Four chairs are placed in a row: Photocells Variables A B

Chapter 4, Problem 4.25

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QUESTION:

 Four chairs are placed in a row:

                   

Each chair may be occupied (1) or empty (0). Give the minterm and maxterm expansion for each logic function described.

(a) F(A, B, C, D) is 1 iff there are no adjacent empty chairs.

(b) G(A, B, C, D) is 1 iff the chairs on the ends are both empty.

(c) H(A, B, C, D) is 1 iff at least three chairs are full.

(d) J(A, B, C, D) is 1 iff there are more people sitting in the left two chairs than in the right two chairs.

Questions & Answers

QUESTION:

 Four chairs are placed in a row:

                   

Each chair may be occupied (1) or empty (0). Give the minterm and maxterm expansion for each logic function described.

(a) F(A, B, C, D) is 1 iff there are no adjacent empty chairs.

(b) G(A, B, C, D) is 1 iff the chairs on the ends are both empty.

(c) H(A, B, C, D) is 1 iff at least three chairs are full.

(d) J(A, B, C, D) is 1 iff there are more people sitting in the left two chairs than in the right two chairs.

ANSWER:

Step 1 of 5

Given:

Four chairs are placed in a row:

                                                                            

Each chair may be occupied (1) or empty (0).

Consider the table for the given set as:

       
Inputs Outputs
A B C D F G H J
0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0
0 0 1 0 0 1 0 0
0 0 1 1 0 0 0 0
0 1 0 0 0 1 0 1
0 1 0 1 1 0 0 0
0 1 1 0 1 1 0 0
0 1 1 1 1 0 1 0
1 0 0 0 0 0 0 1
1 0 1 1 0 0 0 0
1 0 1 0 1 0 0 0
1 0 0 1 1 0 1 0
1 1 0 0 0 0 0 1
1 1 0 1 1 0 1 1
1 1 1 0 1 1 1
1 1 1 1 1 0 1 0

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