The material on Karnaugh Maps is covered in Ch.12 of the Book. The Wikipedia article is good for those who want to dig deeper.
You may find it helpful to use Karnaugh mAPP, a tool created by Arkadiusz Mikolajczak as a part of his honours project here at the University of Edinburgh
We begin by revisiting the idea of a universal model. If we have only n predicates then we can distinguish only 2n kinds of individual. So we only need to consider 2 2n universes. For example, for three predicates we only need to consider 256 universes; for four predicates this gives 64Ki universes. So to keep it simple we'll look no further, for the time being.
In logic, we call the things in the universal model valuations; they are Boolean-values functions defined on the set of predicates.
In computer science we often call these states, because, as we will see later, they are often used to represent states of a computing system.
We picture a system as a black box with a number of lights that tell the state of the system. A simple example is a traffic signal with three lights, red (R), green (G), and amber (A). Traffic lights in the UK cycle through four states: R; RA; G; A; R.
We use four lights, amber, green, red, blue, to present a 4-bit Karnaugh Map. A Karnaugh map represents a system in which changes only one light at a time. States that differ in only one bit are adjacent in the Karnaugh Map>
This video introduces the four-bit Karnaugh Map.
This video shows you how to find your way through the state space represented by a Karnaugh Map, and introduces features called blocks. In this video we introduce blocks of ones, which correspond to conjunctions of literals.
More on blocks of ones (which correspond to conjunctions of literals).
More on blocks of ones (which correspond to conjunctions of literals).
This video shows how to use a Karnaugh map to represent an arbitrary Boolean function of four variables as a disjunctive normal form (DNF) — a disjunction of conjunctions of literals.
This video shows how blocks of zeros, which correspond to disjund=ctions of literals, lead us to conjunctive normal form (CNF) which we met earlier as the output of our reduction procedure. CNF is in general better than DNF for specification. We will see later that it is also a better form if we want to search for a valuation that satisfies a given set of constraints. We introduce these ideas with a brief discussion of Sudoku.
This video shows how to use a Karnaugh map to represent an arbitrary Boolean function of four variables as a conjunctive normal form (CNF) — a conjunction of disjunctions of literals.
Slides 36..38