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Project 2 Complete

The 2D XYZ barcode will encode text using error detection and correction. It can encode any language into a barcode that can still be read even if the barcode is damaged. The process involves translating text to ASCII, adding error detection with hamming bits, grouping the bits into blocks, and encoding the blocks as a 64x64 pixel barcode pattern. Extra pixels are used to fill out the barcode if the message uses less than the maximum 204 characters.

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The 2D XYZ barcode will be used to take a 64x64 bit array of symbols and translate it into words. Through the translation process the information will be put through a series of Error Detection and Error Correction processes. This barcode will be capable of taking any international language and making a barcode of it and then later reading it back, even with errors such as missing or changed information. The maximum number of Characters a message can contain is 204 Characters. There are 4096 pixels in the barcode each character takes 20 pixels. 4096/20=204 therefore some pixels will not be used for data but to fill up the barcode. The process will begin at the Application Layer where you put in the information you wish to have in the barcode. The example I have decided to use is the word DOG. The application layer will take the input data and translate it into ASCII. I DONT WANT THIS ANYMORE. = 49 20 44 4F 4E 54 20 57 41 4E 54 20 54 48 49 53 20 41 4E 59 4D 4F 52 45 2E The data will then be moved to the Presentation Layer where it will put through the first Error Detection and Correction Process. The first Error Detection and Correction Process is hamming bits. H1 H2 A H3 B C D H4 E F G H. H1 H2 X H3 X X X H4 X X X X 49=0100 1001 == 000010001001 20=0010 0000 == 010101000000 44=0100 0100 == 110110010100 4F=0100 1111 == 100010001111 4E=0100 1110 == 010110011110 54=0101 0100 == 000010110100 20=0010 0000 == 010101000000 57=0101 0111 == 110110110111 41=0100 0001 == 110010010001 4E=0100 1110 == 010110011110 54=0101 0100 == 000010110100 20=0010 0000 == 010101000000 54=0101 0100 == 000010110100 48=0100 1000 == 000110011000 49=0100 1001 == 000010001001 53=0101 0011 == 100110100011 20=0010 0000 == 010101000000 41=0100 0001 == 100010010001 4E=0100 1110 == 010110011110 59=0101 1001 == 110110101001 4D=0100 1101 == 010010011101 4F=0100 1111 == 100010001111 52=0101 0010 == 100010110010 45= 0100 0101 == 110010000101 2E=0010 1110 == 010101011110
This information is now moved to the Data Link Layer where it will be put through the process of 12x12 block parity I have chosen to take the row parity column and place it below the column parity row where the left most bit represents the 1st row’s parity bit. Then the outcome of the block parity will be put through framing I am framing the data with 00110011. BLOCK PARITY: 000010001001||1 010101000000||1 110110010100||0 100010001111||0 010110011110||1 000010110100||0 010101000000||1 110110110111||1 110010010001||1 010110011110||1 000010110100||0 010101000000||1 000111110100 110010111101 000010110100||0 000110011000||0 000010001001||1 100110100011||0 010101000000||1 100010010001||0 010110011110||1 110110101001||1 010010011101||0 100010001111||0 100010110010||1 110010000101||0 010111000101 001010110010 010101011110||1 010101011110 100000000000
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his String of information moves to the Physical Layer where the information is grouped in 3's and converted to the preset symbols and put into a 64 by 64 block. Grouped in 3: 001-100-110-000-100-010-010-011-001-101-010-100-000-000-110-011-110-110-010- 100-001-100-111-000-100-011-110-011-001-101-011-001-111-000-110-011-000-010- 110-100-001-100-110-101-010-000-000-011-001-111-011-011-011-100-110-011-110- 010-010-001-001-100-110-101-100-111-100-011-001-100-001-011-010-000-110-011- 010-110-000-000-011-001-100-011-111-010-000-110-011-110-010-111-101-001-100- 110-000-101-101-000-011-001-100-011-001-100-000-110-011-000-010-001-001-001- 100-111-001-101-000-110-011-001-101-010-100-000-000-110-011-100-010-010-001- 001-100-110-101-100-111-100-011-001-111-011-010-100-100-110-011-010-010-011- 101-001-100-111-000-100-011-110-011-001-110-001-011-001-000-110-011-110-010- 000-101-001-100-110-101-110-001-010-011-001-100-101-011-001-000-110-011-010- 101-011-100-011-001-101-010-101-111-000-110-011-100-000-000-000 Converted to Symbols in 64x64block - > < + > X X | - V X > + + < | < < X > - > ^ + > | < | - V | - ^ + < | + X < > - > < V X + + | - ^ | | | > < | < X X - - > < V > ^ > < | + X < > - > < V X + + | - > | ^ X + < | < X ^ V - > < + X X + | - > | - > + < | + X - - - > ^ - V + < | - V X > + + < | > X X - - > < V > ^ > | - ^ | X > > < | X X | V - > ^ + > | < | - < - | - + < | < X + V - > < V < - X | - > V | - + < | X V | < - > < V X ^ > < | > + + + The rest of the 4096 characters will be filled with empty data(+). - > < + > X X | - V X > + + < | < < X > - > ^ + > | < | - V | - ^ + < | + X < > - > < V X + + | - ^ | | | > < | < X X - - > < V > ^ > < | + X < > - > < V X + + | - > | ^ X + < | < X ^ V - > < + X X + | - > | - > + < | + X - - - > ^ - V + < | - V X > + + < | > X X - - > < V > ^ > | - ^ | X > > < | X X | V - > ^ + > | < | - < - | - + < | < X + V - > < V < - X | - > V | - + < | X V | < - > < V X ^ > < | > + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Inserting errors Removal, Change - > < + > X X | - V X > + + < | < < X > - > ^ + > | < | - V | - ^ + < | + X < > - > < V X + + | - ^ | | | > < | < X X - - > < V > ^ > < | + X < > - > < V X + + | - > | ^ X + < | < X ^ V - > < + X X + | - > | - > + < | + X - - - > ^ - V + < | - V X > + + < | > X X - - > < V > ^ > | - ^ | X > > < | X X | V - > ^ + > | < | - < - | - + < | < X + V - > < V < - X | - > V | - + < | X V | < - > < V X ^ > < | > + + -
Moving from Symbols to 3-bit Binary - > < + > X X | - V X > + + < | < < X > - > ^ + > | < | - V | - ^ + < | + X < > - > < V X + + | - ^ | | | > < | < X X - - > < V > ^ > < | + X < > - > < V X + + | - > | ^ + < | < X ^ V - > < + X X + | - > | - > + < | + X - - - > ^ - V + < | - V X > + + < | > X X - - > < V > ^ > | - ^ | X > > < | X X | V - > ^ + > | < | - < - | - + < | < X + V - > < V < - X | - > V | - + < | X V | < - > < V X ^ > < | > + + - 001-100-110-000-100-010-010-011-001-101-010-100-000-000-110-011- 110-110-010-100-001-100-111-000-100-011-110-011-001-101-011-001- 111-000-110-011-000-010-110-100-001-100-110-101-010-000-000-011- 001-111-011-011-011-100-110-011-110-010-010-001-001-100-110-101- 100-111-100-110-011-000-010-110-100-001-100-110-101-010-000-000- 011-001-100-011-111-000-110-011-110-010-111-101-001-100-110-000- 010-010-000-011-001-100-011-001-100-000-110-011-000-010-001-001- 001-100-111-001-101-000-110-011-001-101-010-100-000-000-110-011- 100-010-010-001-001-100-110-101-100-111-100-011-001-111-011-010- 100-100-110-011-010-010-011-101-001-100-111-000-100-011-110-011- 001-110-001-011-001-000-110-011-110-010-000-101-001-100-110-101- 110-001-010-011-001-100-101-011-001-000-110-011-010-101-011-110- 001-100-110-101-010-111-100-110-011-100-000-000-001 This will now be unframed 00110011000010001001 00110011010101000000 00110011 110110010100 00110011 100010001111 00110011 010110011110 00110011 000010110100 00110011 010101000000 00110011 110110110111 00110011 110010010001 00110011 010110011110 00110011 000010110100 00110011 010101000000 00110011 000111110 00110011 110010111101 00110011 000001001000 00110011 000110011000 00110011 000010001001 00110011 100110100011 00110011 010101000000 00110011 100010010001 00110011 010110011110 00110011 110110101001 00110011 010010011101 00110011 100010001111 00110011 100010110010 00110011 110010000101 00110011 010111000101 00110011 001010110010 00110011 010101011110 00110011 010101011110 00110011 100000000001 The bolded data will now be taken out and the remaining data will be put in a 12x12 block to check block parity.
000010001001||1-Correct 010101000000||1-Correct 110110010100||0-Correct 100010001111||0-Correct 010110011110||1-Correct 000010110100||0-Correct 010101000000||1-Correct 110110110111||1-Correct 110010010001||1-Correct 010110011110||1-Correct 000010110100||0-Correct 010101000000||1-Correct 000111110 --- 3 bits in parity check are missing CCCCCCCCC 110010111101—moved to side 000001001000||0-Correct 000110011000||0-Correct 000010001001||1-Correct 100110100011||0-Correct 010101000000||1-Correct 100010010001||0-Correct 010110011110||1-Correct 110110101001||1-Correct 010010011101||0-Correct 100010001111||0-Correct 100010110010||1-Correct 110010000101||0-Correct 010111000101 CCCCEEEEEECC 001010110010—moved to side 010101011110||1-Correct 010101011110 CCCCCCCCCCCC 100000000001—moved to side. Only 1st bit matters last bit is an error. The data now is taken out of the block and put into 12 bit segments to have the hamming bits checked and taken out.
H1 H2 X H3 X X X H4 X X X X 000010001001--CORRECT 010101000000--CORRECT 110110010100--CORRECT 100010001111--CORRECT 010110011110--CORRECT 000010110100--CORRECT 010101000000--CORRECT 110110110111--CORRECT 110010010001--CORRECT 010110011110--CORRECT 000010110100--CORRECT 010101000000—CORRECT CCCCEEEEEECC 000001001000—Error 000110011000—CORRECT 000010001001—CORRECT 100110100011—CORRECT 010101000000—CORRECT 100010010001—CORRECT 010110011110—CORRECT 110110101001—CORRECT 010010011101—CORRECT 100010001111—CORRECT 100010110010—CORRECT 110010000101—CORRECT 010101011110—CORRECT The hamming bits show which set of numbers is in error and when going back to black parity can allow us to fix it. 000001001000 changes to 000010110100
Now remove the hamming bits and convert to decimal 01001001==49 00100000==20 01000100==44 01001111==4F 01001110==4E 01010100==54 00100000==20 01010111==57 01000001==41 01001110==4E 01010100==54 00100000==20 01010100==54 01001000==48 01001001==49 01010011==53 00100000==20 01000001==41 01001110==4E 01011001==59 01001101==4D 01001111==4F 01010010==52 01000101==45 00101110==2E Finally convert the ASCII HEX numbers back to letters to get the message. 49 20 44 49 4E 54 20 57 41 4E 54 20 54 48 49 53 20 41 4E 59 4D 4F 52 45 2E == I DONT WANT THIS ANYMORE.

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Project 2 Complete

  • 1.
    The 2D XYZbarcode will be used to take a 64x64 bit array of symbols and translate it into words. Through the translation process the information will be put through a series of Error Detection and Error Correction processes. This barcode will be capable of taking any international language and making a barcode of it and then later reading it back, even with errors such as missing or changed information. The maximum number of Characters a message can contain is 204 Characters. There are 4096 pixels in the barcode each character takes 20 pixels. 4096/20=204 therefore some pixels will not be used for data but to fill up the barcode. The process will begin at the Application Layer where you put in the information you wish to have in the barcode. The example I have decided to use is the word DOG. The application layer will take the input data and translate it into ASCII. I DONT WANT THIS ANYMORE. = 49 20 44 4F 4E 54 20 57 41 4E 54 20 54 48 49 53 20 41 4E 59 4D 4F 52 45 2E The data will then be moved to the Presentation Layer where it will put through the first Error Detection and Correction Process. The first Error Detection and Correction Process is hamming bits. H1 H2 A H3 B C D H4 E F G H. H1 H2 X H3 X X X H4 X X X X 49=0100 1001 == 000010001001 20=0010 0000 == 010101000000 44=0100 0100 == 110110010100 4F=0100 1111 == 100010001111 4E=0100 1110 == 010110011110 54=0101 0100 == 000010110100 20=0010 0000 == 010101000000 57=0101 0111 == 110110110111 41=0100 0001 == 110010010001 4E=0100 1110 == 010110011110 54=0101 0100 == 000010110100 20=0010 0000 == 010101000000 54=0101 0100 == 000010110100 48=0100 1000 == 000110011000 49=0100 1001 == 000010001001 53=0101 0011 == 100110100011 20=0010 0000 == 010101000000 41=0100 0001 == 100010010001 4E=0100 1110 == 010110011110 59=0101 1001 == 110110101001 4D=0100 1101 == 010010011101 4F=0100 1111 == 100010001111 52=0101 0010 == 100010110010 45= 0100 0101 == 110010000101 2E=0010 1110 == 010101011110
  • 2.
    This information isnow moved to the Data Link Layer where it will be put through the process of 12x12 block parity I have chosen to take the row parity column and place it below the column parity row where the left most bit represents the 1st row’s parity bit. Then the outcome of the block parity will be put through framing I am framing the data with 00110011. BLOCK PARITY: 000010001001||1 010101000000||1 110110010100||0 100010001111||0 010110011110||1 000010110100||0 010101000000||1 110110110111||1 110010010001||1 010110011110||1 000010110100||0 010101000000||1 000111110100 110010111101 000010110100||0 000110011000||0 000010001001||1 100110100011||0 010101000000||1 100010010001||0 010110011110||1 110110101001||1 010010011101||0 100010001111||0 100010110010||1 110010000101||0 010111000101 001010110010 010101011110||1 010101011110 100000000000
  • 3.
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his String ofinformation moves to the Physical Layer where the information is grouped in 3's and converted to the preset symbols and put into a 64 by 64 block. Grouped in 3: 001-100-110-000-100-010-010-011-001-101-010-100-000-000-110-011-110-110-010- 100-001-100-111-000-100-011-110-011-001-101-011-001-111-000-110-011-000-010- 110-100-001-100-110-101-010-000-000-011-001-111-011-011-011-100-110-011-110- 010-010-001-001-100-110-101-100-111-100-011-001-100-001-011-010-000-110-011- 010-110-000-000-011-001-100-011-111-010-000-110-011-110-010-111-101-001-100- 110-000-101-101-000-011-001-100-011-001-100-000-110-011-000-010-001-001-001- 100-111-001-101-000-110-011-001-101-010-100-000-000-110-011-100-010-010-001- 001-100-110-101-100-111-100-011-001-111-011-010-100-100-110-011-010-010-011- 101-001-100-111-000-100-011-110-011-001-110-001-011-001-000-110-011-110-010- 000-101-001-100-110-101-110-001-010-011-001-100-101-011-001-000-110-011-010- 101-011-100-011-001-101-010-101-111-000-110-011-100-000-000-000 Converted to Symbols in 64x64block - > < + > X X | - V X > + + < | < < X > - > ^ + > | < | - V | - ^ + < | + X < > - > < V X + + | - ^ | | | > < | < X X - - > < V > ^ > < | + X < > - > < V X + + | - > | ^ X + < | < X ^ V - > < + X X + | - > | - > + < | + X - - - > ^ - V + < | - V X > + + < | > X X - - > < V > ^ > | - ^ | X > > < | X X | V - > ^ + > | < | - < - | - + < | < X + V - > < V < - X | - > V | - + < | X V | < - > < V X ^ > < | > + + + The rest of the 4096 characters will be filled with empty data(+). - > < + > X X | - V X > + + < | < < X > - > ^ + > | < | - V | - ^ + < | + X < > - > < V X + + | - ^ | | | > < | < X X - - > < V > ^ > < | + X < > - > < V X + + | - > | ^ X + < | < X ^ V - > < + X X + | - > | - > + < | + X - - - > ^ - V + < | - V X > + + < | > X X - - > < V > ^ > | - ^ | X > > < | X X | V - > ^ + > | < | - < - | - + < | < X + V - > < V < - X | - > V | - + < | X V | < - > < V X ^ > < | > + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
  • 4.
    + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Inserting errors Removal, Change - > < + > X X | - V X > + + < | < < X > - > ^ + > | < | - V | - ^ + < | + X < > - > < V X + + | - ^ | | | > < | < X X - - > < V > ^ > < | + X < > - > < V X + + | - > | ^ X + < | < X ^ V - > < + X X + | - > | - > + < | + X - - - > ^ - V + < | - V X > + + < | > X X - - > < V > ^ > | - ^ | X > > < | X X | V - > ^ + > | < | - < - | - + < | < X + V - > < V < - X | - > V | - + < | X V | < - > < V X ^ > < | > + + -
  • 5.
    Moving from Symbolsto 3-bit Binary - > < + > X X | - V X > + + < | < < X > - > ^ + > | < | - V | - ^ + < | + X < > - > < V X + + | - ^ | | | > < | < X X - - > < V > ^ > < | + X < > - > < V X + + | - > | ^ + < | < X ^ V - > < + X X + | - > | - > + < | + X - - - > ^ - V + < | - V X > + + < | > X X - - > < V > ^ > | - ^ | X > > < | X X | V - > ^ + > | < | - < - | - + < | < X + V - > < V < - X | - > V | - + < | X V | < - > < V X ^ > < | > + + - 001-100-110-000-100-010-010-011-001-101-010-100-000-000-110-011- 110-110-010-100-001-100-111-000-100-011-110-011-001-101-011-001- 111-000-110-011-000-010-110-100-001-100-110-101-010-000-000-011- 001-111-011-011-011-100-110-011-110-010-010-001-001-100-110-101- 100-111-100-110-011-000-010-110-100-001-100-110-101-010-000-000- 011-001-100-011-111-000-110-011-110-010-111-101-001-100-110-000- 010-010-000-011-001-100-011-001-100-000-110-011-000-010-001-001- 001-100-111-001-101-000-110-011-001-101-010-100-000-000-110-011- 100-010-010-001-001-100-110-101-100-111-100-011-001-111-011-010- 100-100-110-011-010-010-011-101-001-100-111-000-100-011-110-011- 001-110-001-011-001-000-110-011-110-010-000-101-001-100-110-101- 110-001-010-011-001-100-101-011-001-000-110-011-010-101-011-110- 001-100-110-101-010-111-100-110-011-100-000-000-001 This will now be unframed 00110011000010001001 00110011010101000000 00110011 110110010100 00110011 100010001111 00110011 010110011110 00110011 000010110100 00110011 010101000000 00110011 110110110111 00110011 110010010001 00110011 010110011110 00110011 000010110100 00110011 010101000000 00110011 000111110 00110011 110010111101 00110011 000001001000 00110011 000110011000 00110011 000010001001 00110011 100110100011 00110011 010101000000 00110011 100010010001 00110011 010110011110 00110011 110110101001 00110011 010010011101 00110011 100010001111 00110011 100010110010 00110011 110010000101 00110011 010111000101 00110011 001010110010 00110011 010101011110 00110011 010101011110 00110011 100000000001 The bolded data will now be taken out and the remaining data will be put in a 12x12 block to check block parity.
  • 6.
    000010001001||1-Correct 010101000000||1-Correct 110110010100||0-Correct 100010001111||0-Correct 010110011110||1-Correct 000010110100||0-Correct 010101000000||1-Correct 110110110111||1-Correct 110010010001||1-Correct 010110011110||1-Correct 000010110100||0-Correct 010101000000||1-Correct 000111110 --- 3bits in parity check are missing CCCCCCCCC 110010111101—moved to side 000001001000||0-Correct 000110011000||0-Correct 000010001001||1-Correct 100110100011||0-Correct 010101000000||1-Correct 100010010001||0-Correct 010110011110||1-Correct 110110101001||1-Correct 010010011101||0-Correct 100010001111||0-Correct 100010110010||1-Correct 110010000101||0-Correct 010111000101 CCCCEEEEEECC 001010110010—moved to side 010101011110||1-Correct 010101011110 CCCCCCCCCCCC 100000000001—moved to side. Only 1st bit matters last bit is an error. The data now is taken out of the block and put into 12 bit segments to have the hamming bits checked and taken out.
  • 7.
    H1 H2 XH3 X X X H4 X X X X 000010001001--CORRECT 010101000000--CORRECT 110110010100--CORRECT 100010001111--CORRECT 010110011110--CORRECT 000010110100--CORRECT 010101000000--CORRECT 110110110111--CORRECT 110010010001--CORRECT 010110011110--CORRECT 000010110100--CORRECT 010101000000—CORRECT CCCCEEEEEECC 000001001000—Error 000110011000—CORRECT 000010001001—CORRECT 100110100011—CORRECT 010101000000—CORRECT 100010010001—CORRECT 010110011110—CORRECT 110110101001—CORRECT 010010011101—CORRECT 100010001111—CORRECT 100010110010—CORRECT 110010000101—CORRECT 010101011110—CORRECT The hamming bits show which set of numbers is in error and when going back to black parity can allow us to fix it. 000001001000 changes to 000010110100
  • 8.
    Now remove thehamming bits and convert to decimal 01001001==49 00100000==20 01000100==44 01001111==4F 01001110==4E 01010100==54 00100000==20 01010111==57 01000001==41 01001110==4E 01010100==54 00100000==20 01010100==54 01001000==48 01001001==49 01010011==53 00100000==20 01000001==41 01001110==4E 01011001==59 01001101==4D 01001111==4F 01010010==52 01000101==45 00101110==2E Finally convert the ASCII HEX numbers back to letters to get the message. 49 20 44 49 4E 54 20 57 41 4E 54 20 54 48 49 53 20 41 4E 59 4D 4F 52 45 2E == I DONT WANT THIS ANYMORE.