NUMBER SYSTEMS

Master Binary, Hex & More

DECIMAL (Base 10)

The number system we use every day. Uses digits 0–9. Each position represents a power of 10.

Example: 542 = 5×10² + 4×10¹ + 2×10⁰

BINARY (Base 2)

How computers think! Only uses 0 and 1. Each position represents a power of 2.

Example: 101 = 1×2² + 0×2¹ + 1×2⁰ = 5

HEXADECIMAL (Base 16)

Compact for programmers. Uses 0–9 and A–F (A=10 … F=15).

Example: 2F = 2×16¹ + 15×16⁰ = 47

OCTAL (Base 8)

Uses digits 0–7. Sometimes used in digital systems.

Example: 37 = 3×8¹ + 7×8⁰ = 31

🔄 Conversion Methods

Learn step-by-step how to convert between different number systems. Choose a conversion type below to see instructions and examples.

📤 Converting FROM Decimal
1
Divide by Target Base
Divide your decimal number by the target base (2, 8, or 16).
2
Record the Remainder
Write the remainder; it becomes a digit of your answer.
3
Repeat with Quotient
Use the quotient as the new number; continue until it’s 0.
4
Read Bottom to Top
Read remainders from last to first.
Example: 25 → Binary
25 ÷ 2 = 12 r 1
12 ÷ 2 = 6 r 0
6 ÷ 2 = 3 r 0
3 ÷ 2 = 1 r 1
1 ÷ 2 = 0 r 1

Answer: 11001
📥 Converting TO Decimal
1
Identify the Base
Know if the source is base 2, 8, or 16.
2
Number the Positions
From right to left: 0, 1, 2, …
3
Calculate Each Term
digit × base^position
4
Add Them Up
Sum the terms to get decimal.
Example: 1A3₁₆ → Decimal
1×16² + 10×16¹ + 3×16⁰ = 256 + 160 + 3 = 419
🔄 Converting Between Non-Decimal Bases
1
Convert to Decimal
Use the “To Decimal” method.
2
Convert from Decimal
Use the “From Decimal” method to the target base.
3
Shortcuts
Binary↔Hex group by 4 bits; Binary↔Octal group by 3 bits.
4
Practice
Start two-step; add shortcuts later.
Example: FF₁₆ → Binary
Answer: 11111111₂
Shortcut: F = 1111; FF = 11111111

🛠️ Interactive Learning Tools

🎲 Random Number Explorer

42

Click the number to see a new random value!

🔧 Live Converter

Result will appear here

📋 Quick Reference Guide

Hex Letters
A=10, B=11, C=12
D=13, E=14, F=15
Powers of 2
2⁰=1, 2¹=2, 2²=4
2³=8, 2⁴=16, 2⁵=32
Powers of 8
8⁰=1, 8¹=8, 8²=64
8³=512, 8⁴=4096
Powers of 16
16⁰=1, 16¹=16
16²=256, 16³=4096
Binary Groups
4 bits = 1 hex digit
3 bits = 1 octal digit
Common Values
15 = F₁₆ = 17₈
255 = FF₁₆ = 377₈
Max Values
4 bits: 15 (F)
8 bits: 255 (FF)
16 bits: 65535 (FFFF)
Binary Patterns
1111 = F₁₆
1010 = A₁₆
1100 = C₁₆