i inclueding this points in the ppt... K-map structure K-map boxes and associated product terms Alternative way to label the k-map Truth table to k-map Representation of standard SOP from on k-map if you want so plz open and download... and if you watch any correction so plz inform me by comment or personal massage..

1. Shri sad vidhya mandal
institute of technology
Sub: Digital electronics
Class: Electrical 2nd year
TOPIC: k-map
Presented
By:
3/17/2017 1
NO NAME ENROLLMENT NO.
1. Patel Shivam 150450109036
2. Sabalpara Harshad 150450109046
3. Modi Sagar 150450109047

2. Content:
K-map structure
K-map boxes and associated product terms
Alternative way to label the k-map
Truth table to k-map
Representation of standard SOP from on k-map
3/17/2017 2

3. What is kmap?
▪ Kmap is simplification technique to reduce the Boolean equation.
▪ Kmap is a graphical method of simplifying a Boolean equation.
▪ It is a graphical chart made up of rectangular boxes.
▪ The information contains in a truth table or available in the SOP or
POS form can be represented on a k-map.
▪ K-maps can be written for 2, 3, 4, ….upto 6 variables.

4. ▪ K-map is ideally suitable for designing the combinational logic
circuit using SOP or POS method.
▪ K-map is drawn for output Y and the input variables (A, B, C,
…..etc) are used for making the entries in the boxes.

5. Kmap(karnaugh-map) structure
▪ K-map is drawn for output Y of any two input combinational circuit
such as a logic gate with input A and B i.e. AB= 00, 01, 10 and 11.
▪ A 2 variable k-map consists of 22
= 4 rectangular boxes . Inside
these boxes we have enter the values of output Y for different
combination of input A and B.
▪ The k-map comprise a box for every line in the truth table for a 2
input combinational circuit there are 4-lines in the truth table .so
there will be 4-boxes in the 2 variable k-map.

6. ▪ For a 3-variable k-map there will be 8 boxes , for a 4 –variable map there will
be 16 boxes.
▪ The 0’s and 1’s written on top or sides of the boxes represent the values of
the corresponding variables.

7. Example of 2-variable k-map
▪ F(x,y)=sum(0,2,3)

8. ▪ Minimization solution to above function.
▪ = y’(x + x’) + xy + xy’
▪ = y’ + x (y+y’)
▪ = y’ + x
▪ Final ans is y’ + x
▪ Example 2: F(x,y)=sum(1, 2, 3)

9. K-map boxes and associated product terms
▪ The rectangular boxes in a k-map are to be filled with the values of
output Y corresponding to different combinations of inputs as
shown in figure.
▪ Each row and column of K-map is labelled by a variable, or a group of
variables or their complements.
3/17/2017 9

10. ▪ This box corresponds to the first row which is labelled by A’ and first
column labelled by B’. Hence the product term written inside this box
is A’B’ as shown in figure.
▪ Another example is the shaded box shown in figure .The first row is
labelled with A’B’ and the first column with C’D’. Hence the product
term written in this box is A’B’C’D’.
▪ Similarly the other product terms have been inserted in the
remaining boxes.
Here, = A’
= B’,C’
3/17/2017 10

11. Alternative way to label the k-map
▪ We can label the rows and columns of K-map in a different way as
shown in figure.
▪ Instead of labeling the rows and columns with the inputs and their
complements (A,A’,AB’ etc) their values in terms of 0s and 1s is used
for labelling.
3/17/2017 11

12. Example:
3/17/2017 12

13. Karnaugh maps
▪ 4 variables Karnaugh map
AB
CD 00 01 11 10
00
01
11
10
5
3
1
7
62
0 4
9
15
13
11
1014
12 8

14. ▪ The Karnaugh map is completed by entering a '1‘(or
‘0’) in each of the appropriate cells.
▪ Within the map, adjacent cells containing 1's (or 0’s)
are grouped together in twos, fours, or eights.
Karnaugh maps

15. 3/17/2017 15