How do you convert from decimal to binary?

You can convert a decimal number to binary by repeatedly dividing the number by 2 and recording the remainders. The binary representation is the sequence of remainders read from bottom to top.

A "bit" is short for binary digit. It is the smallest unit of data in a computer and can have a value of either 0 or 1.

Add, Subtract, Multiply, and Divide Binary Numbers

The Binary Calculator is an essential tool for anyone working with the binary number system. It allows you to perform basic arithmetic—addition, subtraction, multiplication, and division—directly on binary numbers. This is incredibly useful for students of computer science, digital electronics, and programming.

Perform calculations with binary numbers. This calculator supports addition, subtraction, multiplication, and division operations. You can also convert between binary, decimal, hexadecimal, and octal number systems.

Binary Operation

Select Operation:

First Binary Number:

Second Binary Number:

Display Options

Show number system conversions

Show calculation steps

Binary Calculation Results

Result (Binary)

0

Decimal

0

Hexadecimal

0

Octal

0

Input Values in Different Systems

Number	Binary	Decimal	Hexadecimal	Octal

Calculation Steps

About Binary Calculations

Binary is a base-2 number system that uses only two digits: 0 and 1. It is the fundamental language of computers and digital electronics. Understanding binary arithmetic is essential for computer science, programming, and digital systems design.

Binary Operations

Addition: Add two binary numbers following the rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1)
Subtraction: Subtract two binary numbers using borrowing when necessary
Multiplication: Multiply binary numbers similar to decimal multiplication
Division: Divide binary numbers similar to long division in decimal

Bitwise Operations

AND (&): Returns 1 if both bits are 1, otherwise 0
OR (|): Returns 1 if at least one bit is 1, otherwise 0
XOR (^): Returns 1 if bits are different, 0 if they are the same
NOT (~): Inverts all bits (1 becomes 0, 0 becomes 1)
Left Shift (<<): Shifts bits to the left, filling with 0s
Right Shift (>>): Shifts bits to the right

Number System Conversions

Binary numbers can be converted to other number systems:

Decimal (Base-10): The standard number system we use daily
Hexadecimal (Base-16): Uses digits 0-9 and letters A-F, commonly used in computing
Octal (Base-8): Uses digits 0-7, sometimes used in computing and permissions

Formula Reference for Binary Calculations

Binary Addition:
1 + 1 = 10 (carry 1)
Example: 1010 + 0110 = 10000

Binary Subtraction:
0 − 1 = 1 (borrow 1)
Example: 1010 − 0011 = 0111

Binary Multiplication:
Each bit in the second number multiplies the first, then results are added.
Example: 101 × 11 = 1111

Binary Division:
Follow the same process as decimal long division, using base 2.
Example: 1001 ÷ 10 = 100 (with remainder 1)

Bitwise Operations:
AND (&): 1 if both bits are 1
OR (|): 1 if at least one bit is 1
XOR (^): 1 if bits differ
NOT (~): Inverts bits
Left Shift (<<): Moves bits left, adds 0s
Right Shift (>>): Moves bits right

What is the Binary Calculator?

The Binary Calculator is an interactive tool that performs arithmetic and bitwise operations on binary numbers. It helps users understand how computers process and manipulate data using binary digits (0 and 1). The calculator supports addition, subtraction, multiplication, and division, as well as bitwise operations such as AND, OR, XOR, NOT, and bit shifts.

This calculator also converts results between different number systems—binary, decimal, hexadecimal, and octal—making it an educational and practical tool for students, programmers, and digital electronics learners.

Purpose and Benefits

Learn Binary Arithmetic: Understand how computers handle basic math operations using binary digits.
Support for Bitwise Logic: Explore how logic gates and low-level programming operations function.
Number System Conversion: Instantly switch between binary, decimal, hexadecimal, and octal representations.
Step-by-Step Explanations: View each calculation step to reinforce learning and comprehension.
Error Checking: Detect invalid binary inputs and prevent calculation mistakes.

How to Use the Calculator

Follow these simple steps to perform your calculations:

Choose an operation from the dropdown menu (e.g., Addition, Subtraction, Bitwise AND).
Enter your binary numbers in the provided fields (only 0s and 1s are allowed).
Click the Calculate button to see the result in binary form.
Check conversions to other number systems (Decimal, Hexadecimal, Octal) for a complete understanding.
Review the detailed calculation steps if you wish to follow the logic used in the computation.
Press the Reset button to start a new calculation.

Why Use a Binary Calculator?

Binary arithmetic is the foundation of computer operations. By using a binary calculator, you can clearly visualize how digital systems handle calculations. It simplifies learning for computer science students and assists developers in debugging or verifying binary operations during programming and hardware design.

It also saves time by automating conversions and computations that would otherwise require manual bit-by-bit work. Whether you’re working on logic circuit design, programming low-level code, or studying computer architecture, this calculator provides instant, accurate results.

Example Use Case

Suppose you want to calculate the result of 1010 AND 0110:

Step 1: Select “Bitwise AND” from the menu.
Step 2: Enter 1010 and 0110.
Step 3: Click “Calculate.”
Result: 0010 (Binary), which equals 2 in Decimal.

Frequently Asked Questions (FAQ)

1. What is a binary number?

A binary number is a number expressed using only two digits: 0 and 1. Each binary digit (bit) represents a power of 2. For example, the binary number 1010 equals 10 in decimal.

2. Can I use decimal numbers in this calculator?

No, the input must be binary. However, the calculator automatically converts your result to decimal, hexadecimal, and octal for easy understanding.

3. What does the Bitwise NOT (~) operation do?

The NOT operation flips all bits—turning 1s into 0s and 0s into 1s. For example, the binary number 1010 becomes 0101 after applying NOT.

4. What is the difference between arithmetic and bitwise operations?

Arithmetic operations (like addition or multiplication) deal with numerical values, while bitwise operations work directly on each bit, often used in programming and digital logic.

5. How can this calculator help me learn?

It provides clear visual feedback and shows step-by-step explanations, helping you grasp how binary operations and conversions work. It’s useful for studying computer logic, data representation, and hardware-level processing.

Conclusion

The Binary Calculator is a simple yet powerful educational tool for understanding how digital systems perform arithmetic and logic operations. With its easy interface, conversion capabilities, and step-by-step explanations, it’s ideal for anyone learning computer fundamentals or working with binary-based systems.

More Information

Binary Arithmetic Rules:

Binary operations follow simple rules:

Addition: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (0 with a carry-over of 1).
Subtraction: Often performed using methods like two's complement.
Multiplication: Similar to decimal multiplication, where 1*1=1 and anything multiplied by 0 is 0.
Division: Similar to decimal long division.

Our calculator handles these rules automatically, giving you a fast and accurate result.

Frequently Asked Questions

What is the binary number system?: The binary number system is a base-2 number system that uses only two digits: 0 and 1. It is the fundamental language of computers and digital electronics.
How do you convert from decimal to binary?: You can convert a decimal number to binary by repeatedly dividing the number by 2 and recording the remainders. The binary representation is the sequence of remainders read from bottom to top.
What is a bit?: A "bit" is short for binary digit. It is the smallest unit of data in a computer and can have a value of either 0 or 1.

About Us

We provide specialized tools for computer science and mathematics. Our calculators are designed to simplify complex and tedious calculations, helping users understand the fundamental principles of different number systems.