For example, in base 10(999) => 3 digits and in base 2(1111100111) => 10 digits
Currently, I am using a table to estimate this computation, but it is limited to 15 digits in base 10 because JavaScript is restricted by MAX_SAFE_INTEGER. Please refer to the following table (run snippet to view it).
How can we expand this table up to 255 digits in base 10 using a formula?
const TDigits = document.querySelector('#T-Digits tbody')
, MaxDigits = Number.MAX_SAFE_INTEGER.toString().length
;
var x9 = '9';
for (let n=1; n < MaxDigits; n++)
{
let newRow = TDigits.insertRow(-1)
newRow.insertCell(0).textContent = n
newRow.insertCell(1).textContent = (x9-0).toString(2).length
newRow.insertCell(2).textContent = Math.ceil(Math.log2(Math.pow(10,n)))
x9 += '9';
}table { margin:1em}
table thead { background-color: cadetblue }
table td { text-align: center; padding: .2em .5em; border-bottom: 1px solid grey }<table id="T-Digits">
<caption>Max digits corresponding</caption>
<thead>
<tr><td>base 10</td> <td>base 2</td><td> log </td></tr>
</thead>
<tbody>
<tr><td>0</td> <td>1</td><td>1</td></tr>
</tbody>
</table>[edit] include Math.ceil(Math.log2(Math.pow(10,n))) from Jaromanda X, ;)