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.

$2.$ Convert the Boolean equations to a circuit in Logisim. Name the circuit $($in Lo$-$

gisim, not the file name$)$ "ConvertedCircuit". Use the labels given in the truth

tables. Note: This will be one circuit with four $1-$bit inputs and three $1-$bit out$-$

puts. You do not need additional $($sub$)$circuits$!$

$3.$ 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$)$:

$1.$ Submit your document file containing all Boolean equations as a $.$pdf with the

following naming convention: lastname$\_$a$2.$pdf

$2.$ 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.

a b c d P$2$ P$1$ P$0$

$0000100$

$0001010$

$0010100$

$0011001$

$0100000$

$0101001$

$0110001$

$0111010$

$1000010$

$1001100$

$1010001$

$1011000$

$1100100$

$1101010$

$1110000$

$1111001$

Table $1$: Lower case letters are inputs, upper case letters are outputs of the circuit.