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Hex Calculator

Math

Calculate hexadecimal addition, subtraction, multiplication, division, and bitwise logic with instant conversions to Decimal, Binary, and ASCII.

0x
0x
Hex (Base 16) Result
0x49
Decimal (Base 10) 73
Binary (Base 2) 1001001₂
Octal (Base 8) 111₈

How This Calculator Works

Hexadecimal (hex) is a base-16 positional numeral system widely utilized in computer software, embedded firmware, web design, and memory inspection. It uses 16 distinct symbols: digits 0 through 9 represent values zero to nine, and letters A through F represent values ten to fifteen.

📐 Hexadecimal to Decimal Positional Conversion
Decimal = Σ (dᵢ × 16ⁱ) | for hex digits dᵢ at position i (from right, i=0)
A = 10, B = 11, C = 12: Alphabetical representations for two-digit values
D = 13, E = 14, F = 15: Alphabetical representations up to the base-16 radix limit
16ⁱ: Place values: 1, 16, 256, 4096, 65536, ...
0x Prefix: Standard C/Java/Python programming notation denoting hexadecimal

Key Mathematical Rules & Properties

Binary-Hex 4-Bit Equivalence

Because 2⁴ = 16, each hexadecimal digit corresponds exactly to a 4-bit binary nibble (e.g. 0xA = 1010₂, 0xF = 1111₂). Two hex digits represent exactly one 8-bit byte (0x00 to 0xFF).

Hex Addition with Carry

When the sum of digits exceeds 15, subtract 16 and carry 1 to the next left column: 9 + 8 = 17₁₀ = 11₁₆ (1 with carry 1).

HTML / CSS Color Codes

RGB colors use 6 hex digits (#RRGGBB): 2 hex digits each for Red, Green, and Blue intensities from 0 to 255 (e.g., #FFFFFF is white, #000000 is black).

ASCII Text Encoding

Each ASCII character corresponds to a 1-byte hex code (e.g., "A" = 0x41, "B" = 0x42, "a" = 0x61, space = 0x20).

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Worked Example: Converting 2F₁₆ to Decimal

Convert the hexadecimal value 2F₁₆ into decimal.

  1. Identify digits: position 1 is "2", position 0 is "F".
  2. Translate letters: F = 15 in decimal.
  3. Multiply by powers of 16: (2 × 16¹) + (15 × 16⁰).
  4. Evaluate: (2 × 16) + (15 × 1) = 32 + 15 = 47.
Final Answer: 47₁₀ (Binary: 0010 1111₂)

Frequently Asked Questions

Why do computer programmers prefer hex over binary?

Binary numbers are extremely long and error-prone for humans to read (e.g., 1111111111010000₂). Hexadecimal compresses 4 binary digits into a single character (e.g., 0xFFD0), making memory dumps, network packets, and MAC addresses much easier to read.

How does hex subtraction work when borrowing?

When you borrow from the column to the left in hexadecimal, you borrow 16 (not 10 as in decimal). For example, 10₁₆ - 1 = F₁₆ (16 - 1 = 15).

What does the prefix "0x" mean?

In computer programming languages like C, C++, JavaScript, and Python, the prefix 0x informs the compiler that the following literal characters are base-16 hexadecimal numbers (e.g., 0xFF = 255).

What is a GUID or UUID in hexadecimal?

A Globally Unique Identifier is a 128-bit number written as 32 hexadecimal characters grouped with hyphens (8-4-4-4-12, such as 123e4567-e89b-12d3-a456-426614174000).

Understanding your calculation

Method, example and limitations

How the calculation works

Hexadecimal uses base sixteen, with A through F representing decimal values 10 through 15. Each place is a successive power of sixteen.

Example to check

Hexadecimal 2F equals 2 × 16 + 15 = decimal 47.

Before using the result

A hexadecimal value alone does not specify signedness, byte order or character encoding. Check the selected operation and output base.

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