ECE 275: Digital Design I

Class 14

Maxterm K-Maps

F(A, B, C) = πM(0,3,6,7)

F = (A + B + C) (B' + C') (A' + B')

5 Variable K-map

F(A, B, C, D, E)

Imagine 2 planes in 3D space on top of each other Pair in the 3rd dimension as well

E == 0 ^

E == 1 ^

F= ∑m(1, 5, 6, 7, 11, 12, 13, 15)

Groups:

1. ∑m(5,7,13,15)
2. ∑m(1,5)
3. ∑m(12,13)
4. ∑m(11,15)
5. ∑m(6,7)

# of I = 8 PIs = 1, 2, 3, 4, 5 EPIs = 2, 3, 4, 5

Quine-McClusky Method

Will be in exam for 15 points

F = ∑m(0, 1, 2, 5, 6, 7, 8, 10, 14)

Step 1

Group 0: 0 0 0 0 Group 1: 1 2 8 Group 2:

Can only have one bit flip between adjacent groups for all combinations

Do the process again and make sure the dashes align

Bold = Prime Implicants

Prime Implicant Chart

| 0 | 2 5 | 6 | 7 | 8 | 10 | 14 | | -------------- | ----- | ----- | --- | --- | --- | ----- | ----- | --- | ----- | | 0,1: A X X | | | | | | | | 1,5: A'C'D ~~X X | X | | | | | | | 5,7: A'BD X X X X | | X | | | | | 6,7: A'BC | | X ~X~~ | X | | | | | 0,2,8,10: B'D' | ~~ | X | | | X | X | | | 2,6,10,14: C | X | | X | | | X | X |

Essential Prime Implicants have only one X in the column Bold = EPIs

Cross out all columns that have X's in the same row as EPIs Cross out all X's till you have all columns and rows covered

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