**Solving 5 variable SOP and POS expressions
using K map:**

To solve Boolean expression with 5 variables, 2^{5}
cells are required. So we need 32 cells. It can be split into two K map and can
be solved. The numbering of the cells is given below.

Numbering of cells in K map( 5 variable) |

Numbering of cells (5 variables) |

A,B,C,D and E are the five variables. The K map is splitted into two for A=0 and A=1. The values for B,C,D and E are in the both the axis.

Value'1' should be entered in the cell for the respective numbers given in the SOP function. Then they are grouped and the common terms are picked and the minimized equation is written.

### Example 1:

#### Minimize the following 5 variable SOP function using K map:

F(A,B,C,D,E)= ∑m(0,5,6,8,9,10,11,16,20,24,25,26,27)

K map for 5 variable SOP function |

- First fill the cells which are given in the SOP function with ‘1’.
- Group the adjacent cells in group of 1, 2 and 4.
- There are five groups in this K map.

- Group 1: Cells 0 and 16 are grouped. The common term is B'C'D'E'.
- Group 2: Cell number 5 is in group 2 and the Minterm for this group is A'B’CD’E.
- Group 3: Cell number 6 is in group 3 and the Minterm for this group is A'B’CDE’.
- Group 4: Cells 16 and 20 are grouped. The common term is AB'D'E'.
- Group 5: Cells 8, 9, 10, 11, 24, 25, 26 and 27 are grouped. The common term is BC'.

So the minimized SOP expression is

**F(A,B,C,D,E)= B'C'D'E'+ A'B’CD’E+ A'B’CDE’+ AB'D'E' +BC'**

### Example 2:

### Minimize the following 5 variable POS function using K map:

f(A,B,C,D,E)= πM (0,5,6,8,9,10,11,16,20,24,25,26,27)

K map for 5 variable POS function |

- First fill the cells which are given in the POS function with ‘0’.
- Group the adjacent cells in group of 1, 2 and 4.
- There are five groups in this K map.

- Group 1: Cells 0 and 16 are grouped. The common term is B+C+D+E.
- Group 2: Cell number 5 is in group 2 and the Maxterm for this group is A+B+C'+D+E'.
- Group 3: Cell number 6 is in group 3 and the Maxterm for this group is A+B+C'+D'+E.
- Group 4: Cells 16 and 20 are grouped. The common term is A'+B+D+E.
- Group 5: Cells 8, 9, 10, 11, 24, 25, 26 and 27 are grouped. The common term is B'+C.

So the minimized SOP expression is

**f(A,B,C,D,E)= (B+C+D+E).(A+B+C'+D+E').(A+B+C'+D'+E).(A'+B+D+E).(B'+C)**

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