Binary Calculator

- May 09, 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 handy tool designed to help users perform calculations using binary numbers. It allows conversions between different number systems, like binary, decimal, hexadecimal, and octal. Whether you’re a beginner or just need a quick calculation, this tool provides an easy way to understand and manipulate binary data. You can perform basic arithmetic operations and see detailed conversion steps, making it ideal for students and computer enthusiasts alike.

Inputting Your Numbers

When using the Binary Calculator, you start by entering a number. You can choose the base of your input number, whether it’s binary (Base 2), decimal (Base 10), hexadecimal (Base 16), or octal (Base 8). This flexibility allows for a range of calculations. Here’s a quick overview of what you can input:

  • Binary: Use 0s and 1s.
  • Decimal: Use digits 0-9.
  • Hexadecimal: Use digits 0-9 and letters A-F.
  • Octal: Use digits 0-7.

Performing Arithmetic Operations

The Binary Calculator also supports various arithmetic operations. You can select an operation to perform, such as addition, subtraction, multiplication, and division. Additionally, it offers logical operations like AND, OR, and XOR, which are crucial for binary calculations. You can even shift bits left or right. This feature makes it a versatile tool for both simple and advanced calculations.

Viewing Results in Different Bases

One of the most impressive features of the Binary Calculator is its ability to display results in multiple bases. After performing a calculation, you can choose to see the output in binary, decimal, hexadecimal, and octal formats. This is particularly useful for users who need to understand how numbers translate across different systems. You can also view all results at once for a comprehensive overview.

Conversion Steps Explained

The calculator not only gives you results but also shows the steps taken for conversions. This educational aspect is beneficial for anyone looking to learn more about binary math. You can check the steps taken during calculations and conversions, allowing for a deeper understanding of how binary operations work. This feature is perfect for students and anyone wanting to improve their math skills.

Options for Customisation

To enhance your experience, the Binary Calculator offers several display options. You can choose to see the conversion steps, which can help you follow along with the calculations. Additionally, there’s an option to format binary numbers in groups of four, making them easier to read. These customisation features ensure that the calculator meets your specific needs and preferences.

Grasping Number System Basics

To fully utilise the Binary Calculator, it’s helpful to understand the basics of number systems. Each system has unique characteristics:

  • Binary (Base 2): Uses only 0 and 1.
  • Decimal (Base 10): Familiar digits from 0 to 9.
  • Hexadecimal (Base 16): Uses 0-9 and A-F.
  • Octal (Base 8): Only 0-7 are used.

Logical Operations Made Easy

The Binary Calculator also simplifies logical operations, which are essential for programming and digital electronics. Understanding how these operations work can be tough, but this calculator lays it out clearly. You’ll see how AND, OR, XOR, and NOT functions operate on binary numbers, helping you grasp logical reasoning essential in computing. With clear examples provided, you’ll be able to apply these concepts in your projects or studies.