Binary Calculator

Category: Algebra and General
- May 22, 2025
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Convert and calculate between binary, decimal, hexadecimal, and octal number systems. This calculator performs basic arithmetic operations on binary numbers and provides step-by-step conversion details.

Number Input

Operation (Optional)

Display Options

Number System Basics

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

Binary (Base 2)

Uses only 0 and 1. Each position represents a power of 2. For example, binary 1010 = 1×23 + 0×22 + 1×21 + 0×20 = 8 + 0 + 2 + 0 = 10 in decimal.

Decimal (Base 10)

Uses digits 0-9. Most familiar to humans. Each position represents a power of 10.

Hexadecimal (Base 16)

Uses digits 0-9 and letters A-F (where A=10, B=11, ..., F=15). Each position represents a power of 16. For example, hex A = 10 in decimal, and FF = 15×161 + 15×160 = 255 in decimal.

Octal (Base 8)

Uses digits 0-7. Each position represents a power of 8. For example, octal 12 = 1×81 + 2×80 = 8 + 2 = 10 in decimal.

Logical Operations
Operation Description Example
AND (&) 1 if both bits are 1, otherwise 0 1010 & 1100 = 1000
OR (|) 1 if either bit is 1, otherwise 0 1010 | 1100 = 1110
XOR (^) 1 if bits are different, otherwise 0 1010 ^ 1100 = 0110
NOT (~) Inverts all bits ~1010 = 0101 (simplified)
Left Shift (<<) Shift bits left, fill with 0 1010 << 1 = 10100
Right Shift (>>) Shift bits right, discard overflow 1010 >> 1 = 101

Understanding the Binary Calculator

The Binary Calculator is a powerful tool that helps you work with binary numbers. It allows you to convert between different number systems, like binary, decimal, hexadecimal, and octal. Whether you're doing simple Math or complex calculations, this calculator is designed to make it easy and straightforward. You can even see step-by-step conversions, which is great for learning more about how these systems work.

Input Options Made Easy

When using the Binary Calculator, you have several input options. You can enter your number and choose its base. The available bases include:

  • Binary (Base 2)
  • Decimal (Base 10)
  • Hexadecimal (Base 16)
  • Octal (Base 8)

This flexibility means you can work in the number system that suits you best.

Arithmetic Operations at Your Fingertips

The calculator isn’t just for conversions; it also lets you perform various arithmetic operations on binary numbers. You can choose an operation such as addition, subtraction, multiplication, or division. Additionally, logical operations like AND, OR, and NOT are available. This feature makes it ideal for students and professionals alike who need quick and accurate calculations.

Display Your Results in Multiple Formats

With the Binary Calculator, you can choose how you'd like to see your results. You can select the output base, giving you options like:

  • Binary (Base 2)
  • Decimal (Base 10)
  • Hexadecimal (Base 16)
  • Octal (Base 8)
  • All Bases

This means you get the results in the format that’s most useful for your needs.

Step-by-Step Guidance

If you want to understand the calculations better, the Binary Calculator can show you each step of the conversion process. This is especially helpful for students learning about number systems. It breaks down how the numbers change from one system to another, making it easier to grasp the concepts involved.

Logical Operations Explained

Logical operations are a key feature of this calculator. They help you manipulate binary data effectively. You can perform operations like AND, OR, and XOR on your binary numbers. A quick example of how these work includes:

  • AND: 1010 & 1100 = 1000
  • OR: 1010 | 1100 = 1110
  • XOR: 1010 ^ 1100 = 0110

This feature is particularly handy in programming and computer Science applications.

Revisiting Number System Basics

Understanding the different number systems is crucial when using the Binary Calculator. Here's a quick overview:

  • Binary (Base 2): Only uses 0 and 1.
  • Decimal (Base 10): Uses digits 0-9, which most people are familiar with.
  • Hexadecimal (Base 16): Combines digits 0-9 and letters A-F.
  • Octal (Base 8): Uses digits 0-7.

This knowledge helps you gain confidence when converting and calculating with the tool.

Practical Applications of the Binary Calculator

The Binary Calculator is not just a learning tool; it's also practical for various real-world applications. Programmers use it to debug code, while engineers rely on it for calculations in circuit design. Students find it beneficial for homework and projects involving binary operations. Regardless of your background, this calculator can be a valuable resource.