Binary Calculator

Category: Algebra and General

- August 20, 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

Enter Number:

Input Base:

Operation (Optional)

Select Operation:

Display Options

Output Base:

Show conversion steps

Format binary in groups of 4

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

What is the Binary Calculator?

The Binary Calculator is a handy tool designed for anyone working with numbers. It helps you convert between binary, decimal, hexadecimal, and octal number systems. Whether you're a student learning about number systems or just curious, this calculator makes it easy to perform basic arithmetic operations on binary numbers.

How Does it Work?

This calculator allows you to input a number and select its base. You can choose from various number systems, including:

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

After selecting your input base, you can perform operations like addition, subtraction, multiplication, and more, while the results are displayed in the chosen base.

Arithmetic Operations Made Simple

The Binary Calculator offers several operations to make calculations straightforward. You can perform:

Addition (+)
Subtraction (-)
Multiplication (×)
Division (÷)
Logical operations like AND, OR, XOR, NOT
Shifting operations (Left and Right Shift)

With these functions, you can delve into various arithmetic and logical calculations effortlessly.

Displaying Results in Different Bases

<pOne of the great features of this calculator is its ability to show results in multiple bases. You can select:

Binary (Base 2)
Decimal (Base 10)
Hexadecimal (Base 16)
Octal (Base 8)
All bases simultaneously

This flexibility helps you understand how the same value looks in different number systems.

Understanding Number Systems

Number systems use various bases to represent values. Here are the most common systems:

Binary (Base 2): Uses 0s and 1s. Each position represents a power of 2.
Decimal (Base 10): Uses digits from 0 to 9. It’s the system most people use daily.
Hexadecimal (Base 16): Uses 0-9 and A-F. Each position is a power of 16.
Octal (Base 8): Uses digits from 0 to 7. Each position represents a power of 8.

Convenient Conversion Steps

The Binary Calculator can show you the steps involved in conversions. This feature is useful for learning and understanding how to convert numbers from one system to another. It breaks down the process, making it easier to follow along.

Ideal for Learning and Practice

This calculator is perfect for students, educators, and anyone interested in number theory. It provides a user-friendly interface that encourages exploration of different number systems. You can practise your skills in a fun and engaging way.

The Joy of Logical Operations

The Binary Calculator also features logical operations, which are essential in computer Science and programming. You can apply logical AND, OR, and NOT operations to binary numbers. This is vital for understanding how computers perform calculations and make decisions.