文档介绍：Boolean switching algebra
Chapter 2
Karnaugh maps
00
01
11
10
0
1
0
1
2
3
6
7
4
5
AB
C
MSB
LSB
00
01
11
10
AB
CD
00
01
11
10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
MSB=A ; LSB=D
000
001
011
010
ABC
DE
00
01
11
10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
MSB=A ; LSB=E
100
101
111
110
ABC
DE
00
01
11
10
16 20 28 24
17 21 29 25
19 23 31 27
18 22 30 26
MSB=A ; LSB=E
It is a matrix of squares. each square represent a minterm or maxterm from a Boolean equation.
N-variable karnaugh map have 2n squares.
The binary numeral on the sides of k-map is the variable coordinates.
By decoding the binary coordinates, We label the decimal value for each square.
00
01
11
10
0
1
0
1
2
3
6
7
4
5
AB
C
MSB
LSB
The decimal number is the subscript of the relative minterm or maxterm.
So a direct connection can be made between the minterm or maxterm equation list and the appropriate square in karnaugh map.
00
01
11
10
AB
CD
00
01
11
10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
MSB=A ; LSB=D
The squares correspond to the adjacent minterms are adjacent squares.
Across the top and down the side of k- map, only one bit changes occur between adjacent squares for each column and row
Logically adjacent
Adjacent
Symmetrical
(0,8,2,4)
(1,3,9,11)
stack
00
01
11
10
AB
CD
00
01
11
10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
MSB=A ; LSB=D
Describe a switching function by K-map
F(A,B,C,D)=∑m(1,3,5,12,13,14,15)
00
01
11
10
AB
CD
00
01
11
10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
MSB=A ; LSB=D
1
1
1
1
1
1
1
Writing 1 in the square correspond to a minterm.
F(A,B,C,D)=∏M(2,3,5,7,10,11,14,15)
00
01
11
10
AB
CD
00
01
11
10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
MSB=A ; LSB=D
0
0
0
0
0
0
0
0
Writing 0 in the square correspond to a maxterm.
Simplify a equation use N-variable K-map