Ever wondered how a computer stores a negative number? It doesn't have a tiny "minus" symbol inside the hardware. 🤖

Instead, it uses a clever mathematical ritual called Two’s Complement .

The "Flip and Add" Recipe 🍳

If you want to store -5 in an 8-bit char , the computer doesn't just put a sign in front. It follows these three steps:

Start with the Positive: Write 5 in binary $\rightarrow$ 00000101

Flip the Bits: Change every 0 to 1 and every 1 to 0 $\rightarrow$ 11111010

Add 1: Add a binary 1 to that result $\rightarrow$ 11111011

Boom! That’s exactly how -5 sits in your memory.

Why do we do this? (The Genius Part) 🧠

Why not just change the first bit to 1 and call it a day?

Because with Two's Complement , addition and subtraction work perfectly without any extra "brain power" from the CPU. When you add 5 ( 00000101 ) and -5 ( 11111011 ), the bits naturally add up to 0 (after a small overflow).

It turns subtraction into simple addition!…