Developer Tool

Number Base Converter

Type a value into any box below and the other formats will instantly update in real-time. Supports Decimal, Binary, Hexadecimal, and Octal formats flawlessly.

Converting...

Base 10 Decimal (Dec)

Invalid decimal number.

Base 2 Binary (Bin)

Only 0 and 1 are allowed.

Base 16 Hexadecimal (Hex)

Invalid hex characters.

Base 8 Octal (Oct)

Only numbers 0-7 are allowed.

Text ASCII String

Invalid characters for matching base values.

Custom Base

Invalid values for this selected base.

Copied!

Bit Length

Byte Length

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How it works

This tool instantly translates numbers between six distinct formats simultaneously. Type a valid number in any field, and it will be cross-converted perfectly in real-time. It uses JavaScript's native BigInt parsing to handle massive mathematical strings without breaking, decoding ASCII text via UTF-16, and iterating customizable Radix bounds from Base-2 to Base-36.

Dec (10)

Bin (2)

Hex (16)

Oct (8)

ASCII

Base-N

About Number Systems

Welcome to our free Number System Converter. This tool allows developers, students, and engineers to instantly convert values between multiple complex formats in complete synchronization:

Decimal (Base 10): The standard numeric system. Uses digits 0 through 9.
Binary (Base 2): Internal computer processing data. Uses only 0 and 1.
Hexadecimal (Base 16): Often used in computer memory and CSS colors. Uses digits 0-9 and letters A-F.
Octal (Base 8): Originally used for Unix file permissions. Uses digits 0-7.
ASCII String: Translates raw numeric sequences directly into plain English text characters based on the UTF-16 specification mappings.
Custom Radix (Base-N): A specialized mathematical processor letting you manually clamp the algorithm to restrict sequences anywhere from Base-2 (binary) up to Base-36 (alphanumeric).

All algorithm computation occurs strictly client-side instantly in your browser. Absolutely zero data is sent to external servers, protecting your privacy and yielding maximum speed.

Number Systems in Computing - A Practical Guide

Computers store and process everything in binary, but developers work across decimal, hexadecimal, and octal every day. From memory addresses and color codes to permissions and bitwise logic, number system conversion is a core technical skill.

Hex is compact and readable for machine-level values, octal appears in Unix permissions, and decimal remains human-friendly for business logic. Switching quickly between systems helps with debugging, API work, networking, and embedded development.

This converter is built for real-world developer workflows, giving instant conversion across binary, octal, decimal, and hexadecimal for both learning and production troubleshooting.

💻 Developer's Number System Cheat Sheet

Binary in Hardware

Bit flags, registers, and digital circuits use binary at the lowest level. Understanding bit positions helps when working with masks and low-level protocols.

Hex in Web Dev

Hex is used in CSS colors, hashes, and memory dumps. Two hex digits map exactly to one byte, which makes binary data easier to read.

Octal in Permissions

Linux file permissions use octal shorthand like 644 and 755. Each octal digit maps to three permission bits (rwx).

Signed vs Unsigned

Signed integers use the highest bit as sign. Overflow behavior changes by type and language, so conversions help verify edge cases safely.

Number Converter quick facts

Bases:

Decimal, binary, hexadecimal, octal, ASCII text and any base from 2 to 36

Prefixes:

0x, 0b and 0o are accepted, and negative numbers

Precision:

Exact big-number maths

How to use the Number Converter

Type a value into any field.
The other systems update instantly.
Copy the value you need.

Number systems

Computers use binary (base 2), programmers often write hexadecimal (base 16) and some systems use octal (base 8). This converter also handles any base from 2 to 36 and ASCII text.

Worked example

The decimal number 255 is 11111111 in binary, FF in hexadecimal and 377 in octal. 0xFF, 0b11111111 and 0o377 are the same value with prefixes.

Big numbers

It uses exact big-integer arithmetic, so very large values do not lose digits as they would in ordinary floating-point maths.

Frequently asked questions about the Number Converter

What number systems does this tool support?

The tool supports Binary (base-2), Octal (base-8), Decimal (base-10), and Hexadecimal (base-16) conversions. You can convert between any combination of these systems.

What is binary?

Binary is a base-2 number system that uses only the digits 0 and 1. It is the foundation of computing, because digital circuits have two states, on and off. For example, binary 1010 equals 10 in decimal, which you can check with this converter.

What is hexadecimal used for?

Hexadecimal, or base 16, is used in programming for memory addresses, colour codes such as #FF0000 for red, and for showing binary data compactly. Each hex digit stands for four bits, which makes long binary values much easier to read and compare.

Can I convert large numbers?

Yes. The tool uses big-integer arithmetic, so large values stay exact instead of being rounded the way ordinary JavaScript numbers are. You can convert numbers well beyond 64 bits between binary, octal, decimal and hexadecimal without losing any digits.

Is this tool free?

Yes. The Number Converter is free to use with no sign-up and no limit on use. It converts between bases in your browser, so the numbers you enter are not sent to or stored on our servers.

Why do computers use binary instead of decimal?

Binary maps directly to electronic states, on and off. Hardware with two states is simpler, cheaper and more reliable to build than hardware that has to tell ten voltage levels apart, so computers use binary internally and show decimal to people.

Why is octal used in Linux permissions?

Each octal digit represents three bits, which matches the three permission flags read, write and execute. One digit each for the owner, group and others gives a short code such as 755 or 644 that is quick to type and easy to read.

Can this tool help with networking calculations?

Yes. IPv4 addresses, subnet masks and CIDR ranges depend on binary bit boundaries, so converting between decimal and binary helps you see which bits belong to the network and which to hosts, and to check that a range is valid.

What is two's complement?

Two's complement is the standard way computers store negative integers in binary. It lets the same circuit add and subtract numbers, because a negative value is represented so that adding it works like subtracting. It is why signed ranges are lopsided, such as −128 to 127.

Does conversion affect numeric precision?

Converting an integer between bases does not change its value, because only the notation differs. Precision problems come from floating-point numbers, which cannot store some decimals exactly. This tool is for whole numbers, so the result is exact.

Can I use this for interview preparation?

Yes. Converting between binary, hexadecimal and octal, working with bit operations and understanding signed ranges are common topics in software and embedded systems interviews. Practise by converting by hand first, then check your answer with the tool.

How do I convert binary to decimal?

Type the binary number into the binary field and the decimal value appears at once. For example, 1010 is 10. To do it by hand, add the powers of two for each digit that is 1: 8 + 2 = 10.

Free, no sign-up. Reviewed 15 October 2026 by the Gopafy team. See all free tools.