ECE 275: Digital Design I

Class 12

More 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) = ∑m(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 = ∑m(1, 4) + ∑d(3, 5)