Download - Karnaugh maps
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!