# 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 $1$-rows) and the **canonical CNF** (the
  product of full maxterms over the $0$-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 $1,2,4,8,\dots$ (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](../../Lectures/CDM-L05.md) (canonical
forms, Karnaugh maps, minimization), building on
[Lecture 4](../../Lectures/CDM-L04.md). All theory needed is restated,
self-contained, in [2method.md](2method.md).