Free Online Hexadecimal to Decimal Converter & Math Proof Generator
The Telekit Hexadecimal to Decimal Converter is an engineering, computer science, and mathematical utility designed to translate numerical values between base-16 (hexadecimal) and base-10 (decimal). Built with high-precision arbitrary BigInt arithmetic, it renders step-by-step polynomial expansion tables, repeated division proofs, interactive bit flipping, 4-bit binary nibble grouping, signed two's complement integers, and IEEE-754 floating-point decoding.
How to Use the Hexadecimal to Decimal Converter
Type or paste any hex string (e.g. 1A3F, 0xFF, #4A90E2) or decimal integer. Prefixes and spaces are sanitized automatically.
Switch effortlessly between Hex ➔ Decimal and Decimal ➔ Hex using the 1-click swap button or Alt+S shortcut.
Review the interactive mathematical expansion breakdown or division steps to verify calculations and technical specifications.
Copy converted values in 1-click, convert entire lists of numbers in batch mode, or export comprehensive JSON, CSV, or Markdown reports.
Mathematical Formulas for Base-16 Conversions
1. Hexadecimal to Decimal Conversion Formula
Because hexadecimal is a positional base-16 number system, a hex string of length n (from d_n-1 down to d_0) is evaluated by multiplying each digit value by 16^i:
2. Decimal to Hexadecimal Repeated Division Algorithm
To convert decimal to hex, divide the decimal integer $N$ by 16 repeatedly:
- Compute Quotient $Q = \lfloor N / 16 \rfloor$ and Remainder $R = N \bmod 16$.
- Convert $R$ (0–15) to its hex digit equivalent (10 ➔ A, 11 ➔ B, 12 ➔ C, 13 ➔ D, 14 ➔ E, 15 ➔ F).
- Replace $N$ with $Q$ and repeat until $N = 0$.
- Read the remainders in reverse order (bottom-to-top) to form the hexadecimal number.
Power of 16 Exponent Lookup Table
| Exponent (16^n) | Decimal Value | Hexadecimal Equivalent | Common Memory / Hardware Metric |
|---|---|---|---|
| 16⁰ | 1 | 0x1 | 1 Byte unit offset |
| 16¹ | 16 | 0x10 | 1 Nibble step |
| 16² | 256 | 0x100 | 8-bit byte boundary (1 Byte) |
| 16³ | 4,096 | 0x1000 | 4 KB standard page size |
| 16⁴ | 65,536 | 0x10000 | 16-bit word boundary (64 KB) |
| 16⁵ | 1,048,576 | 0x100000 | 1 Megabyte (1 MB) |
| 16⁶ | 16,777,216 | 0x1000000 | 24-bit TrueColor depth (#RRGGBB) |
| 16⁷ | 268,435,456 | 0x10000000 | 256 MB block |
| 16⁸ | 4,294,967,296 | 0x100000000 | 32-bit address space limit (4 GB) |
Hexadecimal, Decimal & Binary 4-Bit Nibble Chart (0–15)
| Hex | Decimal | Binary (Nibble) | Octal | Hex | Decimal | Binary (Nibble) | Octal |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0000 | 00 | 8 | 8 | 1000 | 10 |
| 1 | 1 | 0001 | 01 | 9 | 9 | 1001 | 11 |
| 2 | 2 | 0010 | 02 | A | 10 | 1010 | 12 |
| 3 | 3 | 0011 | 03 | B | 11 | 1011 | 13 |
| 4 | 4 | 0100 | 04 | C | 12 | 1100 | 14 |
| 5 | 5 | 0101 | 05 | D | 13 | 1101 | 15 |
| 6 | 6 | 0110 | 06 | E | 14 | 1110 | 16 |
| 7 | 7 | 0111 | 07 | F | 15 | 1111 | 17 |
Desktop Keyboard Shortcuts Reference
Accelerate your binary, hex, and decimal engineering workflows with native browser keybindings.
| Shortcut Key | Triggered Action | Scope / Target |
|---|---|---|
| Alt + P | Smart Clipboard Auto-Detect & Route | Global |
| Alt + D | Toggle Favorite Starred Tool | Global |
| Alt + S | Toggle Developer API & Code Snippets Modal | Global |
| Alt + V | Toggle 2-Column Split Studio vs Full-Width Stacked Layout | Global |
| Alt + R | Cycle Random Benchmark Presets | Global |
| Alt + W | Swap Conversion Direction (Hex ↔ Dec) | Global |
| Alt + T | Cycle Studio Workspace Tabs | Global |
| Alt + 1..6 | Quick Copy Output (Dec, Hex, Bin, C-Array, Oct, Float) | Output |
| Ctrl + Enter | Copy Primary Converted Value to Clipboard | Global |
| / | Quick Focus Main Input Field | Global |
| Alt + K / ? | Open Keyboard Shortcuts Reference Modal | Global |
| Esc | Dismiss Active Modals / Blur Active Inputs | Global |
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Frequently Asked Questions
How do you convert Hexadecimal to Decimal manually?
To convert a hex number to decimal, multiply each hexadecimal digit by 16 raised to the power of its zero-indexed positional index (starting from 0 on the far right) and add all results together. For example, 1A3F = (1 × 16³) + (10 × 16²) + (3 × 16¹) + (15 × 16⁰) = 4096 + 2560 + 48 + 15 = 6,719.
How do you convert Decimal to Hexadecimal manually?
To convert a decimal integer to hexadecimal, divide the number by 16 repeatedly using integer division. Write down the remainder (0–15, converting 10–15 to A–F) for each step until the quotient is 0. Then read the remainders backwards from bottom to top to assemble the hex string.
What do the hex letters A through F represent in decimal?
In the base-16 hexadecimal system: A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15. The numbers 0 through 9 retain their standard base-10 values.
What is 0xFF in decimal?
0xFF in decimal is 255. In mathematical terms: (15 × 16¹) + (15 × 16⁰) = 240 + 15 = 255. It represents the maximum unsigned integer value that can fit into an 8-bit byte (1111 1111 in binary).
Does this tool support signed negative numbers and Two's Complement?
Yes! When converting negative decimal values (e.g. -42 or -1), the tool automatically derives the standard 8-bit, 16-bit, 32-bit, and 64-bit Two's Complement hexadecimal representations.
Can I inspect IEEE-754 Floating Point numbers from Hex?
Yes! In the Data Types & Float Inspector tab, 32-bit (Single Precision) and 64-bit (Double Precision) hex values are automatically parsed according to the IEEE-754 standard, supporting both Big Endian and Little Endian byte orders.
What keyboard shortcuts are available?
Press 'Alt+P' for DevToys Smart Clipboard Auto-Detect, 'Alt+D' to toggle Star Tool bookmarking, 'Alt+S' for the Developer API Code Studio modal, 'Alt+V' to toggle 2-Column Split Studio vs Full-Width Stacked layout, 'Alt+W' to swap conversion direction (Hex ↔ Dec), 'Alt+R' for random benchmark presets, 'Alt+1..6' to 1-click copy formatted representations (Dec, Hex, Bin, C-Array, Octal, Float), 'Ctrl+Enter' to copy primary result, '/' to focus input, 'Alt+K' or '?' for the Shortcuts Guide, and 'Esc' to clear input or dismiss active dialogs.
Is my numerical data sent to any remote server?
No. 100% of mathematical conversions, string sanitizations, bit matrix simulations, and data parsing run entirely client-side in your browser memory with zero network requests or logging.
How does arbitrary precision BigInt prevent numerical overflow?
Standard JavaScript Numbers lose integer precision above 2^53 - 1 (9,007,199,254,740,991, or 0x1FFFFFFFFFFFFF). This tool utilizes native ECMAScript BigInt arithmetic, allowing you to convert 64-bit, 128-bit, 256-bit cryptographic hashes (such as SHA-256 digests) and arbitrarily large base-16 strings without any truncation or rounding loss.
Can I integrate these conversions into automated scripts and applications?
Yes! Click 'API Code' (Alt+S) in the hero toolbar or navigate to the Code Snippets Studio tab to access copy-paste ready, production-grade conversion syntax across 7 languages: TypeScript/JavaScript, Python 3, C/C++ (C99), Go, Rust, Java, and Bash CLI. You can also download standalone script files directly with language-appropriate file extensions (.ts, .py, .c, .go, .rs, .java, .sh) and copy target filenames in 1-click.