Binary Calculator

Category: Algebra and General
- April 04, 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

Binary and Decimal Calculator: A Guide to Easy Calculations

Welcome to the guide for using a versatile Binary and Decimal Calculator. This tool makes binary arithmetic and conversions straightforward, making it easy for anyone interested in working with binary numbers. Whether you need to do arithmetic operations, convert binary to decimal, or decimal to binary, this calculator has got you sorted.

Features of the Calculator

  • Binary Arithmetic: Add, subtract, multiply, or divide binary numbers with ease.
  • Binary to Decimal Conversion: Quickly find the decimal equivalent of a binary number.
  • Decimal to Binary Conversion: Easily convert a decimal number to its binary form.

Why Use This Calculator?

Binary numbers are crucial in computing and digital systems. However, doing manual calculations can take a lot of time and can lead to mistakes. This calculator removes the hassle, providing accurate and instant results.

How to Use the Calculator

1. Perform Binary Arithmetic

You can use the calculator to add, subtract, multiply, or divide two binary numbers.

  • Steps to Calculate:
  • Enter the first binary number in the first input field (default: 10101010).
  • Select an operator (+, -, *, or /) from the dropdown menu.
  • Enter the second binary number in the second input field (default: 11001100).
  • Click the Calculate button.
  • Result: The output shows both the binary and decimal results of the calculation.

Example:
10101010 + 11001100 = 101110110 (Decimal: 374)

2. Convert Binary to Decimal

This feature allows you to convert a binary number to its decimal equivalent in no time.

  • Steps to Convert:
  • Enter the binary number in the input field (default: 10101010).
  • Click the Convert button.
  • Result: The decimal equivalent is displayed right away.

Example:
Binary: 10101010 = Decimal: 170

3. Convert Decimal to Binary

Need to find the binary representation of a decimal number? This tool does it without any hassle.

  • Steps to Convert:
  • Enter the decimal number in the input field (default: 170).
  • Click the Convert button.
  • Result: The binary equivalent is shown instantly.

Example:
Decimal: 170 = Binary: 10101010

Practical Applications

  • Education: A useful learning tool for students studying binary systems.
  • Programming: Makes binary operations and conversions easier for developers.
  • Data Analysis: Converts numerical formats for digital data processing.

Tips for Effective Use

  • Double-check your inputs to ensure accurate results.
  • Use standard binary and decimal number formats (no extra spaces or invalid characters).
  • Remember that division results are rounded down to the nearest integer for binary calculations.

This calculator is an efficient solution for managing binary and decimal operations, providing reliable results with minimal effort. Start simplifying your calculations today!