How to convert negative numbers to binary?

Negative numbers are represented in binary using Two's Complement. First, convert the positive version of the number to binary. Then, invert all the bits (change 0 to 1 and 1 to 0). Finally, add 1 to the inverted result. The Most Significant Bit (MSB) will always be 1 for negative numbers.

What is the maximum value of a 32-bit integer?

A signed 32-bit integer has a maximum value of 2,147,483,647 and a minimum of -2,147,483,648. An unsigned 32-bit integer uses all bits for magnitude and caps out identically at 4,294,967,295.

Is my data sent to a server?

No. All conversions run 100% in your browser. No numbers or values are transmitted anywhere.

What is the difference between binary, octal, decimal, and hexadecimal?

Binary (base 2) uses digits 0-1 — the native language of computers. Octal (base 8) uses 0-7 — common in Unix permissions. Decimal (base 10) uses 0-9 — the human standard. Hexadecimal (base 16) uses 0-9 and A-F — widely used in memory addresses, colors, and encoding.

What is two's complement?

Two's complement is the standard way computers represent negative integers in binary. To negate a number: flip all bits, then add 1. For example, -1 in 8-bit two's complement is 11111111 (255 unsigned). This representation makes arithmetic circuits simpler.

Why is hexadecimal used in programming?

Each hex digit represents exactly 4 binary bits, making hex a compact human-readable representation of binary data. Memory addresses, color values (#FF5733), byte values, and bitmasks are all naturally expressed in hex.

What is a custom base conversion?

Any integer base from 2 to 36 is supported. Base 36 uses digits 0-9 and letters A-Z, producing compact representations of large numbers — used in URL shorteners and ID generation.

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About the Number Base Converter

Programmers constantly work across number bases — binary in bitwise operations, hex in memory addresses and color values, octal in Unix permissions. Converting between them mentally is error-prone. This tool converts between binary, octal, decimal, hexadecimal, and any custom base from 2 to 36, with two's complement support for signed integers.

Common use cases

Hex ↔ Decimal

Convert memory addresses, color values, and byte sequences between hex and decimal for debugging and documentation.

Binary Bitwise

Visualize bitmasks, flags, and bitwise operations in binary. See exactly which bits are set in a permission mask or status register.

Octal Permissions

Convert Unix chmod octal values (755, 644) to binary to understand exactly which permission bits are set for owner, group, and others.

Two's Complement

Convert signed integers to their two's complement binary representation — essential for understanding how CPUs represent negative numbers.

Pipeline

Chmod Calculator — convert octal permission values to symbolic notation.
Color Converter — convert hex color values to RGB and other formats.

Frequently asked

Is my data sent to a server?: No. All conversions run 100% in your browser. No numbers or values are transmitted anywhere.
What is the difference between binary, octal, decimal, and hexadecimal?: Binary (base 2) uses digits 0-1 — the native language of computers. Octal (base 8) uses 0-7 — common in Unix permissions. Decimal (base 10) uses 0-9 — the human standard. Hexadecimal (base 16) uses 0-9 and A-F — widely used in memory addresses, colors, and encoding.
What is two's complement?: Two's complement is the standard way computers represent negative integers in binary. To negate a number: flip all bits, then add 1. For example, -1 in 8-bit two's complement is 11111111 (255 unsigned). This representation makes arithmetic circuits simpler.
Why is hexadecimal used in programming?: Each hex digit represents exactly 4 binary bits, making hex a compact human-readable representation of binary data. Memory addresses, color values (#FF5733), byte values, and bitmasks are all naturally expressed in hex.
What is a custom base conversion?: Any integer base from 2 to 36 is supported. Base 36 uses digits 0-9 and letters A-Z, producing compact representations of large numbers — used in URL shorteners and ID generation.

Free Online Hex, Binary, Decimal & Octal Base Converter