- K -maps can be used to simplify functions up to 6 variables
- K-maps are graphical representation of truth table
- In k-map each square is adjacent to all the neighboring squares (cells whose binary representation differ by only one bit).

**2-variable k-map:**

**3-variable k-map:**

**4-variable k-map:**

**5-variable k-map:**

**Minimization of switching functions using k-map:**

- Minimal expression is nothing but function having minimum number of sum terms or product terms with minimum number of literals.
- Two min terms are said to be adjacent if they differ by only one bit position in binary representation.

**Procedure of minimization:**

- Always group squares in terms of powers of 2(i.e. 2, 4, 8, 16…)
- Make as large groups as possible
- Use as few no. of groups as possible to cover all min terms.

**SOP Form:**

**Implicant:**

**implicant is a product term that could be used to cover min terms of a function**

Ex: a’bc, ab, b’ etc

**Prime implicant:**prime implicant is an implicant that is not part of any other implicant of the function. As min terms are combined prime implicants are formed

**Essential prime implicant:**is a prime implicant that covers at least one min term that is not covered by any other prime implicant.

**Cover:**cover of a function is a set of prime implicants for which each min term of the function is contained in by at least one prime implicant.

Ex: minimize f= ∑ (3, 4, 5, 6, 7, 11, 12, 13, 15)

f= CD+A’B+BC’

**POS form:**

**Implicate:**is a sum term that is um of one or more literals that could be used to cover max terms of the function.

**Prime implicate:**prime implicate is an implicate that is not covered by any other implicate of the function.

**Essential prime implicate:**an essential prime implicate is a prime implicate that covers at least one max term that is not covered by any other prime implicate.

Ex: minimize f= π (0, 1, 2, 3, 6, 9, 14)

f=(C+D) (A+B’+D) (A’+B+D’)

**Finding complement of a function using k-map:**

Place one’s in the positions of min terms that are not
given in the problem and minimize the k-map. The result is complement of the
function.

Ex: find complement of f=∑ (3, 4, 5, 6, 7,
11, 12, 13, 15)

F’= ∑ (0, 1, 2, 8, 9, 10, 14)

f=B'D'+ACD'+B'C'

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