$2\mathrm{.}54$ A museum has three rooms, each with a motion sensor $,$ 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 $($N$3$ 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

$2\mathrm{.}7$

Step

Step $2$: equations

Convert to circuit

$2$B: Implement as a gatebased 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.

For each output, create a circuit corresponding to the output's equation. $($Sharing gates among multiple outputs is OK optionally.$)$

$50$