Editing Arithmetic coding (section)

===Encoding and decoding: example===
[[Image:Arithmetic encoding.svg|400px|thumb|right|A diagram showing decoding of 0.538 (the round dot) in the example model. The region is divided into subregions proportional to symbol frequencies, then the subregion containing the point is successively subdivided in the same way.]]
Consider the process for decoding a message encoded with the given four-symbol model. The message is encoded in the fraction 0.538 (using decimal for clarity, instead of binary; also assuming that there are only as many digits as needed to decode the message.)

The process starts with the same interval used by the encoder: <nowiki>[0,1)</nowiki>, and using the same model, dividing it into the same four sub-intervals that the encoder must have. The fraction 0.538 falls into the sub-interval for NEUTRAL, <nowiki>[0, 0.6)</nowiki>; this indicates that the first symbol the encoder read must have been NEUTRAL, so this is the first symbol of the message.

Next divide the interval <nowiki>[0, 0.6)</nowiki> into sub-intervals:
* the interval for NEUTRAL would be <nowiki>[0, 0.36)</nowiki>, ''60% of <nowiki>[0, 0.6)</nowiki>''.
* the interval for POSITIVE would be <nowiki>[0.36, 0.48)</nowiki>, ''20% of <nowiki>[0, 0.6)</nowiki>''.
* the interval for NEGATIVE would be <nowiki>[0.48, 0.54)</nowiki>, ''10% of <nowiki>[0, 0.6)</nowiki>''.
* the interval for END-OF-DATA would be <nowiki>[0.54, 0.6)</nowiki>, ''10% of <nowiki>[0, 0.6)</nowiki>''.

Since 0.538 is within the interval <nowiki>[0.48, 0.54)</nowiki>, the second symbol of the message must have been NEGATIVE.

Again divide our current interval into sub-intervals:
* the interval for NEUTRAL would be <nowiki>[0.48, 0.516)</nowiki>.
* the interval for POSITIVE would be <nowiki>[0.516, 0.528)</nowiki>.
* the interval for NEGATIVE would be <nowiki>[0.528, 0.534)</nowiki>.
* the interval for END-OF-DATA would be <nowiki>[0.534, 0.540)</nowiki>.

Now 0.538 falls within the interval of the END-OF-DATA symbol; therefore, this must be the next symbol. Since it is also the internal termination symbol, it means the decoding is complete. If the stream is not internally terminated, there needs to be some other way to indicate where the stream stops. Otherwise, the decoding process could continue forever, mistakenly reading more symbols from the fraction than were in fact encoded into it.