## Description

**Steps**

Simplification is based on the principle of combining the terms present in adjacent cells. The 1s in the adjacent cells can be grouped by drawing a loop around those cells following the given rules:

- Steps to solve expression using SOP form K-map
- Select K-map according to the number of variables
- Identify minterms as given in problem
- For SOP put 1’s in blocks of K-map respective to the minterms (0’s elsewhere)
- Make rectangular groups containing total terms in power of two like 2, 4, 8… (except 1) and try to cover as many elements as you can in one group
- From the groups made in step 4, find the product terms and sum them up for SOP form

**Example**

** **

- SOP form, Z= ∑A,B,C(1, 3, 6, 7)
- K-map

BC

A

B’C’ | B’C | BC | BC’ | ||

00 | 01 | 11 | 10 | ||

A’ |
0 |
0
0 |
1
1 |
1
3 |
0
2 |

A |
1 |
0
4 |
0
5 |
1
7 |
1
6 |

- Sum the product terms
- From red group we get product term A’C
- Fromgreen group we get product term AB

- Final expression (A’C + AB)

** **

**Assignment**

- SOP form, Z= ∑A,B,C(2, 4, 5, 6)
- K-map

- Sum the product terms

Final expression:

- SOP form, Z= ∑A,B,C(0, 1, 6, 7)
- K-map

- Sum the product terms

Final expression:

- SOP form, Z= ∑A,B,C(2, 3, 4, 5)
- K-map

- Sum the product terms

Final expression:

- SOP form, Z= ∑A,B,C(3, 4, 6, 7)
- K-map

- Sum the product terms

Final expression: