CRC Checksum · Computer Networks

CRC Checksum

CSC-263 · Semester IV · Computer Networks

intermediate25 minAvailable

CRC Checksum Lab

Binary polynomial division — compute the remainder and verify error detection

Data bits

Generator polynomial

1000000000000101

width 16 · init 0b0000000000000000

Data: 1011001010

Padded: 10110010100000000000000000

Remainder (CRC): 001001111000100

Transmitted: 1011001010001001111000100

Corrupt a bit — test the detection

No corruption — click the slider to flip a bit

Received: 1011001010001001111000100

Recompute remainder: 001101000100110

Non-zero remainder → error detected, frame rejected

Lab brief

Objective

Compute the CRC of a message with a given generator polynomial, append it to form a valid codeword, and verify that bit errors are detected.

Theory & concepts

CRC treats a message as a binary polynomial and divides it by a generator polynomial G using XOR. The remainder is appended to the message to form the codeword. The receiver divides the full codeword by G: a zero remainder means no detected error, a non-zero remainder means the frame is corrupt.

Rendering diagram…

CRC detects corruption by appending a division remainder and checking it on receipt.

Message: 1101, generator G = 1011 (x^3 + x + 1)
Append 3 zeros: 1101000
XOR division: 1101000 / 1011 -> remainder 010
Codeword transmitted: 1101 010
Flip one bit: 1111010 -> divide by 1011 -> remainder != 0 -> error detected

Prerequisites

Lesson: Error detection: parity, checksum and CRC

Instructions

1Choose a message and a generator polynomial from the presets.
2Watch the XOR long division compute the CRC remainder step by step.
3Append the remainder to form the transmitted codeword.
4Flip one bit in the codeword and re-run the division to observe detection.
5Test with two-bit and burst errors and note which ones slip through.
6Answer the closing questions about detection strength.

Tasks

Compute a CRC
Calculate the CRC for a given message and generator and form the codeword.
Verify an intact codeword
Divide an unmodified codeword and confirm the remainder is zero.
Detect a single error
Flip one bit and confirm the non-zero remainder flags corruption.
Explore limits
Find an error pattern the chosen generator fails to detect.

Self-check

The computed CRC matches the reference remainder.
The student explains the XOR division procedure.
Single-bit and appropriate burst errors are detected.
The student explains why some error patterns can escape detection.

Environment

bit manipulation consolestep-by-step divisionbit flip toolpreset generators