Error Detection & Correction by Hand: Parity Bits, Check Digits, Checksums, CRC Division & Hamming Codes
Learn how data protects itself against mistakes. You will add parity bits, compute and verify check digits, sum checksums, run CRC long division bit by bit, encode and decode Hamming codes that find and fix a flipped bit, and compare how much protection each method buys for its overhead, with every cell checked as you go.
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About this course
This course shows how data protects itself by letting you build every check yourself. You split frames into bits with MID, find flipped bits, bursts and expected error counts, add even and odd parity bits and a 2-D parity row, and compute check digits with a doubling rule and with weighted mod 11 that catches swapped digits. You sum bytes into checksums and check bytes, fold carries in ones'-complement style and find their blind spots. You build XOR from MOD, measure Hamming distance, run CRC long division step by step, encode and correct a Hamming(7,4) word and compare code rates, overhead and correction power.
Lessons
- Bits & Errors: Bit Strings, Flipped Bits, Bursts and Expected Error Counts Pro
- Parity Bits: Even and Odd Parity, What One Parity Bit Misses and 2-D Parity Grids Pro
- Check Digits: the Doubling Rule (Mod 10), Weighted Mod 11 and Catching Swapped Digits Pro
- Checksums: Byte Sums mod 256, Check Bytes, Ones'-Complement Folding and Their Blind Spots Pro
- XOR without XOR: MOD(a+b,2) Bit by Bit, Masks, Undoing XOR and Hamming Distance Pro
- CRC by Long Division: Generator Bits, MOD-2 Rows, the Remainder and Checking a Received Frame Pro
- Hamming(7,4): Parity Positions, Encoding Four Data Bits, the Syndrome and Correcting a Flipped Bit Pro
- Overhead vs Protection: Code Rates, Detection and Correction Power, and a Comparison Chart Pro