Number Systems & Encoding

Math(s)

Start with familiar decimal numbers, then learn how computers represent values in binary, octal, and hexadecimal. Apply the same ideas to Linux permissions and character encoding through worked examples and practice.

DecimalBinaryOctalHexadecimalPracticeASCII

Start with Decimal →

Your Learning Path

Follow the order below. Each lesson includes a worked example and a checkpoint; practice activities help you apply what you have learned.

Decimal
Start with familiar digits and learn how position changes a digit's value.
Binary
Build a byte, convert in both directions, and explain the range 0–255.
Octal
Group bits in threes and use octal to understand Linux permissions.
Hexadecimal
Group bits in fours and read compact values used in logs, colours, and memory.
Practice
Explore a switchboard, then solve binary, hexadecimal, and permission challenges.
ASCII
Connect characters to numbers and distinguish ASCII from Unicode and UTF-8.

Practice

Demos And Games

Explore the patterns, check your own answers, and apply octal to permission scenarios at your own pace.

Open practice area

Explore: Binary Demo

Toggle bits freely and watch decimal, binary, and hexadecimal update together.

Build the Byte

Build a target number, check your answer, and use a hint when you need one.

Hex Switch Game

Match hexadecimal targets with bits, check each nibble, and try another challenge.

Permissions Calculator

Connect nine permission bits to octal and symbolic modes, then solve file-access scenarios.

Why It Matters

Strong Foundations Make Technical Topics Easier

Binary explains how machines store and process information. Decimal keeps the human view readable. Octal groups bits in threes for permission modes. Hexadecimal compresses long binary values into a format that engineers can scan quickly. ASCII connects numeric codes to visible characters and control symbols.

Once these ideas click, networking, scripting, memory analysis, file formats, and protocol analysis all become easier to reason about.

Quick Reference

Decimal, Binary, Octal, Hex

Dec	Bin	Oct	Hex
0	0000	0	0
1	0001	1	1
2	0010	2	2
3	0011	3	3
4	0100	4	4
5	0101	5	5
6	0110	6	6
7	0111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F