$3-$Bit Comparator

Problem Description

In class, we designed a circuit which was able to perform comparisons of two $1-$bit numbers. In the comparator.circ assignment file, you can see this as the subcircuit titled $1-$bit comparator.

For this assignment you are to use three of the $1-$bit comparator chips to help you build a single $3-$bit comparator. You will be designing in the subcircuit titled $3-$bit comparator. You will see that the subcircuit already contains two $3-$bit numbers for input $($X and Y$),$ three of the $1-$bit comparator chips, and three output pins for results of the three possible comparisons $($X$==$Y$,$ XY$).$

Make necessary connections and add whatever logic gates are necessary to make the $3-$bit comparator work correctly. DO NOT change the locations or the orientations of any of the input or output pins, and do not add any additional input or output pins.

Your goal is to build the simplest possible circuit which will correctly compare the $3-$bit inputs, X and Y$.$

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Testing

A tester circuit has been provided for you $($look for the tester subcircuit$).$ The tester circuit will fully test your $3-$bit comparator to ensure that it works correctly for all $64$ possible input combinations $($two $3-$bit numbers means a total of $6$ input bits, and there are $26$ different combinations$).$

The $3-$bit comparison circuit you are designing has been included as a subcircuit within the tester circuit.

To use the tester, set the Tick Frequency $($under the Simulate menu$)$ to $4$Hz or slower and then enable ticks. The clock will start pulsing and cause the two counters in the circuit to count through all possible X and Y values. You can see the X and Y values that are currently being tested on the logic probes at the top right of the circuit.

The output pins on the right side of the circuit show the output of your $3-$bit comparator circuit for the X and Y values that are currently being tested, and there$$s also an output pin which shows whether your circuit output is correct or incorrect for the values that are currently being tested.

As the tester counts through all $64$ possible input combinations, if you ever see an $$E$$ or a $1$ on the Incorrect output pin, then your circuit is incorrect. Your circuit is logically correct if the Incorrect pin always displays a value of $0.$

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Grading

This project will be completed as a group. Each person in the group who participated in the circuit design will receive the same grade. Points are awarded as follows:

$2$ points: Group members$$ contributions have been documented

$8$ points: Circuit produces correct output for all $64$ possible input combinations

$3$ points: Circuit is designed to be as simple as possible

$1$ point: Circuit must be neat, well organized, and easy to follow.

Assignment Submission

One member of the team should upload the finished project to Canvas before the due date$/$time$.$

All files necessary to open the project must be uploaded, and in the correct folder structure:

$$ Logisim: You only need to upload the modified comparator.circ file.

$$ MS Word: Upload an MS Word document which states the names of each group member who worked on the project, and the contributions that each member made toward the project.