## Hamming Code Detector

Hola Amigos,

Today I am going to discuss about Hamming Code, its parity working and its code detection. Hamming code detection is basically used when there is a single bit error. It is quite fast and efficient method to determine the error bit and replace it with the opposite bit.

Today I am going to discuss about Hamming Code, its parity working and its code detection. Hamming code detection is basically used when there is a single bit error. It is quite fast and efficient method to determine the error bit and replace it with the opposite bit.

Let us take data as – 01001101 and with parity it will be xx0x100x1101.
How are the parity bit set here comes in mind first.

Parity bit is always set at positions which are power of 2 like 1, 2, 4, 8, 16 etc. So

Parity bit is always set at positions which are power of 2 like 1, 2, 4, 8, 16 etc. So

Now what will be at these positions ?

Note down position 1 as P1 position 2 as P2 position 4
as P4 and position 8 as P8

Now for P1 start from position 1. Take first bit and
ignore next and again take another and ignore next. So P1 will be x01010

Similarly for P2 starting bit will be at position 2 so
take two bits at once then ignore next two bit and agin take two and ignore
next two. So P2 will be x00010

Similarly for P4 starting bit position will be 4 so
take 4 bits at once then ignore next 4 then take another 4 and ignore next 4.
So P4 will be x1001

Similarly for P8 we will have P8 as x1101 since we
only have 5 bits left from position 8.

Now P1 has even number of 1s hence its parity is 0
thus P1 = 0.

Similarly P2 has odd number of 1s so odd parity hence
P2 = 1.

Similarly P4 has even number of 1s so P4 = 0

And P8 = 1

Now the data with parity become by replacing P1-8 as
010010011101.

This is our Hamming Code.

Now let there be an error and the data with parity
become this 010010011111. The red bit was 0 but
by noise it becomes 1.

Now follow same procedure to find P1-8

Now P1 has position 1, P2 has position 2, P4 has
position 4, and P8 has 8.

So add the positions whose match is “NO”

1 + 2 + 8 = 11 Thus 11

^{th}bit has the error and we have to replace that bit. Now go and check the position of the colored red bit. Voila its 11
Here is the code for Hamming code

module
Hamming(data,data_parity,clk,out,bit_error,k);

input [7:0]data;

input [11:0]data_parity;

input clk;

output [11:0]out,k;

output [3:0]bit_error;

reg [5:0]p1;

reg [5:0]p2;

reg [4:0]p3;

reg [4:0]p4;

reg [11:0]copy1;

integer i;

initial i = 1;

always @(posedge clk)begin

if(i==1)

copy1 = data_parity;

i = 2;

end

always @(posedge clk)begin

p1 =
{copy1[11],copy1[9],copy1[7],copy1[5],copy1[3],copy1[1]};

p2 = {copy1[10:9],copy1[6:5],copy1[2:1]};

p3 = {copy1[8:5],copy1[0]};

p4 = copy1[4:0];

end

wire o11,o10,o8,o4;

wire [31:0]noise;

count c1(p1,o11,clk);

count c2(p2,o10,clk);

count c3(p3,o8,clk);

count c4(p4,o4,clk);

assign out
={o11,o10,data_parity[9],o8,data_parity[7:5],o4,data_parity[3:0]};

error_detect
err(out,clk,p1,p2,p3,p4,bit_error,k);

endmodule

Code for Count i.e even or odd Parity

module
count(in,out,clk);

input
[5:0]in;

input
clk;

output
reg out;

reg
[5:0]stor;

reg
j;

reg
[2:0]k;

integer
i,m;

initial
begin

i
= 0;

m
= 0;

k
= 3'b0;

end

always
@(in)begin

stor
<= in;

end

always
@(posedge clk)begin

if(k<7)begin

j
= stor[5];

if(j==1)

i
= i + 1;

k
= k + 1;

stor
= stor<<1;

end

if(k==7)begin

if(i%2==0)

out
= 1'b0;

else

out
= 1'b1;

end

end

endmodule

Code for generating error bit

module
error_detect(input [11:0]in,input clk,input [5:0]p1,p2,input [4:0]p3,p4,output
reg [3:0]bit_error,output reg[11:0]k);

reg
[3:0]num;

reg
[31:0]num1;

//integer
bit_error;

initial begin

bit_error
= 0;

num1
= $random();

num
= num1[31:28];

end

always
@(in)

k
<= in;

reg
[5:0]p1x,p2x;reg [4:0]p3x,p4x;

always
@(posedge clk)begin

k[num]
= 1;

p1x = {k[11],k[9],k[7],k[5],k[3],k[1]};

p2x = {k[10:9],k[6:5],k[2:1]};

p3x = {k[8:5],k[0]};

p4x = k[4:0];

end

always
@(p1)begin

if(p1!=p1x)

bit_error
= bit_error + 1;

if(p2!=p2x)

bit_error
= bit_error + 2;

if(p3!=p3x)

bit_error
= bit_error + 4;

if(p4!=p4x)

bit_error
= bit_error + 8;

end

endmodule

TestBench

module
test();

reg [7:0]Data;

reg [11:0]Unknown_Data_Parity;

reg clk;

wire [11:0]Known_Data_Parity;

wire [11:0]Data_With_Noise;

wire [3:0]Bit_Error;

initial begin

clk = 0;

Data = 8'b01001101;

Unknown_Data_Parity = 12'bxx0x100x1101;

end

always #1 clk=~clk;

Hamming
ham(Data,Unknown_Data_Parity,clk,Known_Data_Parity,Bit_Error,Data_With_Noise);

endmodule

Output

So Long

Worked well

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