You're thinking about a sign and magnitude representation, which is not how integers are represented in a modern computer. The modern version is two's compleme

You're thinking about a sign and magnitude representation, which is not how integers are represented in a modern computer. The modern version is two's complement. It still has a sign bit, but negating a number involves more than just changing the sign bit since the representation is modular. https://en.wikipedia.org/wiki/Two%27s_complement https://en.wikipedia.org/wiki/Two%27s_complement https://en.wikipedia.org/wiki/Modular_arithmetic https://en.wikipedia.org/wiki/Modular_arithmetic