Converting binary to decimal is a fundamental skill in computer science and digital electronics. Binary numbers are the foundation of all computing systems. Understanding how to convert these numbers into the more familiar decimal system can help you better grasp how computers process information.

Let’s understand how to convert binary to decimal.

**What is a Binary Number System?**

The binary number system is a method of representing numbers using only two digits: 0 and 1. It’s called “binary” because “bi-” means two. Each digit in a binary number is called a “bit,” which stands for “binary digit.” This system is the backbone of all modern computers and digital devices because it aligns perfectly with how electronic circuits operate. In these circuits, an electrical signal can either be on or off, which corresponds directly to the binary digits 1 and 0, respectively.

In binary, each position represents a power of 2, unlike the decimal system where each position represents a power of 10. For example, the binary number 1011 represents the decimal number 11 because it is calculated as:

- 1×2
^{3}(which is 8) - 0×2
^{2 }(which is 0) - 1×2
^{1 }(which is 2) - 1×2
^{0 }(which is 1)

So,

8+0+2+1=11 in decimal.

**Also Read:** What Are the 4 Types of Data?

**What is a Decimal Number System?**

The decimal number system is the most familiar to most people because it is the standard system for denoting integer and non-integer numbers. It is a base-10 system, which means it uses ten digits from 0 to 9. Each position in a decimal number represents a power of 10. For instance, the number 345 in decimal means:

- 3×10
^{2}(which is 300) - 4×10
^{1}(which is 40) - 5×10
^{0}(which is 5)

So,

300+40+5=345

The decimal system is intuitive for everyday use because it is based on ten digits, likely originating from humans having ten fingers. It’s widely used for arithmetic, finance, and in many aspects of daily life due to its simplicity and ease of understanding.

**What is Binary to Decimal Conversion?**

Binary to decimal conversion is the process of changing a number from the binary system (base-2) to the decimal system (base-10). In the binary system, numbers are represented using only two digits: 0 and 1. In contrast, the decimal system uses ten digits, from 0 to 9. This conversion is essential because computers use binary, but humans find decimal numbers easier to understand and work with.

**Binary to Decimal Conversion Methods**

There are two primary methods for converting binary to decimal:

- Positional Notation Method
- Doubling Method

**Positional Notation Method**

In this method, you multiply each binary digit by 2 raised to the power of its position, starting from 0 on the right. Here’s a step-by-step approach:

- Write down the binary number.
- Assign powers of 2 to each digit, starting from 0 on the right.
- Multiply each binary digit by the corresponding power of 2.
- Add all the resulting values.

**Example:**

Convert binary 1011 to decimal:

- 1 × 2
^{3}+ 0 × 2^{3}+ 1 × 2^{1}+ 1 × 2^{0} - = 8 + 0 + 2 + 1
- = 11

Thus, binary 1011 is equal to decimal 11.

**Doubling Method**

The doubling method is simpler and involves doubling the current total and adding the next digit. Here’s how it works:

- Start with the leftmost digit.
- Double the current total and add the next digit.
- Repeat the process for all digits.

**Example:**

Convert binary 1011 to decimal:

- Start with 1.
- Double it: 1 × 2 = 2, add the next digit: 2 + 0 = 2.
- Double it: 2 × 2 = 4, add the next digit: 4 + 1 = 5.
- Double it: 5 × 2 = 10, add the next digit: 10 + 1 = 11.

So, binary 1011 is equal to decimal 11.

**Also Read:** Structured Data Vs Unstructured Data

**Binary to Decimal Formula**

To convert a binary number to a decimal number, use the positional notation method. The formula is:

Decimal Number=(d_{0}×2^{2})+(d_{1}×2^{1})+(d_{2}×2^{2})+⋯+(d_{n}×2^{n})

Here, d represents each digit in the binary number, starting from the right (least significant bit) to the left (most significant bit). Each digit is multiplied by 2 raised to the power of its position.

Example:

Convert binary 1101 to decimal:

1×2^{3}+1×2^{2}+0×2^{1}+1×2^{0}

=8+4+0+1

=13

So, the binary number 1101 is equal to the decimal number 13

**How to Convert Binary to Decimal?**

- Write the Binary Number:

Write down the binary number you want to convert.

- Assign Powers of 2:

Starting from the rightmost digit, assign powers of 2 (beginning with 2^{0}) to each digit.

- Multiply Each Digit:

Multiply each binary digit by its corresponding power of 2.

- Sum the Results:

Add all the products together to get the decimal value.

**Example Using Positional Notation:**

Convert binary 1010 to decimal:

1×2^{3}+0×2^{2}+1×2^{1}+0×2^{0}

=8+0+2+0

=10

**Example Using Doubling Method:**

- Start with the leftmost digit.
- Double the current result and add the next binary digit.
- Repeat until you reach the rightmost digit.

For binary 1011:

- Start with 1.
- Double it and add the next digit: 1×2+0=2
- Double the result and add the next digit: 2×2+1=5
- Double the result and add the last digit: 5×2+1=11

So, the binary number 1011 is equal to the decimal number 11.

**To Conclude**

Converting binary numbers to decimal may seem challenging at first, but with practice, it becomes straightforward. By mastering this basic concept, you’ll gain a deeper understanding of how digital systems work and be better equipped to handle more complex topics in computing. Keep practicing, and soon, converting between these two number systems will feel like second nature.

**FAQs**

**What is binary to decimal conversion?**

- It converts numbers from binary (base-2) to decimal (base-10).
- Binary uses digits 0 and 1.
- Decimal uses digits 0 to 9.

**How do I convert a binary number to a decimal number?**

- Write down the binary number.
- List the powers of 2 under each digit.
- Multiply each digit by its corresponding power of 2.
- Sum the results.

**What are the common methods for binary to decimal conversion?**

- Positional Notation Method:
- Multiply each digit by 2 raised to its position’s power.
- Sum the results.

- Doubling Method:
- Start with the leftmost digit.
- Double the current result and add the next digit.
- Repeat until all digits are used.

**Why is binary important in computing?**

- Binary aligns with digital circuit states: on (1) and off (0).
- It’s the foundation of computer operations.
- Simplifies processing and storage in digital systems.

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