Is it possible to calculate the value after overflow?

Question

I understand that if 1 is added to INT_MAX it will overflow and we will get the negative maximum. It is connected in a cycle. In the code below can I calculate the value after overflow.

#include<bits/stdc++.h>
using namespace std;
int main()
{
    int a = 100000;
    int b = 100000;
    int c = a*b;
    cout<<c;
    return 0;
}

Output: 1410065408

Is it possible to calculate this number. How is multiplication happening internally in this case

Answer 1

I understand that if 1 is added to INT_MAX it will overflow and we will get the negative maximum.

You've misuderstood. If 1 is added to INT_MAX, then the behaviour of the program is undefined.

can I calculate the value after overflow.

After signed integer overflow, the behaviour of the program is undefined, so doing anything is pointless.

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If you were to use unsigned integers, then the result of any operation will be congruent with the "mathematically correct" result modulo M where M is the number of representable values i.e. max+1.

For example if unsigned is 32 bits, 100'000u * 100'000u would be 10'000'000'000 which is congruent with 1'410'065'408 modulo M=4'294'967'295. You can find the representable congruent value by repeatedly subtracting or adding M until the result is representable.

Another example of modular arithmetic that you may be familiar with is the clock. If you add 123 hours to a 24 hour clock starting from midnight, then what time will it show? If you add 10'000'000'000 hours to a 4'294'967'295 hour clock, what time will it show?