Information coding systems revision notes

Character form of a decimal digit

A decimal digit can represent either a numerical value or a character. These are not the same thing. For example, the pure binary representation of the value 7 is the binary form of the number seven. The character "7", however, must be represented by a character code assigned by a coding system. The code for the character is therefore not automatically the same as the pure binary representation of the value.

This distinction matters when processing data. If a value is needed for arithmetic, it should be interpreted as a number. If the symbol is being stored or displayed as text, it should be interpreted as a character. Treating a character code as though it were the number it represents can produce incorrect calculations.

ASCII and Unicode

ASCII is a character coding system. It assigns codes to character data so that computers can store, process and communicate characters. Unicode is also a character coding system, but it was introduced because a wider range of characters was needed than could be represented conveniently by the earlier ASCII system. Unicode supports character data from many writing systems and provides a common way of representing a much broader collection of characters.

The important distinction is that a coding system maps characters to codes; it does not change a character into its numerical meaning. A digit character remains text unless a program converts it into a numeric value.

Error checking and correction

Error-control techniques add or calculate information that can be used to identify whether data has changed.

Parity bits

A parity bit is an extra bit added to a group of bits. With even parity, the parity bit is selected so that the total number of 1s is even. With odd parity, it is selected so that the total number of 1s is odd. The receiver counts the 1s and checks whether the required rule is satisfied. If it is not satisfied, an error is detected. A parity check does not, by itself, identify every possible error pattern or necessarily show which bit is wrong.

Majority voting

A value can be sent more than once. The receiver compares the copies and chooses the value that occurs most often. For example, if three received copies of a bit are 1, 1 and 0, majority voting selects 1. This can correct a single differing copy when the majority is still correct, but it adds repeated data and can fail if the incorrect value is received by the majority.

Checksums

A checksum is calculated from the data, using an agreed calculation, and the resulting value is stored or transmitted with the data. The receiver performs the same calculation on the received data and compares its result with the received checksum. A mismatch indicates that the data may have been changed. A matching checksum does not prove that every possible error is absent, because different data can sometimes produce the same checking result.

Check digits

A check digit is an extra digit calculated from the other digits in an identifier or number. When the identifier is entered or received, the check-digit calculation is repeated. If the calculated result does not agree with the supplied check digit, an error is detected. A check digit is particularly associated with checking digit strings, whereas a checksum is a calculated checking value for a block of data.

Common errors

Do not say that the character "7" is the same as the binary number 7. Do not claim that parity can correct any error: it is mainly used to detect whether a parity rule has been broken. Do not confuse majority voting with a checksum; majority voting compares repeated copies, while a checksum compares calculated values. A check digit is not the whole identifier; it is the additional digit used for checking.