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POHow many digits in this base?
 

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  1. POHow many digits in this base?
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    <p>The problem is to derive a formula for determining number of digits a given decimal number could have in a given base.</p> <p>For example: <strong>The decimal number 100006 can be represented by 17,11,9,8,7,6,8 digits in bases 2,3,4,5,6,7,8 respectively.</strong></p> <p>Well the formula I derived so far is like this : (log10(num) /log10(base)) + 1.</p> <p>in C/C++ I used this formula to compute the above given results.</p> <p><code>long long int size = ((double)log10(num) / (double)log10(base)) + 1.0;</code></p> <p>But sadly the formula is not giving correct answer is some cases,like these :</p> <pre><code>Number 8 in base 2 : 1,0,0,0 Number of digits: 4 Formula returned: 3 Number 64 in base 2 : 1,0,0,0,0,0,0 Number of digits: 7 Formula returned: 6 Number 64 in base 4 : 1,0,0,0 Number of digits: 4 Formula returned: 3 Number 125 in base 5 : 1,0,0,0 Number of digits: 4 Formula returned: 3 Number 128 in base 2 : 1,0,0,0,0,0,0,0 Number of digits: 8 Formula returned: 7 Number 216 in base 6 : 1,0,0,0 Number of digits: 4 Formula returned: 3 Number 243 in base 3 : 1,0,0,0,0,0 Number of digits: 6 Formula returned: 5 Number 343 in base 7 : 1,0,0,0 Number of digits: 4 Formula returned: 3 </code></pre> <p>So the error is by 1 digit.I just want somebody to help me to correct the formula so that it work for every possible cases.</p> <p><strong>Edit :</strong> As per the input specification I have to deal with cases like 10000000000, i.e 10^10,I don't think log10() in either C/C++ can handle such cases ? So any other procedure/formula for this problem will be highly appreciated.</p>
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    1. COIt looks like you're having an off by one issue on the edge cases.
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    2. COI used to do this in school on my calculator; I forget the formula I used back then but when I was taught the `log()` function I was, like, wow this is much simpler!
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    3. COyeah, but unable to figure out the required modification.
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