Binary Calculator | Perform Binary & Decimal Calculations

Binary Calculation

Binary Number 1:

Binary Number 2:

Results:

Binary Result:

Decimal Result:

Decimal to Binary Converter

Decimal Number:

Binary Equivalent:

What is a Binary Calculator?

A binary calculator is a tool that performs arithmetic operations on binary numbers. Binary numbers are base-2 numbers, consisting only of 0s and 1s, which are fundamental to digital systems and computer programming.

This calculator allows you to perform addition, subtraction, multiplication, and division on binary numbers, as well as convert between decimal and binary formats.

How to Use This Calculator

Enter two binary numbers in the respective input fields.
Select an operation (+, -, ×, ÷) by clicking on the corresponding button.
The selected operation will be highlighted in blue.
Click the "Calculate" button to perform the operation.
The result will be displayed in both binary and decimal formats.
Use the "Decimal to Binary Converter" section to convert decimal numbers to binary.

Applications of Binary Calculations

Computer programming and software development
Digital electronics and circuit design
Data transmission and network communications
Cryptography and security systems
Understanding how computers represent and process data

Binary System Basics

The binary system uses only two digits, 0 and 1, to represent numbers. Each digit in a binary number is called a bit. The position of each bit determines its value, which is a power of 2.

For example, the binary number 1011 is equivalent to 11 in decimal:
1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11

Understanding Binary Arithmetic

Binary arithmetic is essential for computer science and digital systems. Here's a brief overview of the basic operations:

Binary Addition

Binary addition works similarly to decimal addition, but with only two digits. The rules are:

0 + 0 = 0
0 + 1 = 1
1 + 1 = 0, carry 1
1 + 1 + 1 = 1, carry 1

Example: 101 + 110 = 1011 (5 + 6 = 11)

Binary Subtraction

Binary subtraction follows these rules:

0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1, borrow 1

Example: 110 - 101 = 001 (6 - 5 = 1)

Binary Multiplication

Binary multiplication is similar to decimal multiplication:

0 × 0 = 0
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1

Example: 101 × 11 = 1111 (5 × 3 = 15)

Binary Division

Binary division is similar to decimal division, but uses binary subtraction:

Example: 110 ÷ 10 = 11 (6 ÷ 2 = 3)

Note: Division by zero is undefined in both binary and decimal systems.

Binary vs. Decimal System

Aspect	Binary System	Decimal System
Base	2	10
Digits Used	0, 1	0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Place Values	Powers of 2 (2⁰, 2¹, 2², ...)	Powers of 10 (10⁰, 10¹, 10², ...)
Example Number	1010 (10 in decimal)	10 (ten)
Usage	Computers, digital systems, programming	Everyday arithmetic, general mathematics

Why Use a Binary Calculator?

Programming

Essential for low-level programming, bitwise operations, and understanding how computers store and process data.

Electronics

Used in digital electronics for circuit design, logic gates, and understanding binary signals.

Education

A valuable learning tool for students studying computer science, digital systems, and mathematics.