Logic Circuit Design Homework Solutions

[hallerman]

Homework Statement

1. A nuclear power plant contains three danger sensors X, Y and Z that can shut down the plant. Sensor Z is in such a senstive location that it has a backup B. The plant is to be shut down if two of the three sensors indicate danger. However, with exception, sensor Z is the only registering danger sensor so that the plant to be shut down. Design the logic circuit of danger sensors.

2. Let A, B, C and D represent the binary digits of a decimal number in the range 0 to 15. Construct a simplified expression and draw the logic circuit diagram that will give a prime number checker.

Homework Equations

Karnaugh map and truth table

The Attempt at a Solution

1. I have no idea how to incorporate the back-up and also what the third sentence means. Any clues, please?

2. I got Y = A'B'C + B'CD + A'BD + BC'D from the Karnaugh map. Is that the correct simplified expression?

 

[NascentOxygen]

A nuclear power plant contains three danger sensors X, Y and Z that can shut down the plant. Sensor Z is in such a senstive location that it has a backup B. The plant is to be shut down if two of the three sensors indicate danger. However, with exception, sensor Z is the only registering danger sensor so that the plant to be shut down. Design the logic circuit of danger sensors.

That is too ambiguous to arrive at a single solution.

However, were it an exam question there is no point in evading it, so I'd nominate the interpretation I'd use and arrive at a solution based on that interpretation.

If B is the backup for Z, then it is probably intended that the plant shut down if 2 out X,Y and B go high, in addition to shutting down if Z goes high.

However, I am not comfortable with this interpretation as it deprecates the term "backup", because I don't have B acting as a true backup. But I can't see any other way of including the "2 out of 3" guide.

2. Let A, B, C and D represent the binary digits of a decimal number in the range 0 to 15. Construct a simplified expression and draw the logic circuit diagram that will give a prime number checker.

2. I got Y = A'B'C + B'CD + A'BD + BC'D from the Karnaugh map. Is that the correct simplified expression?

Write the list of numbers that this expression will signal as prime.

 

[freezer]

If you have a k map, you have at least went through part of the design process. Why are you questioning your k map? Are you not sure of the truth table or that you have processed the k map correctly?

 

[LCKurtz]

Homework Statement

1. A nuclear power plant contains three danger sensors X, Y and Z that can shut down the plant. Sensor Z is in such a senstive location that it has a backup B. The plant is to be shut down if two of the three sensors indicate danger. However, with exception, sensor Z is the only registering danger sensor so that the plant to be shut down. Design the logic circuit of danger sensors.

1. I have no idea how to incorporate the back-up and also what the third sentence means. Any clues, please?

How can you hope to implement a design if you don't understand the specifications? You expect us to guess what the problem is? Ask your teacher what he means and get back to us.

 

[hallerman]

If you have a k map, you have at least went through part of the design process. Why are you questioning your k map? Are you not sure of the truth table or that you have processed the k map correctly?

I have done the k map. I'm only hoping that you might check if the answer's correct, as I might have made a mistake in my solution. Please!

 

[hallerman]

How can you hope to implement a design if you don't understand the specifications? You expect us to guess what the problem is? Ask your teacher what he means and get back to us.

I've talked with the teacher. The backup has no utility in this problem. I did the problem by two different methods:

1. Output = XY + YZ + ZX + Z = XY + Z
2. I formed the truth table for X, Y, Z & Output, and then, I did a k map and got the same answer.

Are both methods equally valid?

 

[LCKurtz]

I've talked with the teacher. The backup has no utility in this problem. I did the problem by two different methods:

1. Output = XY + YZ + ZX + Z = XY + Z
2. I formed the truth table for X, Y, Z & Output, and then, I did a k map and got the same answer.

Are both methods equally valid?

Yes, both methods are valid but sometimes a K-map gives a simpler implementation. But I have no confidence in what the problem actually requires. Your solution is to shut down the plant if either Z or both X and Y activate. If that is what is required, why doesn't the problem say that, and why does it mention the backup B if it is irrelevant?

I would give your instructor an F for that problem statement if you have quoted him exactly.

 

[hallerman]

I would give your instructor an F for that problem statement if you have quoted him exactly.

I think I agree with you. :rofl:

 

[hallerman]

Btw, I got Y = A'B'C + B'CD + A'BD + BC'D for the four-bit prime number checker. I'm wondering if there's any way to further simplify this expression. I haven't found any way, hence my question.