How to represent a number in base 2³²?

Question

If I have some base 10 or base 16 number, how do I change it into base 2³²?

The reason I'm trying to do this, is for implementing BigInt as suggested by other members here Why to use higher base for implementing BigInt?

Will it be the same as integer (base 10) till 2³²? What will happen after it?

Answer 1

You are trying to find something of the form

a0 + a1 * (2^32) + a2 * (2^32)^2 + a3 * (2^32)^3 + ...

which is exactly the definition of a base-2³² system, so ignore all the people that told you that your question doesn't make sense!

Anyway, what you are describing is known as base conversion. There are quick ways and there are easy ways to solve this. The quick ways are very complicated (there are entire chapters of books dedicated to the subject), and I'm not going to attempt to address them here (not least because I've never attempted to use them).

One easy way is to first implement two functions in your number system, multiplication and addition. (i.e. implement BigInt add(BigInt a, BigInt b) and BigInt mul(BigInt a, BigInt b)). Once you've solved that, you will notice that a base-10 number can be expressed as:

b0 + b1 * 10 + b2 * 10^2 + b3 * 10^3 + ...

which can also be written as:

b0 + 10 * (b1 + 10 * (b2 + 10 * (b3 + ...

so if you move left-to-right in your input string, you can peel off one base-10 digit at a time, and use your add and mul functions to accumulate into your BigInt:

BigInt a = 0;
for each digit b {
    a = add(mul(a, 10), b);
}

Disclaimer: This method is not computationally efficient, but it will at least get you started.

Note: Converting from base-16 is much simpler, because 2³² is an exact multiple of 16. So the conversion basically comes down to concatenating bits.