement laws;
- build a Karnaugh map from a truth table or canonical DNF, group adjacent $1$s in blocks of (using the wrap-around/cylinder adjacency), and read off a minimal DNF; and obtain a minimal CNF by grouping the $0$s;
- explain why minimization matters (fewer literals ⇒ fewer gates, less area and power, shorter delay).
The class consolidates Lecture 5 — Boolean algebra (canonical forms, Karnaugh maps, minimization), building on Lecture 4. All theory needed is restated, self-contained, in 2method.md.