How do you convert binary to decimal?

Multiply each binary bit by 2 raised to its positional index: `Decimal = Σ(bit × 2^position)`. For example, binary 1011 = `(1×8) + (0×4) + (1×2) + (1×1) = 11`.

How do you convert binary to hexadecimal?

Group the binary digits into 4-bit nibbles from right to left, then replace each 4-bit group with its corresponding hex digit (0-9, A-F). For example, 1010 1111 = AF.

What does hexadecimal base 16 mean?

Hexadecimal uses 16 unique symbols: numbers 0 through 9, followed by letters A (10), B (11), C (12), D (13), E (14), and F (15).

Can this tool convert negative binary numbers?

Yes, the converter supports signed two's complement representation for 8-bit, 16-bit, 32-bit, and 64-bit integer values.

What is octal base 8 used for?

Octal (digits 0–7) groups binary into 3-bit sequences and is widely used in Linux file permissions (e.g., chmod 755 = rwxr-xr-x).

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Number Base Converter (Binary, Decimal, Hex & Octal)

Convert numbers between Binary, Octal, Decimal, and Hexadecimal radix bases instantly.

TL;DR: Number Base Converter transforms integers between Base-2 (Binary), Base-8 (Octal), Base-10 (Decimal), Base-16 (Hexadecimal), and arbitrary custom bases (2 to 36).

Value

From base

How Do You Convert Decimal to Binary and Hexadecimal?

To convert Decimal to Binary, repeatedly divide by 2 and record the remainders in reverse order. To convert Decimal to Hexadecimal, repeatedly divide by 16, mapping remainders 10–15 to letters A–F. For example, decimal 255 becomes binary 11111111 and hex FF.

How to Use the Number Base Converter

Our Number Base Converter performs high-precision mathematical operations directly in your browser with zero latency and complete client-side privacy.

Enter a number into any radix input field (Decimal, Binary, Hex, or Octal).
Specify source and target base systems (supports Base 2 through Base 36).
Observe the real-time automatic synchronization across all base representations.
Review the bit breakdown, byte alignment (8/16/32-bit), and two's complement.
Copy the encoded numerical string for software development or hardware programming.

Mathematical Formula & Equations

Converts numerical values across Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16).

\[ N_{10} = \sum d_i \cdot b^i, \quad N_{10} \xrightarrow{\text{repeated division}} N_{\text{target}} \]

Calculation Example

Decimal $255_{10} = 11111111_2 = 377_8 = \text{FF}_{16}$.

100% Client-Side Privacy & Data Security

All calculations, amortization schedules, variables, and sensitive numerical datasets execute 100% locally in your web browser memory. Your financial, medical, and personal values are never transmitted, logged, or uploaded to any external server.

Frequently Asked Questions

: Multiply each binary bit by 2 raised to its positional index: `Decimal = Σ(bit × 2^position)`. For example, binary 1011 = `(1×8) + (0×4) + (1×2) + (1×1) = 11`.
: Group the binary digits into 4-bit nibbles from right to left, then replace each 4-bit group with its corresponding hex digit (0-9, A-F). For example, 1010 1111 = AF.
: Hexadecimal uses 16 unique symbols: numbers 0 through 9, followed by letters A (10), B (11), C (12), D (13), E (14), and F (15).
: Yes, the converter supports signed two's complement representation for 8-bit, 16-bit, 32-bit, and 64-bit integer values.
: Octal (digits 0–7) groups binary into 3-bit sequences and is widely used in Linux file permissions (e.g., chmod 755 = rwxr-xr-x).

Cite This Calculator

Need to reference this online calculator in a financial proposal, academic paper, blog post, or classroom curriculum? Copy a citation below.

NexLove.org. (2026). Number Base Converter [Online Calculation Tool]. https://nexlove.org/tools/number-base-converter

“Number Base Converter.” NexLove.org, 2026, nexlove.org/tools/number-base-converter.

NexLove.org (2026) Number Base Converter. Available at: https://nexlove.org/tools/number-base-converter (Accessed: 2026).

@misc{nexlove_number_base_converter,
  title = {Number Base Converter},
  author = {{NexLove.org}},
  year = {2026},
  url = {https://nexlove.org/tools/number-base-converter}
}

Embed This Tool

Add the live Number Base Converter to your own website with this snippet — it loads the real, working calculator in an iframe.

<iframe src="https://nexlove.org/embed/number-base-converter.html" width="100%" height="600" style="border:1px solid #e2e8f0;border-radius:12px" title="Number Base Converter — NexLove.org" loading="lazy"></iframe>

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