The Elias gamma code is a universal code that is used to encode a sequence of positive integers. It is developed by Peter Elias. It is most useful when the upper-bound of integers cannot be determined beforehand.
Formula:
Elias Gamma Coding=Unary(1+floor(log2(x)))+Binary representation of ‘x’ without MSB
Example: Let’s consider an example where we want to decode 0001001,
Apply Step 1: Count the number of '0's from MSB until you reach the first '1' and store the count in K. In our example(0001001) K=3 Apply Step 2: Read 3 more bits including the first '1'=1001 Apply Step 3: Convert the final binary into integer which gives us the original number. Decimal(1001)=9
Stepwise Implementation
Step 1: Count the number of ‘0’s from MSB until you reach the first ‘1’ and store the count in K.
# define the function def Elias_Gamma_Decoding(x):
# convert to list
x = list (x)
# initialize k to 0
K = 0
while True :
# check if k is not 0 in through
# list index
if not x[K] = = '0' :
break
# increment k value
K = K + 1
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Step 2: Consider that ‘1’ as the first digit and read ‘K’ more bits from the current ‘1’
x = x[K: 2 * K + 1 ] # Reading K more bits from '1'
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Step 3: Convert the final binary into an integer which gives us the original number.
# Converting binary to integer for i in range ( len (x)):
if x[i] = = '1' :
n = n + math. pow ( 2 , i)
return int (n)
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Below is the complete implementation of the above approach.
# import the math module import math
# function def Elias_Gamma_Decoding(x):
x = list (x)
K = 0
while True :
if not x[K] = = '0' :
break
K = K + 1
# Reading K more bits from '1'
x = x[K: 2 * K + 1 ]
n = 0
x.reverse()
# Converting binary to integer
for i in range ( len (x)):
if x[i] = = '1' :
n = n + math. pow ( 2 , i)
return int (n)
# value input x = '0001001'
# call the function print (Elias_Gamma_Decoding(x))
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Output:
9