Unary coding: Difference between revisions

Revision as of 17:34, 31 May 2025

Revision as of 17:38, 31 May 2025

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==Symmetric unary codes==

The following set ofsymmetric unary codes arecan symmetricbe read and instantaneously decoded in either direction:

{| class="wikitable" style="text-align: center;"

! n (strictly positive) !! Unary code

!Alternative

!n (non-negative)

!n (strictly positive)

|-

| 1 || 1

|0

|0

|1

|-

| 2 || 00

|11

|1

|2

|-

| 3 || 010

|101

|2

|3

|-

| 4 || 0110

|1001

|3

|4

|-

| 5 || 01110

|10001

|4

|5

|-

| 6 || 011110

|100001

|5

|6

|-

| 7 || 0111110

|1000001

|6

|7

|-

| 8 || 01111110

|10000001

|7

|8

|-

| 9 || 011111110

|100000001

|8

|9

|-

| 10 || 0111111110

|1000000001

|9

|10

|-

| colspan="4" | ...

|}

These symmetric codes can be read and instantaneously decoded in either direction.

== Canonical unary codes ==

For unary values where the maximum is known, one can use canonical unary codes that are of a somewhat numerical nature and different from character based codes. It involves starting with numerical '0' or '-1' ( <math>\operatorname2^{n} - 1\,</math>) and the maximum number of digits then for each step reducing the number of digits by one and increasing/decreasing the result by numerical '1'.

{| class="wikitable"