Problem 44971. Convert base 10 to base x (2-16)

Created by David Hill

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Convert input number(s) (cell array of character arrays) in base 10 to base x (2 through 16). Output should be a cell of character arrays. Compute output to a maximum of 50 decimal places.
For example: Convert 1376.5 base 10 into base 2.
answer: {'10101100000.1'}

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Last Solution submitted on May 16, 2024

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Tim on 7 Oct 2019

The exact solution for 38.59 in base 15 is the repeating decimal 28.8cb3b3b3b3b3b3b3..., which means the given solution 28.8cb3b3b3b3b42d4a contains some "junk digits" at the end; it's not really fair to ask for those junk digits as opposed to any others. Also, it looks like trailing zeros are supposed to be removed, but some of the base 2 solutions contain a trailing zero.

David Hill on 10 Oct 2019

Tim,
You are correct. Thanks for the comment. Fixed the errors you detected as well as a few others. Should be good now.

Alfonso Nieto-Castanon on 24 Aug 2020

Hi David, nice problem but there are still I believe a few precision issues remaining in the testsuite. For example the number "7285.4" as a float can only be precisely encoded up to ~1e-12 (since eps(7285.4)=9.0949e-13), so its base-15 representation cannot be defined with 16-decimal places (as that would require >1e-19 precision). I believe perhaps you could fix that simply entering the input decimal numbers using chars, which would avoid any limited-precision issues? (or by relaxing the requirements to fewer decimal places)

David Hill on 25 Sep 2020

Changed and fixed the problem. Input is now cell array of character arrays.

Rafael S.T. Vieira on 25 Oct 2020

It seems the precision issues were indeed fixed. :)

David Hill on 25 Oct 2020

Not sure what the problem was, but I changed #6 and added some additional test problems.

Rafael S.T. Vieira on 26 Oct 2020

Oh, the problem was with my algorithm, sorry. I am indeed using python's long int (for multiplication of large integers), but I was relying on str2num for some operations (which apparently introduced floats back in my code). After removing it, it worked out fine.

PS: This new update knocked out some wrong solutions (including some of mine). Awesome. :)

William on 23 Apr 2021

In each of test3, test4 and test5, there is a number with a decimal fractional part 0.0962. It appears as thought it was converted in each case as though the fractional part was 0.962.

David Hill on 30 Jun 2022

Corrected tests 3,4,5. Answers should all be good now.

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Problem 44971. Convert base 10 to base x (2-16)

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Problem 44971. Convert base 10 to base x (2-16)

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