BravoCalc

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:

Position2726252423222120
Value1286432168421
Example10101101

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:

  1. Convert between binary, decimal, and hexadecimal number systems
  2. Perform binary arithmetic operations (addition, subtraction, multiplication, division)
  3. View step-by-step solutions for binary operations
  4. 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.