# Questions in Error correction codes

*label*Mathematics

*timer*Asked: Feb 3rd, 2019

*account_balance_wallet*$40

### Question Description

Here are some questions in Error Correction Codes,

Questions number 1 and 2 written in the pictures that written by hand , the other picture is showing the exercises that are required to solve question number 2,

Please I want you to make sure that you give me a 100% correct solutions,

And please illustrate all the steps of the solutions so I can understand every single step ,

I’m going to use this solutions to prepare for exam,

Here is the link of the textbook that you should use to solve the questions,

http://www.fen.bilkent.edu.tr/~franz/lect/codes.pdf

Thanks in advance

**Tags:**math mathematics codes coding code ISBN mathematical logic and information error correction http://www.fen.bilkent.edu.tr/~franz/lect/codes.pdf

## Tutor Answer

By the way here's the complete solution, with answer for 1st question also.

1)

Answer:

Let’s assume that a digit x of the ISBN number is in error. Let’s assume that the digit has been

modified to be x+r instead of just x.

Now, for the original ISBN number, this will hold:

(

)

(

)

)

(

[Distributive property of

modulus] [Equation A]

where n is integer between 1 and 9 (inclusive) which depends on the position of digit x in the ISBN

number, and C is the check-bit.

Now after the digit x has been altered, assuming that the error goes undetected, the check-bit must

still be valid,

(

(

))

[

(

)

(

)]

[Distributive

property of modulus]

(

)

(

)

(

)

[Distributive property of modulus] [Equation B].

Now let’s subtract equation A from equation B,

(

)

(

)

(

)

(

)

(

)

(

)

This means the number

must be a multiple of 11 for the modulu...

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