# The Shorter The Better

Alice and Bob wants to send a binary number (base 2) with 2400 digits to Chris. However, the internet speed is ridiculously slow and transmit such a long number can take forever. In order to shorten the length of the number, each of them propose a plan :

Alice: we should convert the number to base 64.
Bob: we should convert the number to base 16.

Let the number generated by Alice and Bob be $$A$$ and $$B$$ respectively, and $$d(x)$$ denote the number of digits in $$x$$.

Which option best describe the value of $$\dfrac{d(A)}{ d(B)}$$?

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