How to Represent Signed Integers?

So far, we learned how to represent positive integers in different bases. However, how do we represent signed integers (including negative ones) using base $2$?

We'll see 4 such ways: (1) sign & magnitude, (2) 1's complement, (3) 2's complement, and (4) biased system.

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When using sign & magnitude, you use the leftmost bit to represent the sign ($1$ for 'negative' and $0$ for 'positive',) while the rest of the bits contain the number itself.

Example: $101101_2$ is negative $01101_2$, which is $-13_{10}$. The leftmost $1$ means it's a negative integer.

We can even add two integers together! We'll see a couple of examples on the following slide. Binary numbers are added just as decimal numbers are: we'll use column addition to show how everything works.