Binary to Decimal

A Binary to Decimal Converter is a specialized tool that converts numbers written in binary (base-2)—the language of computers—into decimal (base-10), which is the standard numeric system used in everyday life. This conversion is vital in computer science, digital electronics, and educational contexts.

Binary numbers use only two digits: 0 and 1, while decimal numbers use ten digits: 0 through 9.

Conversion Principle:

Each binary digit (bit) represents an increasing power of 2, starting from the right.

To convert binary to decimal, multiply each bit by 2 raised to its positional index and sum them.

Example:

Binary 1011 → Decimal

= (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)

= 8 + 0 + 2 + 1 = 11

Common Uses for Binary to Decimal Conversion:

• Computer Science & Programming: Understanding memory addresses, bitwise operations, and logic gates.
• Digital Electronics: Reading and interpreting binary output from hardware.
• Data Transmission: Decoding binary data in communication systems.
• Mathematics & Education: Teaching number systems and base conversions.
• Cybersecurity & Networking: Analyzing IP addresses, subnetting, and encryption keys.

Key Features of Binary to Decimal Converter:

• High Precision: Accurately converts even large binary numbers into decimal.
• Instant Output: Get real-time results as you input binary digits.
• Bit-by-Bit Breakdown: Helps visualize each step of the conversion process.
• Error-Free: Eliminates manual calculation mistakes.
• User-Friendly Interface: Designed for students, professionals, and engineers.
• Supports Both Integers and Fractions: Converts binary integers and binary decimals (e.g., 101.1).

The Binary to Decimal Converter helps bridge digital data with real-world interpretation.

Enter the Binary Number:

Input binary digits like 1010 or 1101.01.

View the Decimal Output:

The tool instantly displays the decimal equivalent (e.g., 1010 → 10).

Understand the Calculation:

Each bit is multiplied by 2 raised to its respective position and summed up.

Use Across Applications:

Useful in academic exercises, digital system designs, and programming workflows.

Formula:

Decimal = (bₙ × 2ⁿ) + (bₙ₋₁ × 2ⁿ⁻¹) + ... + (b₀ × 2⁰)

Example 1:

Binary: 1101

= (1×2³) + (1×2²) + (0×2¹) + (1×2⁰)

= 8 + 4 + 0 + 1 = 13

Example 2 (Fractional):

Binary: 101.1

= (1×2²) + (0×2¹) + (1×2⁰) + (1×2⁻¹)

= 4 + 0 + 1 + 0.5 = 5.5

Binary

Decimal

0

0

1

1

10

2

11

3

100

4

101

5

110

6

111

7

1000

8

1001

9

1010

10

1100

12

1111

15

10000

16

Steps to Convert Binary to Decimal:

1. Write down the binary number.
2. Assign powers of 2 from right to left (starting with 0).
3. Multiply each binary digit by 2 to the power of its position.
4. Add the resulting values to get the decimal number.

Formula:

Decimal = Σ (bit × 2^position)