MA19.FM.31

Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.31
Apply error-detecting codes and error-correcting codes to determine accuracy of information processing.

Unpacked Content

Knowledge

Students know:

How to perform modular arithmetic.
Binary numbers

Skills

Students are able to:

Determine if a code such as a zip code or a UPC code contains an errors.
Determine if a code can be corrected.
Identify situations where errors should be corrected or just detected.

Understanding

Students understand that:

Data that is transferred can contain errors and codes can be used to detect errors.
Error correcting codes can be used to increase the likelihood of accuracy.

Vocabulary

Check digits
Information digits
Barcodes
UPC codes
Binary digits or bits
Substitution error
Transposition error
Maximum likelihood decoding
Hamming distance, minimum distance

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