Binary Calculator
What is Binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. It is the fundamental language of computers and digital systems, where each digit represents a power of 2.
Binary Number System
In the binary system, each position represents a power of 2, starting from the rightmost digit:
Position | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 |
---|---|---|---|---|---|---|---|---|
Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Example | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
The example binary number 10101101 equals 128 + 32 + 8 + 4 + 1 = 173 in decimal.
Binary Operations
Binary Addition
Rules for binary addition:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (carry the 1)
Binary Subtraction
Rules for binary subtraction:
- 0 - 0 = 0
- 1 - 0 = 1
- 1 - 1 = 0
- 0 - 1 = 1 (borrow 1)
Binary Multiplication
Rules for binary multiplication:
- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1
Binary Division
Binary division follows the same principles as decimal division but uses binary arithmetic rules.
Applications of Binary
Binary is fundamental to computing and digital systems:
- Computer memory and storage
- Digital logic and circuit design
- Machine code and low-level programming
- Data transmission and networking
- Error detection and correction codes
How to Use the Binary Calculator
Our binary calculator offers several functions:
- Convert between binary, decimal, and hexadecimal number systems
- Perform binary arithmetic operations (addition, subtraction, multiplication, division)
- View step-by-step solutions for binary operations
- Perform bitwise operations (AND, OR, XOR, NOT)
Simply enter your values, select the operation you want to perform, and click "Calculate" to see the results.