Binary Calculator Online – Perform Binary Calculations Easily

Intro

A Binary Calculator online is a smart and user-friendly tool designed to perform calculations in the binary number system. Binary is a base-2 system that uses only two digits, 0 and 1. It is the foundation of modern computing and is used in programming, networking, digital electronics, and data processing.

Instead of converting binary numbers to decimal and doing manual calculations, a Binary Calculator lets you quickly add, subtract, multiply, divide, and convert binary numbers into decimal, octal, or hexadecimal formats. This saves time and eliminates errors.

Whether you are a student learning digital logic, a programmer working with low-level code, or a networking professional, the Binary Calculator is an essential tool for quick and accurate results.

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Formula / Working

Binary arithmetic follows the same principles as decimal arithmetic but works with only two digits (0 and 1).

1. Binary Addition Rules:

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 10 (carry 1 to the next column)

2. Binary Subtraction Rules:

• 0 – 0 = 0
• 1 – 0 = 1
• 1 – 1 = 0
• 0 – 1 = 1 (borrow 1 from the next digit)

3. Binary Multiplication Rules:

• 0 × 0 = 0
• 0 × 1 = 0
• 1 × 1 = 1

4. Binary Division Rules:

• Works like decimal division but with base 2.

5. Conversion Formula (Binary → Decimal):

Decimal Value=∑(Binary Digit×2position)\text{Decimal Value} = \sum (\text{Binary Digit} \times 2^{\text{position}})Decimal Value=∑(Binary Digit×2position)

Example: 10112=(1×23)+(0×22)+(1×21)+(1×20)=11101011_2 = (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) = 11_{10}10112​=(1×23)+(0×22)+(1×21)+(1×20)=1110​

The Binary Calculator automates all of these operations instantly.

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Step-by-Step Usage

Here’s how to use the Binary Calculator online:

1. Enter the binary number(s) (only 0s and 1s).
2. Choose the operation (addition, subtraction, multiplication, division, or conversion).
3. If converting, select the target format (decimal, octal, hex).
4. Click Calculate.
5. The result will display instantly.

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Examples

Example 1: Binary Addition

Add 1011 (binary) + 110 (binary).

Convert to decimal:

• 1011 = 11
• 110 = 6
  11 + 6 = 17

Convert back to binary:
17 ÷ 2 → 10001

✅ 1011 + 110 = 10001 (binary)

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Example 2: Binary to Decimal Conversion

Convert 11101 (binary) to decimal. (1×24)+(1×23)+(1×22)+(0×21)+(1×20)(1 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) (1×24)+(1×23)+(1×22)+(0×21)+(1×20) =16+8+4+0+1=29= 16 + 8 + 4 + 0 + 1 = 29=16+8+4+0+1=29

✅ 11101 (binary) = 29 (decimal)

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Example 3: Binary Multiplication

Multiply 101 (binary) × 11 (binary).

Convert to decimal:

• 101 = 5
• 11 = 3
  5 × 3 = 15

Convert back to binary:
15 ÷ 2 → 1111

✅ 101 × 11 = 1111 (binary)

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FAQs

1. What is a Binary Calculator?
A Binary Calculator is an online tool that performs arithmetic and conversions in the binary (base-2) number system.

2. Why is binary important in computing?
Binary represents how computers process and store data. Every piece of digital information is stored in 0s and 1s.

3. Can the Binary Calculator convert binary to decimal, octal, and hex?
Yes, it allows easy conversion across multiple number systems.

4. Is the Binary Calculator free to use?
Yes, it is completely free and works instantly online.

5. Can I use the Binary Calculator on my mobile phone?
Yes, it is mobile-friendly and can be accessed from any device with internet access.