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I was studying about redundancy bits and I came across this equation and table. Now I am not sure how they get the "minimum number" redundancy bits column.

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So how would they get maximum and minimum number of redundancy bits r require to correct n bits of data

Bic B
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1 Answers1

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By definition: it's the smallest integer value of r that satisfies the stated equation, 2ʳ ≥ n + r + 1.

I don't see anything about "maximum number of redundancy bits."

Matt Ball
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    Now, if you're asking how to _solve_ that equation - not a question for SO. – Matt Ball Aug 22 '12 at 15:52
  • http://wiki.answers.com/Q/What_is_the_minimum_number_of_redundant_bits_that_error-correcting_code_requires_for_data_units_that_are_5_bits_long have a look at this question, isnt the answer suppose to be 3 bits? – Bic B Aug 22 '12 at 15:55
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    @AmberArroway `n=5` and `r=3` does not satisfy the inequality in the text, as it's not true that `8 >= 9`. So for `n=5` the "smallest integer such that" the inequality holds is `4`, as given both in the table and that link. – AakashM Aug 22 '12 at 15:58
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    No, the answer is not supposed to be 3 bits. Fill in the equation for `r=3` and `n=5`. It is not satisfied for those values. `2³ ≥ 5 + 3 + 1` but `8` is not greater than or equal to `9`. – Matt Ball Aug 22 '12 at 15:59
  • @AmberArroway for 10 bits, you need to solve this: `2ʳ - r ≥ 11`. By trial and error, it's easy to find that the smallest value of `r` that satisfies that equation is ... `4`. – Matt Ball Aug 22 '12 at 16:00