Convert Binary To Decimal

• Blockchain Council
• August 26, 2024

Binary to Decimal

Binary to decimal conversion means changing a number from the binary system (base-2) to the decimal system (base-10). In the binary system, numbers are expressed using only two digits: 0 and 1. In contrast, the decimal system uses ten digits: 0 through 9. Converting from binary to decimal involves calculating the decimal value of the binary number based on its digits and their positions.

Examples:
1/8 in decimal form is 0.125

2/3 as a decimal is 0.666

3/8 as a decimal is 0.375

2/3 as a decimal is 0.666

5/9 as a decimal is 0.556

Conversion Methods

Two common methods for converting binary numbers to decimals are positional notation and doubling.

Positional Notation Method

• Write Down the Binary Number: Start by writing the binary number you want to convert.
• List Powers of 2: Write the powers of 2 (1, 2, 4, 8, etc.) below each binary digit, starting from the right.
• Multiply and Sum: Multiply each binary digit by its corresponding power of 2, then sum all these values to get the decimal number.

Example: Convert 1101 to decimal:

• Binary: 1 1 0 1
• Powers of 2: 8 4 2 1
• Calculation: 1×8+1×4+0×2+1×1=8+4+0+1=13

So, 1101 in binary is 13 in decimal.

Doubling Method

• Start from Left: Take the leftmost binary digit.
• Double and Add: Double the current result and add the next binary digit.
• Repeat: Continue this process until you have included all binary digits.

Example: Convert 1101 to decimal:

• Start with the leftmost 1: Result = 1
• Next digit (1): 1×2+1=3
• Next digit (0): 3×2+0=6
• Last digit (1): 6×2+1=13

So, using this method, 1101 in binary is also 13 in decimal.

Also Read: What is Unstructured Data?

Binary to Decimal Formula

The binary-to-decimal formula helps convert a number from the binary system (base-2) to the decimal system (base-10). Here’s the formula:

Decimal Number=(d0×22)+(d1​×21)+(d2×22)+…+(dn×2n)

In this formula:

• 𝑑0,𝑑1,𝑑2,…,𝑑n are the binary digits.
• The exponent n is the position of the digit, starting from 0 on the right.

How to Convert Binary to Decimal?

To convert a binary number to a decimal, follow these simple steps:

• Write Down the Binary Number: Note each digit from right to left.
• List Powers of 2: Start from 0 and increase by one as you move left.
• Multiply Each binary digit by two raised to its position power.
• Sum the Results: Add all the products to get the decimal number.

Example

Let’s convert the binary number 11012 to decimal:

• Write the binary number: 11012
• List powers of 2: 23,22,21,20
• Multiply each binary digit:
  • 1×23=8
  • 1×22=4
  • 0×21=0
  • 1×20=1
• Sum the results: 8+4+0+1=13

So, 11012=1310

Another Example

Convert 10102 to decimal:

• Write the binary number: 10102
• List powers of 2: 23,22,21,20
• Multiply each binary digit:
  • 1×23=8
  • 0×22=0
  • 1×21=2
  • 0×20=0
• Sum the results: 8+0+2+0=10

So, 10102=1010

What is a Binary Number System?

The binary number system is a way to represent numbers using only two digits: 0 and 1. It is a base-2 system, which means each digit in a binary number represents a power of 2. For example, the binary number 101 represents 1×22+0×21+1×20 , which equals 5 in the decimal system.

Binary is crucial for computers because they operate using digital circuits, which have two states: on (1) and off (0). This makes binary a natural fit for digital electronics and computing.

Also Read: What are the 4 Types of Data?

What is a Decimal Number System?

The decimal number system is the standard system for denoting integers and non-integers. It is also known as the base-10 system because it is based on ten digits: 0 through 9. Each position in a decimal number represents a power of 10. For instance, the number 345 represents 3×102+4×101+5×100.

We use the decimal system daily for counting and calculations, making it the most familiar number system to humans. It’s easy to understand and use because it aligns with our ten fingers for counting.

Conclusion:

Converting binary to decimal is an essential skill in the world of computing. By following the steps outlined in this guide, you can quickly transform binary numbers into decimals. Practice with different binary numbers, and soon, you’ll find the process intuitive and quick.

FAQ’s

What is binary to decimal conversion?

• Binary to decimal conversion means changing a number from base-2 (binary) to base-10 (decimal).
• In binary, numbers use only 0 and 1.
• In decimal, numbers use digits from 0 to 9.
• Conversion helps in understanding and using numbers processed by computers.

How do you convert binary to decimal using positional notation?

• Write down the binary number.
• List powers of 2 below each digit, starting from 0 on the right.
• Multiply each binary digit by its corresponding power of 2.
• Sum all the products to get the decimal value.

How does the doubling method work for binary-to-decimal conversion?

• Start with the leftmost binary digit.
• Double the current total and add the next digit.
• Repeat the process for all digits.
• The final result is the decimal value.

Why is binary important in computing?

• Binary aligns with digital circuits, which have two states: on (1) and off (0).
• It simplifies the design of electronic systems.
• Understanding binary helps in learning how computers and digital systems work.
• Many programming and computer science concepts are based on binary operations.