CA$3$: $7-$Bit Hamming Code

Due: Fri May $17,202411$:$59$pmDue: Fri May $17,202411$:$59$pm

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Hamming codes are used for error detection and correction. The simplest one is a distance$-3$ hamming code, which consists of $4$ data bits and $3$ parity bits carefully ordered.

Watch the following two videos from Neso Academy to get an understanding of how it works:

Hamming Code $--$ Error Detection Links to an external site.

Hamming Code $--$ Error Correction Links to an external site.

The implementation is shown below.

Distance$-3$ Hamming Decoder

Design this Hamming code in verilog. Create one module for the $3-$to$-8$ decoder $($dec$3$to$8)$ and a top module $($hc$7)$ that instantiates dec$3$to$8$ and add all the XOR gates. In the Hamming code design, you should use all three levels of modeling at least once: dataflow $($assign$),$ behavioral $($always$),$ and structural $($instantiation$).$

Use the following testbench to run your simulation. Include the waveform.

module top$\_$module $()$;

reg clk$=0$;

always #$5$ clk $=$ ~clk; $//$ Create clock with period$=10$

initial $`$probe$\_$start; $//$ Start the timing diagram

$`$probe$($clk$)$; $//$ Probe signal $"$clk$"$

$//$ A testbench

reg $[7$:$1]$ in$=0$;

initial begin

$//$the first $16$ valid cases, followed by $8$ invalid codes

$//$ p$4=$ b$7^$b$6^$b$5,$ p$2=$ b$7^$b$6^$b$3,$ p$1=$ b$7^$b$5^$b$3$

$//$ order: b$7$b$6$b$5$p$4$b$3$p$2$p$1$

#$10$ in $<=7\text{'}$b$000\_0000$; $//$ b$7$b$6$b$5$b$3=0000=>$ p$4$p$2$p$1=000$

#$10$ in $<=7\text{'}$b$000\_0111$; $//$ b$7$b$6$b$5$b$3=0001=>$ p$4$p$2$p$1=011$

#$10$ in $<=7\text{'}$b$001\_1001$; $//$ b$7$b$6$b$5$b$3=0010=>$ p$4$p$2$p$1=101$

#$10$ in $<=7\text{'}$b$001\_1110$; $//$ b$7$b$6$b$5$b$3=0011=>$ p$4$p$2$p$1=110$

#$10$ in $<=7\text{'}$b$010\_1010$; $//$ b$7$b$6$b$5$b$3=0100=>$ p$4$p$2$p$1=110$

#$10$ in $<=7\text{'}$b$010\_1101$; $//$ b$7$b$6$b$5$b$3=0101=>$ p$4$p$2$p$1=101$

#$10$ in $<=7\text{'}$b$011\_0011$; $//$ b$7$b$6$b$5$b$3=0110=>$ p$4$p$2$p$1=011$

#$10$ in $<=7\text{'}$b$011\_0100$; $//$ b$7$b$6$b$5$b$3=0111=>$ p$4$p$2$p$1=000$

#$10$ in $<=7\text{'}$b$100\_1011$; $//$ b$7$b$6$b$5$b$3=1000=>$ p$4$p$2$p$1=111$

#$10$ in $<=7\text{'}$b$100\_1100$; $//$ b$7$b$6$b$5$b$3=1001=>$ p$4$p$2$p$1=100$

#$10$ in $<=7\text{'}$b$101\_0010$; $//$ b$7$b$6$b$5$b$3=1010=>$ p$4$p$2$p$1=010$

#$10$ in $<=7\text{'}$b$101\_0101$; $//$ b$7$b$6$b$5$b$3=1011=>$ p$4$p$2$p$1=001$

#$10$ in $<=7\text{'}$b$110\_0001$; $//$ b$7$b$6$b$5$b$3=1100=>$ p$4$p$2$p$1=001$

#$10$ in $<=7\text{'}$b$110\_0110$; $//$ b$7$b$6$b$5$b$3=1101=>$ p$4$p$2$p$1=010$

#$10$ in $<=7\text{'}$b$111\_1000$; $//$ b$7$b$6$b$5$b$3=1110=>$ p$4$p$2$p$1=100$

#$10$ in $<=7\text{'}$b$111\_1111$; $//$ b$7$b$6$b$5$b$3=1111=>$ p$4$p$2$p$1=111$

#$10$ in $<=7\text{'}$b$111\_1110$; $//$ b$7$b$6$b$5$b$3=1111=>$ p$4$p$2$p$1=111$

#$10$ in $<=7\text{'}$b$111\_1101$; $//$ b$7$b$6$b$5$b$3=1111=>$ p$4$p$2$p$1=111$

#$10$ in $<=7\text{'}$b$111\_1011$; $//$ b$7$b$6$b$5$b$3=1111=>$ p$4$p$2$p$1=111$

#$10$ in $<=7\text{'}$b$111\_0111$; $//$ b$7$b$6$b$5$b$3=1111=>$ p$4$p$2$p$1=111$

#$10$ in $<=7\text{'}$b$110\_1111$; $//$ b$7$b$6$b$5$b$3=1111=>$ p$4$p$2$p$1=111$

#$10$ in $<=7\text{'}$b$101\_1111$; $//$ b$7$b$6$b$5$b$3=1111=>$ p$4$p$2$p$1=111$

#$10$ in $<=7\text{'}$b$011\_1111$; $//$ b$7$b$6$b$5$b$3=1111=>$ p$4$p$2$p$1=111$

$display $("$Hello world! The current time is $(\%0$d ps$)",$ $time$)$;

#$20$ $finish; $//$ Quit the simulation

end

hc$7$ DUT $(.$in$($in$))$; $//$ Sub$-$modules work too.

endmodule

module hc$7($input $[7$:$1]$ in$,$ output $[7$:$1]$ out, output no$\_$error$)$;

wire p$4,$ p$2,$ p$1$;

wire $[2$:$0]$ pos $=\{$p$4,$p$2,$p$1\}$;

wire $[7$:$0]$ dec$\_$out;

$//$ add your code here

$`$probe$($in$)$; $`$probe$($pos$)$; $`$probe$($no$\_$error$)$; $`$probe$($out$)$;

endmodule