How do I convert decimal to binary?

Repeatedly divide the decimal number by 2 and record the remainders. Reading remainders from bottom to top gives the binary representation. For example, 13 = 8+4+1 = 1101 in binary. The tool does this automatically — enter a decimal number and the binary value appears immediately.

Why is hexadecimal used in programming?

Hexadecimal is a compact representation of binary data. Each hex digit (0-F) represents exactly 4 bits, so an 8-bit byte is two hex digits (e.g., 0xFF = 11111111). This makes hex much more readable than raw binary for memory addresses, color codes, and bytecode.

What is two's complement?

Two's complement is the standard way computers represent negative integers in binary. To negate a number, invert all bits and add 1. For example, in 8-bit: 5 is 00000101, so -5 is 11111010 + 1 = 11111011.

What is octal used for?

Octal (base 8) is used in Unix/Linux file permissions. Permissions like chmod 755 or 644 are octal numbers where each digit represents three permission bits (read=4, write=2, execute=1).

Can this tool handle large numbers?

Yes. The tool handles arbitrarily large integers. Very large numbers are displayed in full without truncation.

All Tools›Algorithm›

Binary / Hex Converter

Free · No Server

Live-sync between Decimal, Binary, Hex and Octal — with step-by-step explanations.

Number Base Converter

Binary · Decimal · Hexadecimal · Octal — live synced

Bit Width

Signed

DecimalBase 10

BinaryBase 2

HexadecimalBase 16

OctalBase 8

What is Binary Converter?

The Binary Converter on AiTechWorlds converts numbers between binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8) instantly. Number base conversions come up constantly in computing: reading memory addresses in hex, understanding bit flags in binary, converting color codes, debugging network protocols, and studying computer science. Converting between bases manually involves successive division or multiplication and is error-prone for large numbers. This tool converts in all directions simultaneously — enter a number in any base and see all other base representations update instantly. It also handles signed two's complement representation for negative numbers in binary. All conversion runs in your browser with no server call. AiTechWorlds provides this as an instant reference for developers, students, and hardware engineers.

How to Use

1
Enter a number
Type a number in any of the four base fields: binary, decimal, hex, or octal.
2
See all conversions
All other base fields update instantly with the equivalent values.
3
Handle negatives
Toggle two's complement mode to work with negative numbers in binary.
4
Copy any result
Click the copy icon next to any field to copy that representation.

Common Use Cases

CS students learning binary and hexadecimal for coursework
Embedded systems developers reading memory addresses and register values in hex
Frontend developers converting color hex codes to decimal RGB values
Network engineers working with IPv4 addresses and subnet masks in binary
Developers debugging bitwise operations by checking binary representations

Key Features

Simultaneous conversion between binary, decimal, hex, and octal
Two's complement negative number support
Arbitrary precision for large numbers
Copy individual base representations
Clear input validation with error messages for invalid digits
100% browser-based
Grouped digit display for readability (e.g., 1010 1101)

🔒

100% Private — No Server Required

All processing happens directly in your browser. No data is uploaded, stored, or transmitted to any server.

Frequently Asked Questions

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AiTechWorlds

What is Binary Converter?

How to Use

Enter a number

Type a number in any of the four base fields: binary, decimal, hex, or octal.

See all conversions

All other base fields update instantly with the equivalent values.

Handle negatives

Toggle two's complement mode to work with negative numbers in binary.

Copy any result

Click the copy icon next to any field to copy that representation.

Common Use Cases

CS students learning binary and hexadecimal for coursework

Embedded systems developers reading memory addresses and register values in hex

Frontend developers converting color hex codes to decimal RGB values

Network engineers working with IPv4 addresses and subnet masks in binary

Developers debugging bitwise operations by checking binary representations

Key Features

Simultaneous conversion between binary, decimal, hex, and octal

Two's complement negative number support

Arbitrary precision for large numbers

Copy individual base representations

Clear input validation with error messages for invalid digits

100% browser-based

Grouped digit display for readability (e.g., 1010 1101)