Practical Work 4 — Minimizing Boolean Functions: Canonical Forms and Karnaugh Maps
Fourth practical class of Computer Discrete Mathematics. Working by hand, you write a Boolean function’s canonical forms (canonical DNF/CNF), reduce it to a minimal form both algebraically and with a Karnaugh map.
At a glance
| Topic | Boolean minimization: canonical DNF/CNF, algebraic reduction, Karnaugh maps, minimal DNF/CNF |
| Prerequisite lectures | L05 — Boolean algebra (built on L04) |
| Mode | In-class problem solving — pen and paper, no computer |
| Deliverable | Worked solutions to the tasks in 3classroom.md |
Contents
| # | Part | File |
|---|---|---|
| 1 | Objective | 1purpose.md |
| 2 | Methodical guidelines (self-contained theory) | 2method.md |
| 3 | Classroom tasks with solutions | 3classroom.md |
| 6 | Control questions | 6questions.md |
Conventions
- Language — all work is written in English.
- By hand. Minimise using the laws of Boolean algebra and Karnaugh maps, not a computer-algebra tool; show the grouping on the map and the term each group yields.
- Notation is fixed and self-contained. An overline means ; juxtaposition means ; and (sometimes written ) is OR. The terms literal, minterm, maxterm, canonical DNF/CNF, minimal DNF/CNF are defined in 2method.md; no outside reference is needed.
- Every task has a full solution. 3classroom.md gives each task together with a complete worked answer, including the Karnaugh map and the groups.
Summary
A Boolean function can be written many ways; this practical is about finding a small one. From a truth table we read the canonical DNF and CNF (a sum of full minterms / a product of full maxterms), then shrink them — algebraically with the laws (De Morgan, distributivity, combining, absorption) and visually with a Karnaugh map, where adjacent $1$s combine into ever-larger groups that drop variables. Fewer literals in the resulting minimal DNF/CNF mean a simpler circuit — fewer gates, less power, and shorter delay — which is why minimization is a core skill of logic design.