Binary

A number system that uses Base 2 compared to the normal decimal system that uses Base 10
The only possible values are 0 and 1, so all numbers are comprised of a bunch of 0’s and 1’s
A number in binary of length k and can represent $2^{k} - 1$ values
Each digit going from right to left is 2 to the power of the digits position. If there’s a one in that spot, add that to your decimal number, otherwise go to the next.
Here’s a better example.
Binary is used very commonly in computer science, so it is important to know
A common representation of binary numbers starts with 0bNUMBER
- The number above would be, 0b10011011

Hexadecimal

To aid in expressing binary values, we use Hexadecimal
Hexadecimal is very similar to binary, except it uses base 16 instead of base 2.
The values for Hex are - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Hex offers two main advantages
- More compact than binary, allowing for shorter representations
- Since sixteen is a power of two, conversion between binary and hex is fairly easy
Hex basically groups each group of four bits as a single hex digit
Example of hexadecimal encoding, converting binary string to hexadecimal
Hexadecimal numbers are most often written as 0xNUMBER to denote that the number is in Hex and not anything else.
- As an example, the number from figure 3.5 above is written as 0xDEC90949