Numbers in code

In this lesson we will learn how numbers function inside of programming languages!

Numbers in c++

In c++ if we look at an integer int a = 178, it is stored as a binary number, so : 1011 0010, but there is another thing to consider!

It is actually stored as: 0000 0000 0000 0000 0000 0000 1011 0010

That is because int is a 32-bit data structure.
That means that every number stored will have exactly 32 bits, which are either 0 or 1

Since the first bit determines the sign(+, or -), and we have to account for the number 0, the largest number we can store is 2^31 - 1, or 2147483647

Integers larger than 32 bits?

What happens when we try to store a number that can't fit into 32 bits?

For example 2^31 = 2147483648?

Let's see:

int main(){

	int a = 2147483647;

	int b = a + 1;

	cout<<a<<'\n';
	cout<<b;
}

Output:
2147483647
-2147483648

The minus is not a typo! Here is what happened:

We had a = 0111 1111 1111 1111 1111 1111 1111 1111

When we add one to it, we get b = 1000 0000 0000 0000 0000 0000 0000 0000
Since the first bit stores the sign, this is -2147483648

Our numbers just went in a circle! a was the largest positive number we can store, and b became the smallest negative number we can store.

This phenomenon is called integer overflow! It should be avoided at all costs!

How to store numbers >2^31?

If we want to store larger numbers (which is common in competitive programming), we need to use a larger integer type : long long, which is a 64-bit data structure,

So the largest number we can store is 2^63-1

Note:
Since long long is twice the size of int, it takes up twice as much space, so only use it when you need it!

Long long is enough for 99% of cases, but if we need to store even bigger numbers, then we have to store them as strings, and implement operations with them manually (more on this later)