Binary & Hexadecimal
Understand number systems — convert between binary, decimal, and hexadecimal with interactive tools.
Category: Math
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Step 1 of 4
Step 1: Number Systems
Computers store everything as binary (base 2) — just 0s and 1s. Developers also use hexadecimal (base 16) as a compact way to represent binary data.
Decimal (Base 10) — what you already know
Each digit is a power of 10:
| Place | 103 | 102 | 101 | 100 |
|---|---|---|---|---|
| Value | 1000 | 100 | 10 | 1 |
| Example | 1 | 3 | 5 | 7 |
1357 = (1 × 1000) + (3 × 100) + (5 × 10) + (7 × 1)
Binary (Base 2) — how computers think
Each digit (called a bit) is a power of 2. Only two digits: 0 and 1.
| Place | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 |
|---|---|---|---|---|---|---|---|---|
| Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| Example | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
10101010 = 128 + 32 + 8 + 2 = 170 in decimal
Hexadecimal (Base 16) — compact binary
Uses digits 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15). Each hex digit represents exactly 4 bits.
| Place | 163 | 162 | 161 | 160 |
|---|---|---|---|---|
| Value | 4096 | 256 | 16 | 1 |
| Example | 1 | A | 3 | F |
0x1A3F = (1 × 4096) + (10 × 256) + (3 × 16) + (15 × 1) = 6719 in decimal
About This Lab
Computers think in binary (base 2), but developers often work with hexadecimal (base 16) too. In this lab, you'll learn how these number systems work, practice converting between them, and build intuition for how data is represented at the lowest level.
How It Works
- Read each step's explanation of number systems
- Use the interactive converter to experiment
- Practice bit manipulation visually
- Complete the quiz to test your understanding