KARNAUGH KARNAUGH MAPSMAPS (K (K MAPS)MAPS)

DLD FINAL PROJECT

PRESENTATION

Course supervision by:SIR HAQ NAWAZ LASHARI

GROUP MEMBERS

1.MOIN ALI SHAH (14CS27)2.MUDASIR NAZAR (14CS28)3.UMERFAROOQ (14CS73)

KARNAUGH MAPS

• Karnaugh maps, or K-maps, are a lot used to simplify logic problems with 2, 3 or 4 variables.

BA

For the case of 2 variables, we form a map consisting of 22=4 cellsas shown in Figure

AB 0 1

0

1

Cell = 2n ,where n is a number of variables

00 1001 11

AB 0 1

0

1

AB 0 1

0

1

BABA AB

BA BA

BA BA

Maxterm Minterm

0 2

1 3

KARNAUGH MAPS

• 3 variables Karnaugh map

CBA

ABABCC 00 01 11 10

0

1

CBA CAB CBA

CBA BCA ABC CBA

0 2 6 4

531 7

Cell = 23=8

KARNAUGH MAPS

• 4 variables Karnaugh mapABAB

CDCD 00 01 11 10

00

01

11

10

5

3

1

7

62

0 4

9

15

13

11

1014

12 8

Cell = 24=16

KARNAUGH MAPS

• The Karnaugh map is completed by entering a ‘1‘(or ‘0’) in each of the suitable cells .• Within the map, adjacent cells containing

1's (or 0’s) are grouped together in twos, fours, or eights .

EXAMPLE

A

BY

A B Y0 0 00 1 11 0 11 1 1

2-variable Karnaugh maps are small but can be used to present the methods you need to learn . The map for a 2-input OR gate looks like this:

AB 0 1

0

1

111

BB

AA

A+BA+B

EXAMPLE

AA BB CC YY00 00 00 1100 00 11 1100 11 00 0000 11 11 0011 00 00 1111 00 11 1111 11 00 1111 11 11 00

CA

CAB B

ABABCC 00 01 11 10

0

1

11

1 1

1

DO YOU MEAN 00,01,11,10 IN ITS PLACE OF 00,01,10,11?• If so, it's because in the first sequence, each entry differs in

only one bit whereas in the second sequence the transition from 01 to 10 changes two bits which produces a race condition. In asynchronous logic, nothing ever happens at the same time, so 01 to 10 is either 01 00 10 or 01 11 10 and that causes problems.

• References: http://stackoverflow.com/questions/9047009/why-k-map-has-states-in-sequence-of-00-01-11-10-instead-of-00-01-11-10

• Just for remember: 3d example

THANKS!THANKS!