Only boolean equations needed SER $232-$ Assignment $2$

$[10$ Points$]$

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 Logisim, 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.

$\backslash$table$[[a,b,c,d,E,F,G$