Number Base Converter 2025

Current Decimal Value

255

Binary: 11111111

Hex: FF

Octal: 377

Convert Number Base

Binary (Base 2)(0b)

Valid digits: 01

Octal (Base 8)(0o)

Valid digits: 01234567

Decimal (Base 10)()

Valid digits: 0123456789

Hexadecimal (Base 16)(0x)

Valid digits: 0123456789ABCDEF

Conversion Info

All Bases

Binary:0b11111111

Octal:0o377

Decimal:255

Hexadecimal:0xFF

Binary Conversion Steps

255 in decimal to binary:

255 ÷ 2 = 127 remainder 1

127 ÷ 2 = 63 remainder 1

63 ÷ 2 = 31 remainder 1

31 ÷ 2 = 15 remainder 1

15 ÷ 2 = 7 remainder 1

7 ÷ 2 = 3 remainder 1

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Read remainders from bottom to top: 11111111

Quick Number Presets

Programming Prefixes

Binary: 0b11111111

Octal: 0o377

Hex: 0xFF

Number Base Comparison Table

Decimal	Binary	Octal	Hexadecimal
0	0	0	0
1	1	1	1
2	10	2	2
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
32	100000	40	20
64	1000000	100	40
100	1100100	144	64
128	10000000	200	80
255	11111111	377	FF
256	100000000	400	100
1024	10000000000	2000	400

What is Number Base Conversion?

Number base conversion transforms numbers between different numeral systems: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Essential for computer science, programming, and digital electronics.

Our converter supports all major bases with real-time conversion and step-by-step explanations. Perfect for programmers, students, and anyone working with different number systems.

How to Use

1Enter number in any base (binary, octal, decimal, hex)
2All other bases update automatically in real-time
3View conversion steps to understand the process
4Copy programming prefixes (0x, 0b, 0o)
5Use quick presets for common numbers

Number Bases Explained

🔢 Binary (Base 2)

Digits: 0, 1 only

Used in: Computers, digital electronics

Prefix: 0b (e.g., 0b1010 = 10)

Example: 1101₂ = 13₁₀

💡 Each position represents power of 2

🔢 Octal (Base 8)

Digits: 0-7

Used in: Unix permissions, old computing

Prefix: 0o (e.g., 0o12 = 10)

Example: 17₈ = 15₁₀

💡 Each position represents power of 8

🔢 Decimal (Base 10)

Digits: 0-9

Used in: Everyday counting, math

Prefix: None (standard)

Example: 255₁₀ = 255

💡 The number system we use daily

🔢 Hexadecimal (Base 16)

Digits: 0-9, A-F

Used in: Colors, memory addresses, programming

Prefix: 0x (e.g., 0xFF = 255)

Example: FF₁₆ = 255₁₀

💡 Compact representation of binary

Number Base Conversion Examples

Decimal	Binary	Octal	Hexadecimal
0	0	0	0
1	1	1	1
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
32	100000	40	20
64	1000000	100	40
100	1100100	144	64
128	10000000	200	80
255	11111111	377	FF
256	100000000	400	100
1024	10000000000	2000	400

How to Convert Between Bases

Binary to Decimal

Method: Multiply each digit by 2^position

Example: 1011₂ to decimal

1×2³ + 0×2² + 1×2¹ + 1×2⁰

= 8 + 0 + 2 + 1

= 11₁₀

Decimal to Binary

Method: Divide by 2, track remainders

Example: 13₁₀ to binary

13 ÷ 2 = 6 remainder 1

6 ÷ 2 = 3 remainder 0

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Read up: 1101₂

Hexadecimal to Decimal

Method: Multiply each digit by 16^position

Example: 2F₁₆ to decimal

2×16¹ + F×16⁰

= 2×16 + 15×1

= 32 + 15

= 47₁₀

Binary ⇄ Hexadecimal

Method: Group binary in 4s

Example: 11010110₂ to hex

1101 0110

D 6

= D6₁₆

Programming Applications

💻 Common Use Cases

Binary: Bitwise operations, flags, permissions
Octal: Unix file permissions (chmod 755)
Hex: Color codes (#FF5733), memory addresses
IP Addresses: Converting between decimal & binary
Data Storage: Bytes, KB, MB calculations
Networking: Subnet masks, MAC addresses

🎨 Color Codes (Hex)

#FF0000 = Red (255,0,0)

#00FF00 = Green (0,255,0)

#0000FF = Blue (0,0,255)

#FFFFFF = White (255,255,255)

Frequently Asked Questions

1. How do I convert binary to decimal?

To convert binary to decimal, multiply each digit by 2 raised to its position power (from right, starting at 0) and sum the results.

Example: 1010₂ to decimal

1×2³ + 0×2² + 1×2¹ + 0×2⁰

= 1×8 + 0×4 + 1×2 + 0×1

= 8 + 0 + 2 + 0

= 10₁₀

2. Why is hexadecimal used in programming?

Hexadecimal is used because it's a compact way to represent binary data. Each hex digit represents exactly 4 binary digits (bits).

Key Advantages:

Shorter representation (FF vs 11111111)
Easy conversion to/from binary (4 bits = 1 hex)
Used in color codes, memory addresses, MAC addresses
1 byte = 2 hex digits (00 to FF = 0 to 255)

3. What are the programming prefixes for different bases?

Programming languages use prefixes to indicate number bases. This helps distinguish between different numeral systems.

Standard Prefixes:

Binary: 0b or 0B (e.g., 0b1010 = 10)

Octal: 0o or 0O (e.g., 0o12 = 10)

Hexadecimal: 0x or 0X (e.g., 0xA = 10)

Decimal: No prefix (e.g., 10)

Related Tools

QuikCalcTools

🔢 Advanced Base Converter

Convert Number Base

Conversion Info

Binary Conversion Steps

Quick Number Presets

Programming Prefixes

Number Base Comparison Table

What is Number Base Conversion?

How to Use

Number Bases Explained

🔢 Binary (Base 2)

🔢 Octal (Base 8)

🔢 Decimal (Base 10)

🔢 Hexadecimal (Base 16)

Number Base Conversion Examples

How to Convert Between Bases

Binary to Decimal

Decimal to Binary

Hexadecimal to Decimal

Binary ⇄ Hexadecimal

Programming Applications

💻 Common Use Cases

🎨 Color Codes (Hex)

Frequently Asked Questions

1. How do I convert binary to decimal?

2. Why is hexadecimal used in programming?

3. What are the programming prefixes for different bases?

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