The Shorter The Better

Computer Science Level 2

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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