# Elias Delta Decoding in Python

• Difficulty Level : Expert
• Last Updated : 28 Nov, 2021

In this article, we are going to implement Elias Delta Decoding using python.

Peter Elias devised the Elias delta code, which is a universal system for encoding positive integers.

Syntax:

Elias Delta Encoding(X)= Elias Gamma encoding (1+floor(log2(X))) + Binary representation of X without MSB.

## Approach:

• Import required libraries and read the encoded binary string from the user.
• Read/Count the number of zero’s from the most significant bit until you see the first ‘1’  and store it in a variable named ‘L’

Syntax:

```L=0
while True:
if not x[L] == '0':
break
L= L + 1```
• Consider that ‘L’ as 1st digit and read L more bits and drop all bits until current L bit.
• Take out the remaining bits and prepend ‘1’ in the Most significant bit.

Syntax:

x.insert(0,’1′)

• Convert the final binary into integer which gives us the original number.

### Example:

Let the input encoded string is 01111

Step1: Read/Count the number of zeros from most significant bit until you see the first ‘1’ and store it in ‘L’ until you see the first ‘1’

In our case, L=1

Step2: Consider that ‘1’ as first digit read L more bits (1 more bit) and drop everything.

01111= 11

Step3: Takeout the remaining bits and prepend with ‘1’ in MSB.

111

Step4: Convert the final binary string into integer which gives us 7.

Below is the implementation.

Example 1: Example to produce Elias Delta Decoding value corresponding to some value.

## Python3

 `import` `math`` ` ` ` `def` `Elias_Delta_Decoding(x):``    ``x ``=` `list``(x)``    ``L ``=` `0``    ``while` `True``:``        ``if` `not` `x[L] ``=``=` `'0'``:``            ``break``        ``L ``=` `L ``+` `1``         ` `    ``# Reading L more bits and dropping ALL    ``    ``x ``=` `x[``2``*``L``+``1``:]  ``     ` `    ``# Prepending with 1 in MSB``    ``x.reverse()``    ``x.insert(``0``, ``'1'``)  ``    ``n ``=` `0``     ` `    ``# Converting binary to integer``    ``for` `i ``in` `range``(``len``(x)):  ``        ``if` `x[i] ``=``=` `'1'``:``            ``n ``=` `n``+``math.``pow``(``2``, i)``    ``return` `int``(n)`` ` ` ` `x ``=` `'01111'``print``(Elias_Delta_Decoding(x))`

Output:

`7`

Example 2: Example to produce Elias Delta Decoding value corresponding to some value.p

## Python

 `import` `math`` ` `def`  `Elias_Delta_Decoding(x):``    ``x ``=` `list``(x)``    ``L``=``0``    ``while` `True``:``        ``if` `not` `x[L] ``=``=` `'0'``:``            ``break``        ``L``=` `L ``+` `1``     ` `    ``# Reading L more bits and dropping ALL``    ``x``=``x[``2``*``L``+``1``:] ``     ` `    ``# Prepending with 1 in MSB``    ``x.insert(``0``,``'1'``) ``    ``x.reverse()``    ``n``=``0``     ` `    ``# Converting binary to integer``    ``for` `i ``in` `range``(``len``(x)): ``        ``if` `x[i]``=``=``'1'``:``            ``n``=``n``+``math.``pow``(``2``,i)``    ``return` `int``(n)`` ` `x ``=` `'0111100'``print``(Elias_Delta_Decoding(x))`

Output:

`28`

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