Mathematics for hacking

This content set explains mathematical concepts that are needed for, or worth knowing when, making hacks.
Note that, to avoid confusion as much as possible and to keep things easy to understand, mathematical rigor is not a particular concern here. The explanations are only as rigorous as practical use requires.

<Note>
Each page in this content set uses MathJax to display formulas. If your browser settings block script execution, the formulas on the pages will not be displayed correctly.

Contents of this section

Binary and hexadecimal
Explains binary and hexadecimal, the number systems most commonly used in computers.

Boolean algebra
Explains Boolean algebra (logic algebra) and logical operations.

Trigonometric functions
Explains trigonometric functions and their applications.

Matrix transformations
Explains the basics of matrix operations and the coordinate transformations that use them (scaling and rotation).

Fixed-point numbers
Explains how to represent and calculate with fixed-point numbers, which let a CPU that can only handle integers deal with fractions.

Logarithms and decibels
Explains the basics of logarithms and the decibel, which expresses ratios of volume.

Pitch and frequency
Explains the relationship between pitch and frequency, twelve-tone equal temperament, and how they correspond to DSP pitch values.

Sampling and digital filters
Explains the basics of digital audio processing, such as sampling, aliasing, FIR/IIR filters and frequency response.