Binary Representation

All values in a computer are represented using binary, the base-2 counting system using digits 0 and 1.

A bit is a single binary digit. A nibble is a 4-bit sequence. A byte is an 8-bit sequence.

A binary number of $n$ bits can represent numbers between $0$ and $2^n-1$. As such, in order to represent a number $x$ using unsigned binary representation, $\lceil lo{g}_2(x)\rceil$ bits are required.

Representing Negative Numbers §

Negative Numbers can be represented using two’s complement, where the most significant bit represents $-2^n$ rather than $2^n$. This allows us to represent numbers between $-2^n$ and $2^n-1$ (inclusive) with $n$ bits. Addition of numbers in two’s complement works in the same way as unsigned addition.