Question

A gold vault has 3 locks with a key for each lock. Key A is owned by the

Answer 1

Answer:

i) Truth Table:

A      |     B     |     C     |     O

0      |     0     |     0     |      0

0      |     0     |     1      |      0

0      |     1      |     0     |      0

0      |     1      |     1      |      0    (condition 2 not satisfied)

1       |     0     |     0     |      0

1       |     0     |     1      |      1    (both conditions satisfied)

1       |     1      |     0     |      1    (both conditions satisfied)

1       |     1      |     1      |      1    (both conditions satisfied)

ii) The minimized sum of products (SOP) expression is

O = AC + AB

Explanation:

We have three inputs A, B and C

Let O is the output.

We are given two conditions to open the vault door:

1. At  least two people must insert their keys into the assigned locks at the same  time.

2. The trainee bank teller (C) can only open the vault when the bank  manager (A) is present in the opening.

i) Construct the Truth Table

A      |     B     |     C     |     O

0      |     0     |     0     |      0

0      |     0     |     1      |      0

0      |     1      |     0     |      0

0      |     1      |     1      |      0    (condition 2 not satisfied)

1       |     0     |     0     |      0

1       |     0     |     1      |      1    (both conditions satisfied)

1       |     1      |     0     |      1    (both conditions satisfied)

1       |     1      |     1      |      1    (both conditions satisfied)

ii) SOP Expression using Karnaugh-Map:

A 3 variable Karnaugh-map is attached.

The minimized sum of products (SOP) expression is

O = AC + AB

The orange pair corresponds to "AC" and the purple pair corresponds to "AB"

Bonus:

The above expression may be realized by using two AND gates and one OR gate.  

Please refer to the attached logic circuit diagram.