$2\mathrm{.}54$ A museum has three rooms, each with a motion sensor $,$ and $m2$ that output $1$ 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 $2\mathrm{.}5.$

$2\mathrm{.}7$

Combinational Logic Design Process

$\backslash$table$[[\backslash$table$[[$Step $1$:$],[$Capture$],[$behavior$]],\backslash$table$[[$Capture the$],[$function$]],\backslash$table$[[$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.$]]],[\backslash$table$[[$Step $2$ :$],[$Convert$],[$to circult$]],\backslash$table$[[2$A: Create$],[$equations$],[28$ : Implement$],[$as a gate$-],[$based circuit$]],\backslash$table$[[$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.$)]]]]$