Binary To Decimal

Binary to Decimal Conversion

Binary to decimal conversion is a process used to translate binary numbers into decimal numbers. This conversion is essential for understanding how computers process and store data.

How to Convert Binary to Decimal

The conversion process involves several steps:

1. Positional Notation Method:
   • Start with the rightmost digit of the binary number.
   • Multiply each digit by the corresponding power of 2, starting from 2020 for the rightmost digit.
   • Add the results of all the multiplications to get the decimal number.
2. Doubling Method:
   • Start from the leftmost digit of the binary number.
   • Double the previous result and add the current digit.
   • Continue this process until all digits are processed.

Example: Converting Binary to Decimal

Let's convert the binary number 1011 to decimal using the positional notation method:

1. Write the Binary Number: 1011
2. Multiply Each Digit by the Corresponding Power of 2:
   • Rightmost digit (1): 1×20=11×20=1
   • Next digit (1): 1×21=21×21=2
   • Next digit (0): 0×22=00×22=0
   • Leftmost digit (1): 1×23=81×23=8
3. Add the Results Together: 1+2+0+8=111+2+0+8=11

So, the decimal equivalent of 1011 is 11.

Tools for Binary to Decimal Conversion

Several online tools are available for converting binary to decimal, such as:

• Cuemath Binary to Decimal Converter: Offers detailed explanations and examples for conversion.
• GeeksforGeeks Binary to Decimal Converter: Provides a step-by-step guide and examples.
• BYJU'S Binary to Decimal Converter: Includes formulas and tables for conversion.

Why Convert Binary to Decimal?

Converting binary to decimal is important for several reasons:

• Readability: Decimal numbers are more readable and understandable than binary.
• Data Interpretation: It helps in interpreting binary data stored or transmitted by computers.
• Communication: Enables communication between humans and computers by translating machine language into human-readable numbers.

Python Program for Binary to Decimal Conversion

Here is a simple Python program that converts binary to decimal:

python

def binary_to_decimal(binary):    decimal = int(binary, 2)    return decimal binary = "1011" print("Decimal Representation:", binary_to_decimal(binary))

This program uses the built-in int() function with base 2 to convert binary to decimal.