## Arithmetic Coding Solved Numerical for Exams | ECE Topics

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Today we have a lot of techniques and algorithms to be solved and prepared for the exams in colleges or universities. One of such technique or algorithm is the Arithmetic Coding Technique .This technique is quite  popular due to number of its pros. If you are preparing for college or university exams and belong to Electronic and Communication stream , this post will really help you as here are some of the basic  Arithmetic Coding solved Numerical that will be helpful while doing any relevant assignment or preparing for  mid terms .As we know , visual study has greater impact as compare to simple reading so we are also posting one of the video based on Arithmetic Coding College so as to clear any  kind of doubts that may arise .

## Arithmetic Coding Solved Numerical

We would suggest you to have a basic idea about what Arithmetic Coding is all about and what are its advantages over the other coding techniques . Student must be aware of using it over the others such as Huffman Coding. Let us start with the steps to solve Arithmetic Coding Numerical .

In simple, Arithmetic Coding varies with the Huffman Coding in a way that Arithmetic perform encoding the whole message or signal into a single number rather than separating it into the component symbols and changing each with the code.

### Steps to solve arithmetic coding numerical:

Here are the simple steps to start with in order to solve the coding numerical in a simple and easy way .

1. We have given source symbols with given probabilities (s1 : 0.5, s2: 0.2, s3: 0.2, s4: 0.1) with transmitted symbol as “abbc”.
2. Now, draw vertical line with upper and lower limits as 1 and 0 respectively.
3. Next step is to  divide this line in segment equal to number of given symbols (Mark points at line from lower limit 0 to 0.5, 0.5 to 0.7, 0.7 to 0.9, 0.9 to 1) as per the given probabilities.
4. Mark each segment with a, b, c and d starting from lower limit respectively.
5. Now as the first symbol is a (abbc), open the lower and upper limit as 0 and 0.5 respectively.
6. Take the difference of the upper limit and lower limit at step 5 ; 0.5 – 0 = 0.5
7. Multiply each given probability with the difference we get at step 6 and add this with the previous lower limit.
0.5 * 0.5 = 0.25 + 0.00 = 0.25
and 0.5 * 0.2 = 0.10 + 0.25 = 0.35
0.5 * 0.2 = 0.10 + 0.35 = 0.45
0.5 * 0.1 = 0.05 + 0.45 = 0.50 (which is upper limit for symbol a).
8. We will mark the opening with following (0, 0.25, 0.35, 0.45 and 0.50) and mark each segment with a, b, c, d respectively.
9. Now as for the next symbol is “b”, we will open the upper limit and lower limit f b as 0.35 and 0.25 respectively.
10. Follow the same step as 6,7 and 8 till we reach the last transmited symbol “c”.
11. The average of upper and lower value of “c” obtained by following this process is calculated.
b = (Upper Limit+Lower Limit) / 2 (0.319 for the given example)
12. This value of “b” is used for the decoding process.

## Arithmetic Coding Example

In below video you can find the best arithmetic coding tutorial with arithmetic coding solved example. You can easily follow the steps to solve arithmetic coding numerical and prepare the same for the test and exam.

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