Solve the Superbowl Public Works Problem with a Binary Circuit | Homework Guide

[Blues_MTA]

Homework Statement

Using AND, OR, NOT, NAND, NOR gates construct a circuit for the following problem

7. One of the more interesting public works problems is the “Superbowl” problem. At
the beginning of halftime during the Superbowl, 35 million toilets are flushed almost
simultaneously. The resulting loss of water pressure wreaks havoc on many
municipal water systems. Here you will solve the problem for a “three toilet” system.
Devise a logic circuit whose “1” inputs represent “flushes” and whose “1” outputs
represent opened water-feed valves. If no more than one toilet is flushed, that toilet’s
water valve opens, and the others remain closed. If more than one toilet is flushed,
all the water valves remain closed.

Homework Equations

I Made a table of Values, but i have been banging my head against my desk for now designing various circuits, here is the link to the circuit builder

http://www.jhu.edu/~virtlab/logic/logic.htm"

Here is the Table that i came up with

IN OUT
001 001
010 010
011 000
100 100
101 000
110 000
111 000
000 000

Any Help is GREATLY Appreciated, thank you so much!

The Attempt at a Solution

 

[Zryn]

How about if you interpret the problem differently. Think of taking in 3 inputs to determine whether 1 action happens or not, and then combining whether 1 action happens or not with each of the 3 inputs, to determine which output the action is happening to?

Do you have a maximum number of gates allowed?

 

[Blues_MTA]

Wow, thanks for the insight, ill give that a try, I've been working on it for hours so I am a little exhausted at this point, thank you very much, any other advice is greatly appreciated

There are no limits as to how many gates we can use, just three input, three output

 

[Zryn]

One issue that may arise would be caused by propagation delays between input and output, depending on how fast things need to react.

If the inputs A B & C in the picture are one set of values and then they change to a different set, there may be a memory effect for a short period of time, where the new set of inputs get to the 'Valve T/F' decision box and the old set's 'Action T/F' outcome has not updated yet.

This can be fixed by figuring out the delay times through each gate in the 'Action T/F' box and then putting a 'Delay' box on each of the A B & C lines composed of multiple pairs of NOT gates. This will do nothing to the signal except add a delay between the input and 'Valve T/F' box, which is a cheesy way of fixing the problem, but sometimes works ;)

 

[DeeNos]

I would approach this problem by first identifying the key components and their functions. In this case, the inputs are the number of toilets flushed (represented as binary numbers) and the output is the opening of water-feed valves (also represented as binary numbers).

To solve this problem, I would use a combination of AND, OR, and NOT gates to create a logic circuit. The first step would be to use an AND gate to ensure that only one toilet flush is registered at a time. This can be achieved by connecting all the inputs to the AND gate and the output of the AND gate to the first input of an OR gate.

Next, I would use another OR gate to combine the output of the first OR gate with the input of the NOT gate. The NOT gate will invert the signal, which will ensure that if more than one toilet is flushed, the output of the second OR gate will be 0, indicating that all water valves should remain closed.

The final step would be to connect the output of the second OR gate to the remaining inputs of the first OR gate, completing the circuit. This will ensure that if only one toilet is flushed, its corresponding water valve will open while the others remain closed.

In order to test this circuit, I would use the table of values provided and input each binary number one at a time, checking the output to ensure it matches the expected result. If there are any discrepancies, I would revise the circuit until it accurately solves the problem.

Using this approach, I believe a functional circuit can be created to solve the Superbowl Public Works Problem.