Step1 . Build a (7, 4) hamming code generator using even parity bits. (10 points

Question

Step1. Build a (7, 4) hamming code generator using even parity bits. (10 points)

Hint: (optional) First, you might need to determine the use of each bit position by drawing a “Bit-position” table, e.g., which bit is supposed to be a parity bit and which bit is not. (optional) Then, draw the truth table for each parity bit (). (optional) Draw K-maps for each parity bit. Implement and import all the parity-generating circuits into your hamming code generator. Complete your hamming code.

Step2. Build an appropriate hamming code checker for the hamming code generated in Step1’s circuit. Additionally, attach a LED display to your outputs. The LED should be turned on if and only if there is no error on a received hamming code. (10 points)

           Hint: Do not forget that your hamming code checker will need one more bit to check each of the parity bits in a received hamming code.

Explanation / Answer

Hamming Code :

              In Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950. At the time, Hamming worked at Bell Telephone Laboratories and was frustrated with the error-prone punched card reader, which is why he started working on error-correcting codes.

           The Hamming code adds three additional check bits to every four data bits of the message. Hamming's (7,4) algorithm can correct any single-bit error, or detect all single-bit and two-bit errors. In other words, the minimal Hamming distance between any two correct codewords is 3, and received words can be correctly decoded if they are at a distance of at most one from the codeword that was transmitted by the sender

10 points in eample of Hamming code :

Data                     Transform

(d1,d2,d3,d4)  

0000                      0000000
1000                      1110000
0100                      1001100
1100 0111100
0010                       0101010
1010                       1011010
0110                         1100110
1110                         0010110
0001    1101001
1001                         0011001
0101    0100101
1101       1010101
0011    1000011
1011 0110011
0111    0001111
1111                         1111111

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.