Binary (base-2) uses only two digits: 0 and 1. It is the fundamental number system used by computers, as digital circuits have two states: on (1) and off (0).

Hexadecimal (base-16) uses digits 0-9 and letters A-F. It is commonly used in computing to represent binary data more compactly (1 hex digit = 4 binary digits).

Octal (base-8) uses digits 0-7. It was historically used in computing because 3 binary digits map to 1 octal digit. It is still used in Unix file permissions.

Number Base Converter

Convert between Binary, Octal, Decimal, Hexadecimal and custom bases (2-36)

Enter Number

Value

Base

Results

Binary (Base 2)

11111111

Octal (Base 8)

377

Decimal (Base 10)

255

Hexadecimal (Base 16)

Base Systems Explained

Binary (Base 2): Uses 0, 1. Each digit is a power of 2. Used by computers.

Octal (Base 8): Uses 0-7. Used in Unix file permissions (e.g., chmod 755).

Decimal (Base 10): Uses 0-9. The everyday number system.

Hexadecimal (Base 16): Uses 0-9, A-F. Used for colors (#FF0000), memory addresses.

How Number Base Conversion Works

A number base (or radix) determines how many unique digits are used to represent numbers. To convert between bases, first convert to decimal (base 10), then to the target base.

Converting to Decimal

Multiply each digit by its positional power of the base and sum. E.g., binary 1101 = 1x8 + 1x4 + 0x2 + 1x1 = 13.

Converting from Decimal

Repeatedly divide by the target base and collect remainders in reverse order. E.g., 13 in binary: 13/2=6 R1, 6/2=3 R0, 3/2=1 R1, 1/2=0 R1 → 1101.

Frequently Asked Questions

What is binary?

Binary (base-2) uses only 0 and 1. Computers use it because circuits have two states: on and off.

What is hexadecimal?

Hexadecimal (base-16) uses 0-9 and A-F. 1 hex digit = 4 binary digits, making it compact for representing binary data.

How do you convert decimal to binary?

Divide by 2 repeatedly and record remainders in reverse. Example: 13 → 1101.

What is octal used for?

Octal is used in Unix/Linux file permissions (chmod 755) and some legacy computing contexts.

Go deeper

Read the SnoopTool guide behind this tool

The calculator gives you the number. These SnoopTool guides explain the method, the assumptions and the decision — with worked examples, data tables and FAQs.

Best Free Online Unit Converters (2026)Free online unit converters for length, weight, temperature, speed, area, volume, energy and data storage. Instant, accurate, no sign-up. Plus the...

Browse all SnoopTool guides →

Answers, not just a number

Short, exact answers to the questions people ask alongside this tool — the number first, then the working.

All 67 SnoopTool answersOne question per page, with the working shown

For teams, not just visitors

Want this calculator on your own site?

We build the calculators on SnoopTool as embeddable widgets in your branding, wired to your own lead form — the same maths, your colours, your domain, your leads. Tell us which one and we will send back a working demo you can put in front of your team.