ECE 275: Digital Design I

Class 13

K-Maps (Karnough Maps)

Allows you to simplify expressions without using the theorems

F(A, B)

Truth table

A B F
0 0 1
0 1 1
1 0 0
1 0 0

F = A'B' + A'B If you simplify using theorems, then you would find F= A'

K-map for F

A\B 0 1
0 1 1
1 0 0

You can pair up the ones so you get A'

3 Variable K-Maps

(A, B, C) Only have one bit change

A\BC 00 01 11 10
0
1

Could also do this

AB\C 0 1
00
01
11
10

Solve a problem

Truth table:

A B C F
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
A\BC 00 01 11 10
0 0 0 1 1
1 1 0 0 1

F = AC' + A'B

A\BC 00 01 11 10
0 0 1 1 0
1 0 1 1 0

F = C

4 Variable K-Maps

AB\CD 00 01 11 10
00
01
11
10
AB\CD 00 01 11 10
00 m0 m1 m3 m2
01 m4 m5 m7 m6
11 m12 m13 m15 m14
10 m8 m9 m11 m10

F = ∑m(0, 2, 3, 5, 6, 7, 8, 10, 11, 14, 15)

AB\CD 00 01 11 10
00 1 1 1
01 1 1 1
11 1 1
10 1 1 1

F = C + A'BD + B'D'

F= ∑m(1, 3, 5, 7, 9) + ∑d(6, 12, 13);

AB\CD 00 01 11 10
00 1 1
01 1 1 X
11 X X
10 1

F = A'D + C'D