Error Detection & Correction by Hand: Parity Bits, Check Digits, Checksums, CRC Division & Hamming Codes

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Split a sent frame into single bits, compare it with the received frame, find the flipped bits and the burst they form, and estimate how many bits a noisy link flips per day.
• Add even and odd parity bits to four code words, build a column parity row for a 2-D grid, and check a received word – then see a double error slip through.
• Compute check digits for fictional sensor IDs with a doubling rule and with weighted mod 11, then show that the weighted scheme catches two swapped digits.
• Compute a simple checksum and a check byte for eight data bytes, a simplified ones'-complement checksum with a folded carry, and find a two-byte error that the simple checksum cannot see.
• Build the XOR truth table with MOD, XOR a data byte with a mask and back again, and measure the Hamming distance between two code words – the tools the CRC and Hamming labs need.
• Run a CRC as long division: find the leading bit of each step, XOR the generator into the message row by row, read the 3-bit remainder as the CRC and let the receiver judge a damaged frame.
• Complete the encoder of a Hamming(7,4) code, compute the syndrome of a damaged word, read the position of the flipped bit from it and correct it.
• Compare six ways of protecting 4 data bits: their code rate and overhead, how many errors each detects and corrects, and a chart of the code rates.