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Hex to Decimal Converter
Convert hexadecimal numbers to decimal and binary. Supports uppercase and lowercase hex digits with step-by-step calculation.
Enter hex digits (0-9, A-F). 0x prefix optional.
Decimal⧉
6,719.00
Base-10 integer representation
Hexadecimal⧉
0x1A3F
Grouped: 1A3F
Binary⧉
0001 1010 0011 1111
16 bits total
Octal⧉
0o15077
Base-8 representation
Storage Size⧉
2 byte(s)
16 bits needed to represent this value
Hex Digits⧉
4 digits
16 bits of information
Digit Position Breakdown
| Position | Digit | Value | Weight (16ⁿ) | Binary | Contribution |
|---|---|---|---|---|---|
| 3 | 1 | 1 | 4,096.00 | 0001 | 4,096.00 |
| 2 | A | 10 | 256.00 | 1010 | 2,560.00 |
| 1 | 3 | 3 | 16.00 | 0011 | 48.00 |
| 0 | F | 15 | 1.00 | 1111 | 15.00 |
| Total | 6,719.00 | ||||
Hex Digit Visual
1
A
3
F
Common Hex Values Reference
| Hex | Decimal | Binary | Description |
|---|---|---|---|
| 0x00 | 0.00 | 0 | Zero / Black channel |
| 0x0A | 10.00 | 1010 | Newline (ASCII LF) |
| 0x20 | 32.00 | 100000 | Space (ASCII) |
| 0x41 | 65.00 | 1000001 | Letter "A" (ASCII) |
| 0xFF | 255.00 | 11111111 | Max byte / Full channel |
| 0xFFFF | 65,535.00 | 1111111111111111 | 16-bit max (unsigned) |
Planning notes, formulas, and examples
About the Hex to Decimal Converter
The Hex to Decimal Converter converts hexadecimal (base-16) numbers to decimal (base-10) and binary (base-2) representations. Enter a hex value and review the converted values with a step-by-step breakdown of the positional calculation.
Hexadecimal is the number system of choice in computing because each hex digit represents exactly 4 binary bits, making it a compact notation for binary data. Memory addresses, color codes, MAC addresses, and machine code all use hexadecimal. Converting hex to decimal is essential for programmers, network engineers, and web developers.
The converter handles both uppercase (A–F) and lowercase (a–f) hex digits and optionally strips the common 0x prefix. It also shows the binary equivalent and explains the positional expansion for learning purposes.
When This Page Helps
Programmers and engineers frequently need to convert between hex and decimal for debugging, color codes, memory addresses, and network configuration. It pairs the converted values with a step-by-step explanation you can verify against the raw digits.
How to Use the Inputs
- Enter a hexadecimal number (digits 0–9 and A–F).
- The 0x prefix is optional and will be stripped automatically.
- View the decimal equivalent in the result panel.
- Check the binary representation for bit-level analysis.
- Review the step-by-step positional expansion.
Formula used
decimal = Σ(digit_value × 16^position)
Positions count from right (0) to left.
Hex digits: 0–9 = 0–9, A=10, B=11, C=12, D=13, E=14, F=15.Example Calculation
Result: 6,719
1A3F in hex: F×16⁰ = 15, 3×16¹ = 48, A×16² = 2560, 1×16³ = 4096. Sum = 15 + 48 + 2560 + 4096 = 6,719. In binary: 0001 1010 0011 1111.
Tips & Best Practices
- Each hex digit maps to exactly 4 binary bits: 0=0000, F=1111.
- Colors in CSS use hex: #FF0000 = red (R=255, G=0, B=0).
- Memory addresses in debuggers are shown in hex for compact representation.
- The 0x prefix in code (like 0xFF) denotes a hexadecimal literal.
- To quickly estimate: each hex digit position is worth 16× the next.
Hexadecimal in Computing
Hexadecimal is ubiquitous in computing. It represents binary data compactly (1 hex digit = 4 bits), appears in memory dumps, MAC addresses, IPv6 addresses, Unicode code points, CPU registers, and file signatures (magic bytes). Understanding hex is fundamental for any programmer or IT professional.
Positional Number Systems
Decimal uses powers of 10, binary uses powers of 2, and hex uses powers of 16. The conversion formula is the same for all bases: multiply each digit by the base raised to its position, then sum. This positional notation concept applies to octal (base-8) and any other base.
Common Hex Values to Know
FF = 255 (max byte), 100 = 256, FFFF = 65,535 (max 16-bit), 7FFFFFFF = 2,147,483,647 (max signed 32-bit). These appear frequently in programming and are worth memorizing.
Sources & Methodology
Last updated:
Frequently Asked Questions
Hexadecimal (hex) is a base-16 number system using digits 0–9 and letters A–F (representing values 10–15). It's widely used in computing because it provides a human-readable representation of binary data — each hex digit equals exactly 4 binary bits.
Multiply each hex digit by 16 raised to its position (starting from 0 on the right). Then sum all the products. For example, 2B = (2 × 16¹) + (11 × 16⁰) = 32 + 11 = 43.
0xFF is hexadecimal FF, which equals 255 in decimal (15 × 16 + 15 = 255). The 0x prefix tells programming languages that the number is hexadecimal. 0xFF is the maximum value for a single byte.
CSS colors use 3 bytes (6 hex digits) to represent Red, Green, and Blue channels. Each channel ranges from 00 (0) to FF (255). #FF8800 means R=255, G=136, B=0 (orange). Hex is a compact notation for these byte values.
Replace each hex digit with its 4-bit binary equivalent: 0=0000, 1=0001, ..., 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. For example, 3F = 0011 1111.
One byte holds 8 bits, or 2 hex digits. The maximum value is FF in hex = 255 in decimal. For 2 bytes: FFFF = 65,535. For 4 bytes: FFFFFFFF = 4,294,967,295.
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