Number System Explorer

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Number System Converter

Enter a number:

Input Base: Decimal (Base 10) Binary (Base 2) Hexadecimal (Base 16)

Output Base: Binary (Base 2) Decimal (Base 10) Hexadecimal (Base 16)

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Place Value Breakdown

Binary Bits Explorer

Click on the bits to toggle them and see the decimal value change!

Decimal value: 0

Decimal to Binary Converter

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Conversion Challenge

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Decimal System (Base 10)

The decimal system is what we use every day. It uses 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Each position in a number represents a power of 10:

• 1's place (10⁰ = 1)
• 10's place (10¹ = 10)
• 100's place (10² = 100)
• 1000's place (10³ = 1000)

Example:

The number 357 means:

3 × 100 + 5 × 10 + 7 × 1

3 × 10² + 5 × 10¹ + 7 × 10⁰

300 + 50 + 7 = 357

Binary System (Base 2)

The binary system only uses 2 symbols: 0 and 1. It's the language of computers!

Each position represents a power of 2:

• 1's place (2⁰ = 1)
• 2's place (2¹ = 2)
• 4's place (2² = 4)
• 8's place (2³ = 8)
• 16's place (2⁴ = 16)

Example:

Binary 1011 means:

1 × 8 + 0 × 4 + 1 × 2 + 1 × 1

1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰

8 + 0 + 2 + 1 = 11 decimal

Hexadecimal System (Base 16)

Hexadecimal uses 16 symbols: 0-9 and A-F, where:

A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

Each position represents a power of 16:

• 1's place (16⁰ = 1)
• 16's place (16¹ = 16)
• 256's place (16² = 256)

Example:

Hexadecimal 2AF means:

2 × 256 + 10 × 16 + 15 × 1

2 × 16² + A × 16¹ + F × 16⁰

512 + 160 + 15 = 687 decimal

Why Different Number Systems?

Decimal (Base 10)

Why we use it: Easy for humans because we have 10 fingers

Used for: Everyday counting, math, and most human calculations

Binary (Base 2)

Why we use it: Perfect for computers because electronic circuits have two states (on/off)

Used for: All data inside computers, from text to images to programs

Hexadecimal (Base 16)

Why we use it: Compact way to represent binary (every 4 binary digits = 1 hex digit)

Used for: Computer memory addresses, color codes (like #FF00CC), and programming

Real-World Applications

Computer Memory

Memory addresses are often shown in hexadecimal because they can represent large binary values in fewer digits.

Web Colors

Colors on websites use hexadecimal: #FF0000 is red, #00FF00 is green, and #0000FF is blue.

Digital Logic

Computer circuits work with binary signals (on/off), which represent 1s and 0s in the binary system.

Welcome to the Number System Explorer! Click on the tabs to explore different features.