ECE 275: Digital Design I
Class 12More Minterms
4 chairs Occupied = 1 Empty = 0
F(A, B, C, D) = 1 if no adjacent chairs are empty G(A, B, C, D) = 1 if both ends are empty H(A, B, C, D) = 1 if at least 3 chairs are occupied J(A, B, C, D) = 1 if there are more people sitting on the left 2 chairs than the right 2
Represent F in minterms
A | B | C | D | F | Minterms | G | Minterms | H | Minterms | J | Minterms |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 1 | m0 | 0 | 0 | |||
0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ||||
0 | 0 | 1 | 0 | 0 | 1 | m2 | 0 | 0 | |||
0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | ||||
0 | 1 | 0 | 0 | 0 | 1 | m4 | 0 | 1 | m4 | ||
0 | 1 | 0 | 1 | 1 | m5 | 0 | 0 | 0 | |||
0 | 1 | 1 | 0 | 1 | m6 | 1 | m6 | 0 | 0 | ||
0 | 1 | 1 | 1 | 1 | m7 | 0 | 1 | m7 | 0 | ||
1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | m8 | |||
1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ||||
1 | 0 | 1 | 0 | 1 | m10 | 0 | 0 | 0 | |||
1 | 0 | 1 | 1 | 1 | m11 | 0 | 1 | m11 | 0 | ||
1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | m12 | |||
1 | 1 | 0 | 1 | 1 | m13 | 0 | 1 | m13 | 1 | m13 | |
1 | 1 | 1 | 0 | 1 | m14 | 0 | 1 | m14 | 1 | m14 | |
1 | 1 | 1 | 1 | 1 | m15 | 0 | 1 | m15 | 0 |
F(A,B,C,D) = âm(5,6,7,10,11,13,14,15)
Question 2
A
D B
C
F(A, B, C, D) = 1 if no adjacent chairs are empty G(A, B, C, D) = 1 if both ends are empty H(A, B, C, D) = 1 if at least 3 chairs are occupied J(A, B, C, D) = 1 if there are more people sitting on the left 2 chairs than the right 2
A | B | C | D | F | Minterms |
---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | |
0 | 0 | 0 | 1 | 0 | |
0 | 0 | 1 | 0 | 0 | |
0 | 0 | 1 | 1 | 0 | |
0 | 1 | 0 | 0 | 0 | |
0 | 1 | 0 | 1 | 1 | m5 |
0 | 1 | 1 | 0 | 0 | |
0 | 1 | 1 | 1 | 1 | m7 |
1 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 1 | 0 | |
1 | 0 | 1 | 0 | 1 | m10 |
1 | 0 | 1 | 1 | 1 | m11 |
1 | 1 | 0 | 0 | 0 | |
1 | 1 | 0 | 1 | 1 | m13 |
1 | 1 | 1 | 0 | 1 | m14 |
1 | 1 | 1 | 1 | 1 | m15 |
Incompletely Specified Fuctions
W -> +----+ -> A -> +----+
X -> | N1 | -> B -> | N2 | -> F
Y -> | | -> C -> | |
Z -> +----+ +----+
ABC cannot == 011 or 101 Called "don't cares"
A | B | C | F |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | X |
1 | 0 | 0 | 1 |
1 | 0 | 1 | X |
1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 |
F = âm(1, 4) + âd(3, 5)