Binary to Decimal
Binary to Decimal Converter
Binary to Decimal Overview
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.
How It Works
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.
Examples
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
Reference Tables
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:
- Write down the binary number.
- Assign powers of 2 from right to left (starting with 0).
- Multiply each binary digit by 2 to the power of its position.
- Add the resulting values to get the decimal number.
Formula:
Decimal = Σ (bit × 2^position)
Additional Information
A Unique Explanation for the Binary to Decimal Converter:
Binary (base-2) is the core of digital systems—each bit (0 or 1) represents the on/off state of a transistor in a circuit.
Decimal (base-10), used in everyday life, allows human-friendly calculations.
For example:
Convert binary 11101 to decimal:
= 1×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰
= 16 + 8 + 4 + 0 + 1 = 29
This conversion is essential when transitioning between computer-level binary code and human-readable formats.
Binary to Decimal Conversion Table
Binary
Decimal
0001
1
0010
2
0100
4
1000
8
0101
5
1010
10
1111
15
11000
24
100100
36
FAQs
1. What is binary to decimal conversion?
It’s the process of converting numbers from base-2 (binary) to base-10 (decimal).
2. How do I manually convert binary to decimal?
Multiply each binary digit by 2 raised to the position index, then sum all values.
3. Can this converter handle fractional binary numbers?
Yes, it converts both whole numbers and binary decimals like 101.11.
4. What is the binary of decimal 25?
25 in decimal = 11001 in binary.
5. Who uses binary to decimal conversion?
It is widely used by computer scientists, electronics engineers, software developers, and students.