How Does Binary Numbers and Base Systems as Fast as Possible Work?

Binary numbers and base systems are just special kinds of number languages that computers use to count really fast.

Imagine you have only two types of blocks: red and blue. You can build towers with them, like this:

• 1 red = 1
• 1 blue = 0

If you stack them up, like red-blue-red, it means 101 in binary, which is the same as 5 in regular counting.

Computers think with switches, they're either on or off. That’s just like your light switch at home: on = 1, off = 0. So instead of using all the numbers from 0 to 9 (like we do), computers use only two: 1 and 0.

This is called a base-2 system, because it uses powers of 2:

• 1st position = $2^0$ = 1
• 2nd position = $2^1$ = 2
• 3rd position = $2^2$ = 4

So 101 means:

1 × 4 + 0 × 2 + 1 × 1 = 5

Just like how we count with fingers (base-10), computers count super fast by using only two choices, and that’s why they’re so quick!