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Suppose that a mathematician is developing a program to multiply extremely large (prime) numbers. Further suppose...

Suppose that a mathematician is developing a program to multiply extremely large (prime) numbers. Further suppose that the mathematical decides to perform such multiplications in base-2. Briefly explain why this is a bad idea.

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Answer #1

It is a bad idea due to the following reasons:

(i) The base-2 representation of any number is the most complicated ones. For large prime numbers the representation will be complicated.

(ii) The base-2 representation of any number will require a specific number of bits for the representation. But the numbers are prime and extremely large. So, storing the result will require a greater number of bits than what is used for the representation. In many cases, it will cause overflow.

(iii) There will be a lot of steps involved in the process. So, the program will have a very high time complexity.

(iv) The space complexity of the program will be very high.

(v) There will be requirement for additional memory spaces.

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