OE$30201$ T$232$

Assignment #$3$

Design and Implementation of a Quadratic Equation Solver in Verilog

Objective:

Your task is to model a digital circuit using Verilog that solves quadratic equations. This circuit should be

capable of handling signed fixed$-$point numbers for its calculations. You will apply your knowledge of Verilog

coding and digital circuit design to create an efficient and accurate solver that adheres to the specifications

outlined below.

Parameters:

$$ WIDTH: Specifies the width $($in bits$)$ of the fixed$-$point numbers used in this assignment.

$$ SCALE: Specifies the number of bits used for the fractional part in the fixed$-$point representation.

Note: All fixed$-$point numbers used for this assignment must be signed.

Inputs:

$$ reset: Resets the circuit to the initial state.

$$ go: This input signal is used to initiate the reading of equation coefficients, a$,$ b$,$ and c$.$

$$ din: A WIDTH$-$bit data input port through which the coefficients a$,$ b$,$ and c are sequentially read.

Outputs:

$$ rdy: An output signal that indicates when the output $($solution to the equation$)$ is ready to be consumed.

$$ dout: A WIDTH$-$bit data output port that serially outputs the solutions $($real and imaginary parts$)$ over

four consecutive clock cycles.

Algorithm:

$1.$ rdy $<=1$

$2.$ wait for $+$ve edge on go

$3.$ a $<=$ din; rdy $<=0$;

$4.$ wait for $+$ve edge on go

$5.$ b $<=$ din

$6.$ wait for $+$ve edge on go

$7.$ c $<=$ din

$8.$ D $<=$ b$*$b $4*$a$*$c

$9.$ if D $==0//$ simplest case $-->$ Repeated real root

x$0\_$r $<=-$b$/(2*$a$)$; x$0\_$i $<=0$;

x$1\_$r $<=-$b$/(2*$a$)$; x$1\_$i $<=0$;

else if D$>0//$ Two distinct real roots

s $<=$ sqrt$($D$)$; $//$ done in a separate clock cycle than the assignments below it

x$0\_$r $<=(-$b$+$s$)/(2*$a$)$; x$0\_$i $<=0$;

x$1\_$r $<=(-$b$-$s$)/(2*$a$)$; x$1\_$i $<=0$;

else

s $<=$ sqrt$($D$)$; $//$ done in a separate clock cycle than the assignments below it

x$0\_$r $<=(-$b$)/(2*$a$)$; x$0\_$i $<=$ s$/(2*$a$)$;

x$1\_$r $<=(-$b$)/(2*$a$)$; x$1\_$i $<=$s$/(2*$a$)$;

end if

$10.$ rdy $<=1$; dout $<=$ x$0\_$r;

$11.$ dout $<=$ x$0\_$i;

$12.$ dout $<=$ x$1\_$r;

$13.$ dout $<=$ x$1\_$i; goto $2$

Deliverables:

As part of your submission for the Quadratic Equation Sol