$2\mathrm{.}54$ A museum has three rooms, each with a motion sensor $(m0,m1,$ and $m2$ that outputs

$1$ when motion is detected. At night, the only person in the museum is one security

guard who walks from room to room. Create a circuit that sounds an alarm $($by setting

an output A to $1)$ if motion is ever detected in more than one room at a time

$($i$.$e$.,$ in two or three rooms$),$ meaning there must be one or more intruders in the

museum. Start with a truth table.

$2\mathrm{.}58$ Using the combinational design process of Table $2\mathrm{.}5,$ create a $4-$bit prime number

detector. The circuit has four inputs, N$3,$ N$2,$ N$1,$ and N$0$ that correspond to a $4-$bit

number $(N3$ is the most significant bit$)$ and one output $P$ that is $1$ when the input is a

prime number and that is $0$ otherwise.

Table $2\mathrm{.}5.$

Combinational Logic Design Process ${?}_{(})$

Step

Step $1$:

Capture

behavior

Capture the

function

Step $2$:

Convert

to circuit

Description

Create a truth table or equations, whichever is

most natural for the given problem, to describe

the desired behavior of each output of the

combinational logic.

This substep is only necessary if you captured the

function using a truth table instead of equations. Create

an equation for each output by ORing all the minterms

for that output. Simplify the equations if desired.

$2$B: Implement

as a gate$-$

based circuit

For each output, create a circuit corresponding

to the output's equation. $($Sharing gates among

multiple outputs is OK optionally.$)$