# Definition:Check Digit

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## Definition

A **check digit** is a digit or other symbol used as an aid to identifying whether a mistake has been made transmitting a codeword.

It is calculated from the symbols in the codeword itself, and appended to the codeword as an extra symbol.

If a mistake is made transmitting the codeword, the **check digit** will then be incompatible with the rest of the contents of the codeword, and reveal that a transmission error is present.

## Sources

- 1996: John F. Humphreys:
*A Course in Group Theory*... (previous) ... (next): Chapter $6$: Error-correcting codes - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**check digit** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**check digit**