Number Base Converter — Binary, Hex, Octal & Decimal

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How to Number Base Converter Online

1. 1

   Enter a number in the input field on the left — you can type it in decimal, hexadecimal, hex, octal, binary, or custom base format.

2. 2

   The tool auto-detects common prefixes: type '0xFF' for hex, '0b1010' for binary, or '0o377' for octal, or just enter a regular decimal number like '255'.

3. 3

   View instant conversions across all number bases simultaneously: decimal, binary, octal, and hexadecimal in the right panel.

4. 4

   Toggle 'Signed' mode to see two's complement representation for negative numbers across 8-bit, 16-bit, 32-bit, or 64-bit word widths.

5. 5

   Adjust bit width (8, 16, 32, or 64 bits) to see how the number would be stored in different integer types, with visual bit grid representation.

6. 6

   Click on individual bits in the bit grid to toggle them — the value updates in real-time, making it easy to understand binary representation and bitmasks.

7. 7

   Switch to 'IEEE 754' mode to inspect how floating-point numbers are stored as 32-bit single (binary32) or 64-bit double (binary64) precision values, including sign bit, exponent, and mantissa.

8. 8

   Use 'Batch' mode to convert multiple numbers at once by entering one per line with instant tabular conversion.

9. 9

   Copy any individual field value with the 'Copy' button, or use 'Copy All' (⌘⇧C) to copy all conversions at once.

Number Base Converter Features

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  Real-time bidirectional conversion: type in any field and see decimal, binary, octal, hexadecimal, and custom bases update instantly.

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  BigInt support for arbitrary precision — handles numbers with hundreds of digits without floating-point precision loss.

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  Auto-detection of standard programming prefixes (0x for hexadecimal, 0b for binary, 0o for octal) for seamless copy-pasting.

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  Two's complement visualization for signed integers, calculating exact binary masks and boundary overflows for 8, 16, 32, and 64-bit types.

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  Interactive bit grid: click any bit in the visual array to toggle its state and observe real-time value changes across all radices.

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  Configurable bit widths: 8-bit (uint8/int8), 16-bit (uint16/int16), 32-bit (uint32/int32), and 64-bit (uint64/int64) architectures.

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  Endianness toggle (big-endian/little-endian) for analyzing byte ordering in low-level network packets and binary memory dumps.

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  IEEE 754 floating-point inspector: decomposes floats into sign bit, biased exponent, normalized mantissa/significand, denormals, and NaN/Infinity states.

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  Custom radix support: convert to and from any positional numeral base between Base 2 and Base 36.

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  Batch conversion mode: process multi-line lists of memory addresses, hex dumps, or register values in parallel.

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  Client-side execution: all computations run locally in the browser runtime — zero network overhead, 100% data privacy.

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  Shareable state: input parameters and options are preserved in URL query parameters for reproducible sharing.

Supported Formats & Dialects

The Number Base Converter supports 5 syntax formats and dialects for accurate parsing and processing.

Standard Radix Conversion (Base 2–36)

Converts between binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), and arbitrary alphanumeric radices up to base 36 (using digits 0-9 and letters A-Z).

Two's Complement Signed Integer (8/16/32/64-bit)

Encodes signed negative integers into two-complement binary bitmasks and detects arithmetic overflow against fixed hardware integer width limits.

IEEE 754 Floating-Point Decomposition

Deconstructs standard 32-bit single-precision (binary32) and 64-bit double-precision (binary64) IEEE 754 floats into sign, biased exponent, and significand fields.

Interactive Bit Grid & Masking

Visual byte-by-byte bit array allowing interactive bit-flipping, bitwise masking visualization, and instant radix re-computation.

Batch Radix Processing

Parses multiline batches of hexadecimal memory offsets, binary byte streams, or decimal sequences into structured conversion tables.

Frequently Asked Questions

How does this converter handle arbitrary-precision numbers beyond JavaScript limits?

Standard JavaScript Numbers lose integer precision above Number.MAX_SAFE_INTEGER (2^53 - 1, or 9,007,199,254,740,991). Our number base converter leverages native BigInt arithmetic to process integers of arbitrary size—spanning hundreds or thousands of digits—without precision loss or floating-point rounding errors across all supported radices (Base 2 through Base 36).

How is two's complement calculated for signed negative numbers?

In two's complement arithmetic for an N-bit integer, a positive number is stored in standard binary. A negative number -X is represented by taking the binary form of X, inverting all bits (one's complement), and adding 1. For example, -5 in 8-bit two's complement is ~00000101 + 1 = 11111010 + 1 = 11111011 (0xFB). Our tool calculates this representation and warns when values exceed the signed range [-2^(N-1), 2^(N-1)-1].

How does IEEE 754 floating-point inspection work?

The converter passes floating-point values into an ArrayBuffer with a DataView to extract the underlying IEEE 754 binary representation. For 32-bit single precision (binary32), it separates the 1-bit sign, 8-bit exponent (bias 127), and 23-bit mantissa. For 64-bit double precision (binary64), it displays the 1-bit sign, 11-bit exponent (bias 1023), and 52-bit mantissa, correctly flagging normalized, subnormal/denormalized, infinity, and NaN values.

Why is converting directly between binary and hexadecimal faster than decimal conversion?

Hexadecimal (base 16) is a direct power of two (2^4 = 16). This mathematical relationship allows direct 4-to-1 mapping where every 4 binary bits (nibble) correspond to exactly 1 hexadecimal character (e.g., 1010_1111_0011_1100 becomes 0xAF3C). No complex division or multiplication by 10 is needed, making binary-to-hex and hex-to-binary conversions direct and lossless.

What is the difference between Big-Endian and Little-Endian byte ordering?

Endianness defines the sequential order in which multi-byte words are stored in computer memory. Big-Endian stores the most significant byte (MSB) at the lowest memory address (common in network protocols like TCP/IP), whereas Little-Endian stores the least significant byte (LSB) first (standard in x86/x64 and modern ARM processor architectures).

How does prefix auto-detection work with mixed format inputs?

The parser inspects leading characters to identify format specifiers commonly used in C, Rust, Go, Python, and JavaScript: '0x' or '0X' for hexadecimal, '0b' or '0B' for binary, and '0o' or '0O' for octal. If no prefix is present, the converter uses the selected source base or defaults to decimal.

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