Binary to Decimal Converter
Convert between binary, decimal, and hexadecimal instantly. Three-way bidirectional number base converter.
Binary / Decimal / Hex Converter
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The binary to decimal converter handles three-way conversions between binary (base 2), decimal (base 10), and hexadecimal (base 16). Enter a value in any of the three fields and the other two update instantly. It supports any 32-bit unsigned integer (0 to 4,294,967,295). Binary is the fundamental representation of all digital data — computers store and process everything as sequences of 0s and 1s. Hexadecimal is a compact representation of binary that appears constantly in computing: HTML colour codes (#FF5733), memory addresses (0x7FFF), MAC addresses, and file byte viewers all use hex. Understanding how to move between these number bases is a fundamental skill for anyone studying computer science or working with low-level systems. This converter also shows binary values with bit grouping (spaces every 4 bits) for readability — so 11001010 appears as 1100 1010, making it much easier to count bits and verify values.
How to Use the Binary to Decimal Converter
The Binary to Decimal Converter is designed to give you an accurate answer in seconds. Follow these steps:
- 1Select the input format using the pill buttons: Binary, Decimal, or Hexadecimal
- 2Enter your value in the input field
- 3Click Convert to see the equivalent values in all three formats
- 4Results show binary, decimal, and hexadecimal simultaneously
No account or sign-up required. All calculations run locally in your browser — nothing is stored or transmitted to any server.
How It Works
Decimal = Σ(bit × 2^position)
All three number systems are positional notation — digits represent different values based on their position from right to left: Decimal (base 10): each position is a power of 10. 345 = 3×100 + 4×10 + 5×1. Binary (base 2): each position is a power of 2. 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11 decimal. Hexadecimal (base 16): each position is a power of 16. Uses digits 0-9 then A-F (A=10, B=11, ..., F=15). Conversion: Binary → Decimal uses Σ(bit × 2^position). Decimal → Binary uses repeated division by 2, reading remainders from bottom to top. Hex is often treated as shorthand for binary — each hex digit maps exactly to 4 binary bits (a nibble).
Frequently Asked Questions
How do I convert binary to decimal?
Multiply each binary digit by the power of 2 corresponding to its position, then sum the results. Positions count from 0 at the right. Example: 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11. For quick mental conversion, the position values from right are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512... Add up the values where you see a 1 bit.
How do I convert decimal to binary?
Divide the number by 2 repeatedly, recording the remainder at each step, until the quotient is 0. Read the remainders from bottom to top. Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1. Reading remainders bottom to top: 1101. Verify: 1101 = 8+4+0+1 = 13. The converter handles this instantly for any value up to 4,294,967,295.
What is hexadecimal used for in computing?
Hexadecimal is used wherever binary needs to be compact and readable. HTML colour codes (#FF5733) encode red (FF=255), green (57=87), blue (33=51) in 6 hex digits that would be 24 binary digits. Memory addresses (0x00FF1234) use hex for readability. File hex editors show raw bytes as hex pairs. IP address components, MAC addresses, and error codes all use hex. Each hex digit encodes exactly 4 binary bits, making hex the natural shorthand for binary.
What is the largest number this converter handles?
This converter handles 32-bit unsigned integers: 0 to 4,294,967,295 (decimal), 0 to FFFFFFFF (hex), 0 to 11111111 11111111 11111111 11111111 (binary). 32 bits is the standard data width for many computing contexts — IPv4 addresses are 32-bit, and many processor registers are 32-bit. For 64-bit values (up to 18,446,744,073,709,551,615), a specialised big-integer tool is needed.
Is the binary to decimal converter free?
Yes — completely free with no sign-up needed. Enter a value in any of the three fields for an instant conversion. Supports all three number bases with input validation and bit grouping for readability. All conversions run in your browser.