K map

                  Karnough Map

                     It is use to Reduce the long equation.

·        There are 5 types of K map:-

1.       Two variable

2.     Three variable

3.     four variable

4.    Five variable

5.     Six variable

Two variables K Map

In this there are 2 inputs and 1 output.

Ex-Y=∑m(1,2)

A	B	Y
0	0	0
0	1	1
1	0	1
1	1	0

K Map

 See Only 1 output because it is minterm i.e sop

  

Three Variables K Map

In This there are 3 inputs

Ex-Y=∑m(0,3,5,6)

TRUTH TABLE

Decimal	A	B	C	Y
0	0	0	0	1
1	0	0	1	0
2	0	1	0	0
3	0	1	1	1
4	1	0	0	0
5	1	0	1	1
6	1	1	0	1
7	1	1	1	0

K Map

Four Variables K map

        For More reduction we use Grouping 

There are 3 types of grouping:-

• Pair(2)
• Quart(4)
• Octal(8)

Rules:

Groups may not include any cell containing a zero 

                       

Groups may be horizontal or vertical, but not diagonal. 

Groups must contain 1, 2, 4, 8, or in general 2ⁿ cells.
That is if n = 1, a group will contain two 1's since 2¹ = 2.
If n = 2, a group will contain four 1's since 2² = 4. 

Each group should be as large as possible. 

 

Each cell containing a one must be in at least one group. 

Groups may wrap around the table. The leftmost cell in a row may be grouped with the rightmost cell and the top cell in a column may be grouped with the bottom cell. 

Examples:-Y(A,B,C,D)=∑m(0,1,2,3,6,8,9,10,11,12,13)

                           Y=B'+AC'=A'CD'

        


                                         Thankss................