$1.$

Let $x$ be the number to translate: find $p,$ the largest power of $2$ smaller equal to $x$

$p=|\frac{logx}{(log2)}|,n=p$

$2.$

How many times does $2^n$ fit into the number $x?$

$1$ if $2^{n}x,0$ otherwise

$3.$

Set $x$ to the remainder of the number not yet translated.

$4.$

While the remainder $x$ is not zero, reduce $n$ by $1$ and go back to step $2.$

Task: How would you modify the algorithm to incorporate a for loop?

Problem requests a fixed number of mantissa bits: $10$

Can we simplify the algorithm if we know the number of mantissa bits to use?

How would steps $1-4$ need to be changed to convert the algorithm's while loop into a for loop?