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

$2\mathrm{.}7$

Combinational Logic Design Process

Step

Step $1$: Capture behavior

Step $2$: Convert to circuit

Capture the function

$2$A: Create equations

$2$B: Implement as a gate$-$ based 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.$)$

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Dyeta Duare $2$

Copyrigat $62606$

Frakk Tatid

$50$