What is binary (base 2)?

Binary is a base-2 number system using only digits 0 and 1. Each position represents a power of 2. For example, binary 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal. Computers use binary internally to represent all data.

What is hexadecimal (base 16)?

Hexadecimal is a base-16 number system using digits 0-9 and letters A-F (representing 10-15). It's commonly used in programming because each hex digit represents exactly 4 binary digits (bits). For example, hex FF = 255 in decimal = 11111111 in binary.

How do I convert binary to hexadecimal?

Group binary digits into sets of 4 from right to left, then convert each group to its hex equivalent. For example: 11111111 → 1111 1111 → F F → FF. Add leading zeros if needed to complete groups of 4.

How do I convert decimal to binary?

Repeatedly divide the number by 2 and record the remainders. Read the remainders from bottom to top. For example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1. Result: 1101.

What is octal (base 8)?

Octal is a base-8 number system using digits 0-7. Each octal digit represents exactly 3 binary digits. It was popular in older computing systems. For example, octal 17 = 1×8 + 7×1 = 15 in decimal = 1111 in binary.

What bases can I convert between?

This calculator supports conversion between any bases from 2 to 36. Common bases include: Binary (2), Octal (8), Decimal (10), and Hexadecimal (16). For bases above 10, letters A-Z represent values 10-35.

Binary, Hex & Base Converter

Convert numbers between Binary (base 2), Octal (base 8), Decimal (base 10), Hexadecimal (base 16), and any base from 2-36. See step-by-step conversion process.

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Decimal (Base 10)

Binary (Base 2)

1111 1111

Hex (Base 16)

Octal (Base 8)

377

8-bit Visualization

128

Input Values

Input Value

From Base

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Custom From Base

To Base

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Custom To Base

Show Steps

Yes

lightbulb Tips

•Binary is base-2 (0,1)
•Hex is base-16 (0-9, A-F)
•Octal is base-8 (0-7)

table_chart Quick Reference

Dec Bin Hex Oct

0000000 1000111 81000810 151111F17 16100001020 25511111111FF377

How to Use This Calculator

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Enter Your Number

Type the number you want to convert. Use 0x, 0b, or 0o prefixes for auto-detection.

input

Select Source Base

Choose the base of your input number, or use auto-detect.

output

Choose Target Base

Select which base(s) to convert to - single base or all common bases.

visibility

View Results

See your converted number with optional step-by-step explanation.

The Formula

To convert any base to decimal, multiply each digit by the base raised to its position power, then sum all values. For example, binary 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10.

Value = Σ(digit × base^position)

lightbulb Variables Explained

digit Each digit in the number (0-9, A-Z)
base The number system base (2, 8, 10, 16, etc.)
position Position from right, starting at 0

tips_and_updates Pro Tips

Use prefixes to quickly enter numbers: 0b for binary, 0o for octal, 0x for hexadecimal

Each hexadecimal digit equals exactly 4 binary digits - useful for quick mental conversion

When converting large numbers, work in groups of digits for easier calculation

Remember: A=10, B=11, C=12, D=13, E=14, F=15 in hexadecimal

Binary is fundamental - all other conversions go through binary internally in computers

Number Base Converter - Binary, Hex, Octal, Decimal

Convert numbers instantly between binary, hexadecimal, octal, decimal, and any base from 2 to 36. Essential tool for programmers, students, and anyone working with different number systems.

Binary to Decimal Conversion

Binary (base 2) uses only 0 and 1. To convert binary to decimal, multiply each digit by 2 raised to its position power (starting from 0 on the right) and sum the results. Example: 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.

Hexadecimal Conversion

Hexadecimal (base 16) uses 0-9 and A-F. It's popular in programming because each hex digit represents exactly 4 binary bits. FF in hex = 255 in decimal = 11111111 in binary.

Why Different Number Bases?

Computers use binary internally. Hexadecimal provides a compact way to represent binary data. Octal was used in older systems. Decimal is human-friendly. Each base has its purpose in computing and mathematics.