# Binary to Decimal Converter

Enter a number:

## Results

Binary:

Octal:

Decimal:

In today's digital world, binary numbers are the backbone of all computer systems. These numbers, represented in a base-2 numeral system, consist of only two digits: 0 and 1. On the other hand, decimal numbers use a base-10 numeral system, which employs digits from 0 to 9. To bridge the gap between the human-friendly decimal system and the computer-friendly binary system, it is essential to understand how to convert binary numbers to decimal numbers. In this article, we will explore the binary to decimal conversion process and provide examples to illustrate the concept.

1. Understanding Binary and Decimal Number Systems

Before diving into the conversion process, it is crucial to grasp the basics of binary and decimal number systems.

1.1 Binary Numbers

A binary number system uses base-2, which means it consists of only two digits: 0 and 1. Each digit in a binary number represents a power of 2, starting from the rightmost digit (2^0) and increasing exponentially to the left (2^1, 2^2, 2^3, etc.).

For example, the binary number 1010 represents:

(1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (0 × 2^0) = 8 + 0 + 2 + 0 = 10 (in decimal)

1.2 Decimal Numbers

The decimal number system, also known as the base-10 system, uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit represents a power of 10, starting from the rightmost digit (10^0) and increasing exponentially to the left (10^1, 10^2, 10^3, etc.).

For example, the decimal number 325 represents:

(3 × 10^2) + (2 × 10^1) + (5 × 10^0) = 300 + 20 + 5 = 325

1. Binary to Decimal Conversion Process

Converting a binary number to its decimal equivalent involves a simple yet systematic process. Follow these steps:

Step 1: Write down the binary number. Step 2: Starting from the rightmost digit, assign a power of 2 to each digit, increasing the exponent by 1 as you move to the left. Step 3: Multiply each binary digit by its corresponding power of 2. Step 4: Sum up the products obtained in step 3. The result is the decimal equivalent of the binary number.

Example: Convert the binary number 1101 to decimal.

1. Binary number: 1101
2. Assign powers of 2: (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0)
3. Multiply digits by powers of 2: (8) + (4) + (0) + (1)
4. Sum up the products: 8 + 4 + 0 + 1 = 13 (decimal equivalent)

Therefore, the binary number 1101 is equal to 13 in decimal.

Conclusion

Understanding binary to decimal conversion is essential for anyone working with computer systems, programming languages, or digital electronics.