Hex Calculator

Hexadecimal Calculator

Choose a mode and perform calculations directly in hexadecimal

Hexadecimal:

Decimal:

Binary:

Operand 1 (Hex):

Operand 2 (Hex):

Conversion Results

View hexadecimal, decimal, and binary equivalents

Hexadecimal

0x0

Decimal

Binary

Bitwise Result

0x0

Quick Examples

0xFF + 0x01 = 0x100

0xB3 AND 0x0F = 0x03

255 to Hex = 0xFF

How It Works

Select one of three calculation modes, enter hexadecimal values, and get instant results. Our calculator uses standard conversion formulas for accuracy.

Common Uses

Calculate memory addresses, manipulate color codes, perform bitwise operations, and convert between number systems with this versatile programming tool.

Always Accessible

Works completely in your browser - no data sent to servers. Use it anytime, anywhere with full privacy protection and offline capability.

Hexadecimal Conversion Formulas

Hexadecimal to Decimal Conversion

Decimal = Σ(digit_n × 16^n)

digit values: 0-9 = 0-9, A=10, B=11, C=12, D=13, E=14, F=15

Decimal to Hexadecimal Conversion

Process: Repeated division by 16, collecting remainders

Example: 255 ÷ 16 = 15 remainder 15 → FF₁₆

Bitwise Operations

a, b = hexadecimal values, n = shift amount, & = bitwise AND, | = bitwise OR

Step-by-Step Examples

Basic Hexadecimal Addition

0x2A + 0x17 = (42₁₀ + 23₁₀) = 65₁₀ = 0x41

Result: 0x41

Color Mixing (Web Design)

#FFA500 (orange) + #0000FF (blue) = #FFA5FF

Result: Light purple (#FFA5FF)

Bitwise AND Operation

0xB3 AND 0x0F = 10110011₂ AND 00001111₂ = 00000011₂

Result: 0x03

Understanding Hexadecimal Calculations

Hexadecimal (base-16) calculations are essential for programmers, embedded systems engineers, and digital designers. Unlike decimal (base-10) or binary (base-2), hexadecimal provides a compact representation that's easy for humans to read while maintaining a direct relationship to binary data.

What is a Hex Calculator?

A hex calculator is a specialized tool that performs arithmetic operations directly in base-16 format. It eliminates manual conversion errors when working with memory addresses, color codes, network protocols, and machine-level data. Each hex digit represents exactly 4 bits, making it ideal for visualizing binary patterns.

Core Components of Hex Calculations

Hexadecimal calculations involve three key elements:

Digits: 0-9 for values 0-9, A-F for values 10-15
Base: Positional notation with base 16 (16^n for position n)
Prefix: 0x or # prefix distinguishes hex from decimal numbers

Real-World Applications

Hexadecimal is everywhere in computing: memory addresses in RAM, color codes in CSS/HTML, MAC addresses in networking, and machine code in assembly programming. Understanding hex calculations helps you debug low-level code, design digital circuits, and work with binary data efficiently.

Practical Example: Memory Address Calculation

Imagine you're programming a microcontroller and need to calculate a memory offset.

Memory Address Calculation

Scenario:

Base address: 0x1000
Element size: 0x20 bytes
Element index: 0x0A

Calculation:

Convert to decimal: 0x1000 = 4096, 0x20 = 32, 0x0A = 10
Calculate offset: 32 × 10 = 320
Add to base: 4096 + 320 = 4416
Convert back: 4416₁₀ = 0x1140

Result: Target address = 0x1140

Frequently Asked Questions

Why use hexadecimal instead of decimal in programming?

Hexadecimal provides compact representation of binary data. Each hex digit represents exactly 4 bits, making it easier to read and manipulate binary values compared to long strings of 1s and 0s.

What does the 0x prefix mean?

The 0x prefix indicates hexadecimal notation in most programming languages (C, Java, JavaScript, Python). It distinguishes hex numbers from decimal numbers (0xFF vs 255).

How do I convert hex to decimal manually?

Multiply each digit by 16 raised to its position power, starting from rightmost (16⁰). A=10, B=11, C=12, D=13, E=14, F=15. Example: 1A3 = 1×256 + 10×16 + 3×1 = 419.

What are bitwise operations used for?

Bitwise operations manipulate individual bits within binary numbers. AND masks bits, OR sets bits, XOR toggles bits, and shifts move bits left or right. Essential for low-level programming.

How are negative hex numbers represented?

Typically using two's complement notation. For 8-bit: -1 = 0xFF, for 16-bit: -1 = 0xFFFF. The calculator handles sign based on bit length selection.

Can I perform arithmetic directly in hex?

While possible for addition/subtraction, it's error-prone for multiplication and division. Our calculator converts to decimal for accurate arithmetic, then converts back to hex.