Need a logisim circuit
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description
this assignment will introduce the use of logic gates in a circuit and practice converting
between different circuit representations the goal of this assignment is to create derive
boolean

Question

* * *

Need a Logisim circuit

* * *

will drop a like!

Description

This assignment will introduce the use of logic gates in a circuit and practice converting

between different circuit representations. The goal of this assignment is to create derive

Boolean equations from a given truth table and then use those to create a circuit, which

behaves as described in the table.

Tasks

For this assignment, do the following:

Derive the Boolean equations from the truth table below

(

Table

1 -

Lower case

letters are inputs, upper case letters are outputs of the circuit.

) .

You need to

execute the conversion process once for each output. This will yield one Boolean

equation for each output of the circuit. Use the labels given in the truth tables.

You do not have to simplify these equations.

Important: If you decide to simplify the equations, make sure to still submit

the unchanged equations derived from the truth table, which are in the canonical

sum

-

of

-

minterms form. If they are missing, you will not get credit for the Boolean

equations.

Convert the Boolean equations to a circuit in Logisim. Name the circuit

(

in Lo

-

gisim, not the file name

)

"CircuitRepresentation". Use the labels given in the truth

tables. Note: This will be one circuit with four

1 -

bit inputs and three

1 -

bit outputs.

You do not need additional

(

sub

)

circuits

!

Use the "Simulation Tool"

(

hand cursor in the top left; this allows you to change

the value of any input

)

and verify that the circuit behaves as the truth tables

indicates: Change the input values and check if the output values are as stated

in the respective row of the truth table. Test all possible input combinations to

verify the entire circuit behavior.

Any wire can be branched and connected to multiple components at the same time.

Simply click on an existing wire and drag the new wire to the second "target" component.

Tip: You can re

-

use duplicate terms

/

gates between the equations, but this is optional. Deliverables

Submit the following deliverables on Canvas in Module

2

before the due date

(

see Can

-

vas

)

:

Submit your document file containing all Boolean equations as a

.

pdf with the

following naming convention: lastname

_

a

2 .

pdf

Submit your Logisim file with the following naming convention: lastname

_

a

2 .

circ

Important: Make sure to submit both files in one submission. Only the files of the

last submission will be graded. If one is missing, you will receive

0

points for the missing

part.

Table

1

: Lower case letters are inputs, upper case letters are outputs of the circuit.

Holly Whitehead-Allen · Answer

To help you get started with the assignment, I'll provide a step-by-step guide on how to approach it. Let's break down the process using a summary of the tasks you've outlined:

Step 1: Derive Boolean Equations

Understand the Truth Table: Begin by examining the truth table provided in your assignment. Each row in a truth table corresponds to a combination of input values and their resulting output.
Identify Minterms for Each Output: For each output, identify the rows where the output is 1. Each of these rows corresponds to a minterm.
Write Boolean Equations: Write the Boolean equation for each output using canonical sum-of-minterms form. This means you will express the output as a combination of AND operations for inputs (minterms) and OR operations to combine them.
Example: If a truth table row with inputs a, b, c, d (with values 1 or 0) results in an output A, and A is 1 for that combination, the minterm can be represented as $A = a'b'cd$ . Combine all such minterms using OR operations for output A.

Step 2: Convert Equations to a Circuit in Logisim

Open Logisim: Download and install Logisim from sourceforge, if you haven't already.
Create a New Circuit: Open Logisim and create a new project. Name the circuit "CircuitRepresentation".
Place Logic Gates: Use AND, OR, and NOT gates to construct the circuit according to the Boolean equations derived earlier.
Connect Gates Appropriately: Connect gates based on the Boolean equations. Make sure wires are correctly connected. Any single wire can branch off to multiple destinations.
Label Inputs and Outputs: Make sure to label all inputs and outputs according to the truth table for clarity.

Step 3: Verify with the Simulation Tool

Simulation Tool: Use the simulation tool in Logisim (hand cursor) to toggle the inputs and verify that the outputs match the expected results as per the truth table.
Test All Combinations: Ensure that you check every possible combination of inputs to confirm that the circuit behaves as expected.

Step 4: Prepare Deliverables

Save and Export: Once verified, save your Logisim file and convert your Boolean equation notes into a PDF document.
Naming Conventions: Ensure your files follow the specified naming convention (e.g., lastname_a2.pdf and lastname_a2.circ).
Submit Files: Upload both the PDF and Logisim file to your submission platform as specified in your assignment instructions.

Important Tips

Remember not to simplify the Boolean equations unless you are also providing the original canonical form.
Use comments in Logisim to annotate your circuit where necessary for further clarity.
Reusing duplicate terms to simplify the circuit is optional but can be beneficial.

If you need further help with details such as specific logic gates or functionality within Logisim, feel free to ask!

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