Editing Truncated binary encoding (section)

==Example with ''n'' = 5==
For example, for the alphabet {0, 1, 2, 3, 4}, ''n'' = 5 and 2<sup>2</sup> ≤ ''n'' < 2<sup>3</sup>, hence ''k'' = 2 and ''u'' = 2<sup>3</sup> − 5 = 3. Truncated binary encoding assigns the first ''u'' symbols the codewords 00, 01, and 10, all of length 2, then assigns the last ''n'' − ''u'' symbols the codewords 110 and 111, the last two codewords of length 3.

For example, if ''n'' is 5, plain binary encoding and truncated binary encoding allocates the following [[Code word (communication)|codewords]]. Digits shown <del>struck</del> are not transmitted in truncated binary.
{| class="wikitable" style="text-align:center"
|-
! Truncated<br/>binary !!colspan=3| Encoding !! Standard<br/>binary
|-
|align=right| 0 ||bgcolor=silver| <del>0</del> || 0 || 0 ||align=left| 0
|-
|align=right| 1 ||bgcolor=silver| <del>0</del> || 0 || 1 ||align=left| 1
|-
|align=right| 2 ||bgcolor=silver| <del>0</del> || 1 || 0 ||align=left| 2
|-
|align=right| UNUSED ||bgcolor=silver| <del>0</del> ||bgcolor=silver| <del>1</del> ||bgcolor=silver| <del>1</del> ||align=left| 3
|-
|align=right| UNUSED ||bgcolor=silver| <del>1</del> ||bgcolor=silver| <del>0</del> ||bgcolor=silver| <del>0</del> ||align=left| 4
|-
|align=right| UNUSED ||bgcolor=silver| <del>1</del> ||bgcolor=silver| <del>0</del> ||bgcolor=silver| <del>1</del> ||align=left| 5/UNUSED
|-
|align=right| 3 || 1 || 1 || 0 ||align=left| 6/UNUSED
|-
|align=right| 4 || 1 || 1 || 1 ||align=left| 7/UNUSED
|}

It takes 3 bits to encode ''n'' using straightforward binary encoding, hence 2<sup>3</sup> − ''n'' = 8 − 5 = 3 are unused.

In numerical terms, to send a value ''x'', where 0 ≤ ''x'' < ''n'', and where there are 2<sup>''k''</sup> ≤ ''n'' < 2<sup>''k''+1</sup> symbols, there are ''u'' = 2<sup>''k''+1</sup> − ''n'' unused entries when the alphabet size is rounded up to the nearest power of two. The process to encode the number ''x'' in truncated binary is: if ''x'' is less than ''u'', encode it in ''k'' binary bits; if ''x'' is greater than or equal to ''u'', encode the value ''x'' + ''u'' in ''k'' + 1 binary bits.