Hex Calculator

Category: Algebra and General
- April 02, 2025
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Convert between decimal, hexadecimal, binary, and octal number systems. This calculator provides bit-level operations and complete conversion details.

Number Input

Bit Operations

Display Options

About Number Systems

Different number systems use different bases to represent values. The most common are decimal (base 10), hexadecimal (base 16), binary (base 2), and octal (base 8).

Hexadecimal (Base 16)

Hexadecimal uses 16 digits: 0-9 and A-F (where A=10, B=11, ..., F=15). It's commonly used in computing because each hexadecimal digit represents exactly 4 binary digits (bits).

For example, the hexadecimal value 0xFF = 255 in decimal and 0b11111111 in binary.

Bitwise Operations
  • Shift Left (≪): Moves all bits to the left, equivalent to multiplying by 2.
  • Shift Right (≫): Moves all bits to the right, equivalent to dividing by 2.
  • NOT (~): Inverts all bits (0 becomes 1, 1 becomes 0).
  • AND (&): Results in 1 only if both corresponding bits are 1.
  • OR (|): Results in 1 if at least one of the corresponding bits is 1.
  • XOR (⊕): Results in 1 if exactly one of the corresponding bits is 1.
Common Applications
  • Hexadecimal: Memory addresses, color codes (e.g., #FF5733 in HTML), file formats
  • Binary: Digital circuits, computer memory, low-level programming
  • Octal: File permissions in Unix/Linux systems
Decimal to Binary Formula:
Divide the decimal number by 2 repeatedly. Collect the remainders in reverse order to form the binary result.

Decimal to Hexadecimal Formula:
Divide the decimal number by 16 repeatedly. Convert remainders (0–15) into hex (0–9, A–F) and read in reverse order.

Binary to Decimal Formula:
Multiply each binary digit by 2 raised to its position index (starting from right) and sum all the results.

What Is the Hex Calculator?

The Hex Calculator is a versatile and interactive tool that helps you convert numbers between different number systems — decimal (base 10), hexadecimal (base 16), binary (base 2), and octal (base 8). It also includes bitwise operations, giving you full control over binary manipulations. Whether you're working on computer programming, digital electronics, or just exploring number systems, this calculator is a powerful resource.

Why Use a Hex Calculator?

Understanding and converting between number systems is essential for many tasks in computer science and engineering. This calculator saves time and ensures accuracy by handling the conversions and displaying bit-level details instantly. It’s also useful when learning topics such as:

  • Memory addressing and debugging in hexadecimal
  • Understanding binary logic and bitwise operations
  • Working with file formats, permissions, and low-level data
  • Learning base 16 calculations and hexadecimal operations

How to Use the Hex Calculator

Follow these steps to get the most out of this hex math tool:

  • Step 1: Enter a number in the input box.
  • Step 2: Select the number's base: Decimal, Hexadecimal, Binary, or Octal.
  • Step 3: (Optional) Use bitwise buttons like Shift Left, NOT, AND, OR, etc., for binary number operations.
  • Step 4: Click “Convert Number” to see results in all bases.
  • Step 5: Explore additional options like bit width, grouping, and display preferences.

Conversion Results You’ll See

The calculator displays the following:

  • Equivalent values in Decimal, Hexadecimal, Binary, and Octal
  • Bit representation for the specified bit width (8, 16, 32, or 64 bits)
  • Step-by-step breakdown of conversion logic (if enabled)

Bitwise Operations Explained

Bitwise tools in this calculator allow you to manipulate individual bits. These are especially helpful when studying binary logic or writing low-level code:

  • Shift Left (≪): Multiplies the value by 2
  • Shift Right (≫): Divides the value by 2
  • NOT (~): Inverts each bit
  • AND (&): Compares bits with a second value — only keeps 1s if both are 1
  • OR (|): Combines bits — keeps 1s if at least one is 1
  • XOR (⊕): Keeps 1s only if bits differ

Who Can Benefit?

This tool is helpful for a wide range of users:

  • Students learning about digital systems, binary math, and base conversions
  • Programmers working with low-level code, memory, or binary flags
  • Engineers analyzing bitwise logic and hardware behavior
  • Anyone curious about how number systems work

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Frequently Asked Questions (FAQ)

  • Can I use negative numbers? Yes, negative values are shown using two’s complement representation based on selected bit width.
  • What does bit width mean? It defines how many bits are used to represent the number (e.g., 8-bit, 32-bit).
  • What if I enter an invalid number? The calculator will notify you if the input doesn’t match the selected base.
  • How are results grouped? You can set how many digits are grouped together for better readability (e.g., group every 4 binary digits).
  • Why use hexadecimal? Hex is more compact than binary and aligns neatly with byte-sized binary values — commonly used in computing.

Summary

The Hex Calculator is a practical tool for converting values between common number systems and performing bit-level operations. Its easy-to-use interface and detailed output make it valuable whether you're working with base 16 calculations, learning binary logic, or dealing with digital electronics. Explore, experiment, and make sense of numbers — one bit at a time.