Toolzie

Base Converter

Enter a value in any field to see it converted to the other bases.

How to Use the Binary, Decimal & Hex Converter

Enter number in any base (binary, decimal, hex, octal). All conversions show instantly as you type.

Essential for programmers and students. Convert between computing number systems without memorizing tables.

Frequently Asked Questions

Bases?

Binary (base 2), Decimal (base 10), Hexadecimal (base 16), Octal (base 8).

Hex uses?

Memory addresses, color codes (#FF5733), compact binary representation.

Large numbers?

Yes, handles well for typical computing use.

Why binary?

Computers use on/off (1/0) states; understanding binary helps programming, networking, hardware.

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Number systems: decimal, binary, hex

Humans use decimal (base 10): digits 0-9, position values are powers of 10. Computers use binary (base 2): digits 0-1, position values are powers of 2. Hexadecimal (base 16) is a shorthand for binary: digits 0-9 plus letters A-F, position values are powers of 16. One hex digit equals exactly four binary digits. So the binary 11111111 (8 digits) is FF in hex (2 digits) — much easier to read.

Why programmers use hex

Hex is everywhere in programming: memory addresses (0x7FFE3A2B), colors (#FF5733 is RGB 255, 87, 51), character codes (0x41 is ASCII 'A'), bit flags (0x04 means the third bit), hash values (MD5 hashes are 32 hex chars), and MAC addresses (00:1A:2B:3C:4D:5E). Every developer needs to read hex occasionally, and converting to binary reveals the underlying bit patterns.

Quick conversion tricks

To convert binary to hex: group the binary digits in fours from the right (pad with leading zeros if needed), then convert each group. 11010110 → 1101 0110 → D6. To convert hex to decimal: multiply each digit by its position value (16^0, 16^1, 16^2, etc.) and sum. D6 = 13×16 + 6 = 208. To convert decimal to hex: divide by 16 repeatedly, noting remainders. 208 / 16 = 13 remainder 0 → 13 is D, so D6. Our converter does all this for you.

About This Tool

Convert numbers instantly between binary, decimal, and hexadecimal with the Toolzie Number Base Converter. Essential for programming, electronics, computer science students, and anyone working with low-level data.

How to Use

  1. Enter a number in any of the three fields: binary, decimal, or hexadecimal.
  2. The other two fields update automatically as you type.
  3. Use the copy button to grab any result.
  4. Clear the fields to start a new conversion.

Frequently Asked Questions

What is hexadecimal used for?

Hex is used extensively in programming, web colours (e.g. #FF5733), memory addresses, and colour codes in design tools.

How do I convert binary to decimal?

Enter your binary number (e.g. 1010) in the binary field and the decimal value (10) will appear instantly.

Can I convert negative numbers?

The converter handles standard unsigned integers. For signed/two's complement, manual adjustment is needed.

What is the largest number it can convert?

It supports numbers up to 64-bit integers (up to 18,446,744,073,709,551,615 in decimal).