Hand draw the circuit

Problem $1$ : $5$pts

Part $1$: Understanding Logisim Logisim $("$logic simulator"$)$ is a software program for designing

combinational circuits. We will use Logism in this lab and the next lab to help us design complex

circuits. The purpose of this section is to help you become comfortable with Logisim.

Part $2$: Boolean Formulas and Truth Tables $($do it by hand$)$

As you saw in the lecture, every Boolean function has three equivalent representations: a

Boolean formula, a Boolean circuit, and a truth table. One simple example of a Boolean function

is the majority function. Given n inputs, the majority function is true if more than half the

inputs are true; otherwise it is false.

Here is the Boolean formula for the three$-$input version of the majority function:

$($A$*$B$)+($B$*$C$)+($A$*$C$)$quad Recall that the $""$ symbol means AND, and the $"+"$ symbol means

OR$.$ The parentheses are used to specify the order of operations, just like in arithmetic.

Confirm that the Boolean formula given above is correct by completing the truth table

below. Make sure that the final column matches the behavior of the majority function.

$(2$pts$)$

Part $3$: Building Combinational Circuit: Majority$-$of$-3($Build the circuit on Logisim$)$

Construct the majority$-$of$-$three circuit in Logisim.

Your circuit should have three inputs and one output. Use the Boolean formula above to help

you. If you are having trouble getting started, first determine how many gates your circuit will

need. Important: In Logisim, gates can have several inputs. However, you should make sure

that all the gates in your Logisim circuit use only two of their input pins.

Use the Toggle tool to compare the behavior of your circuit to the truth table you

completed in Part $2.$ Confirm that your circuit correctly computes the majority function.

$($capture and show on your report the truth table and K$-$Map generated by the circuit

using Project$-$Analyse Circuit$)(1$pts$)$

Save a picture of your circuit to hand in with your lab report $(1$pt$)$

Generate the circuit that only used NAND gates $(1$pt$)$