## Introduction to Binary to Decimal Conversion

Are you familiar with the concept of binary code? It is the system through which computers store and process information.

Every data point in the digital world is represented as binary digits, also known as bits. Each bit can hold either a 0 or a 1, which indicates the presence or absence of an electrical charge.

However, for humans, it is easier to understand and interpret decimal numbers that range from 0 to 9.

Conversion from binary to decimal format is a crucial task in the digital world.

This article will provide a comprehensive guide on how to convert binary numbers to decimal format. We will start by discussing the basic formula required to carry out the conversion and then move on to the algorithm used to convert binary numbers to decimal equivalents.

## Conversion Method

The primary method used to convert a binary number to its decimal equivalent is by using the formula. Here is the formula that is used to carry out this conversion:

Decimal equivalent = b0 2^0 + b1 2^1 + b2 2^2 + ….

+ bn 2^n

where b0, b1, b2, …. bn represent the binary digits in the number, and n is the total number of digits in the binary number.

## Algorithm to Convert Binary Number to Decimal Equivalent

The following are the step-by-step procedures for converting binary numbers to decimal format.

Step 1: Identify the Decimal Equivalent of the Binary Digits

The binary digits in a number have their own decimal equivalent.

Here is a simple table that will help you identify the decimal equivalent of each binary digit.

## Binary digits Decimal equivalent

0 0

1 1

Step 2: Write Down the Binary Number

Write down the binary number that you want to convert to decimal format.

Step 3: Assign a Weighted Value to Each Binary Digit

Assign a weighted value to each binary digit in the binary number.

The weight of each binary digit depends on its position in the number. For instance, the weight of the first binary digit is 2^0, the second digit is 2^1, the third digit is 2^2, and so on.

Step 4: Multiply Each Binary Digit with its Weighted Value

Multiply each binary digit in the binary number by its weighted value.

Step 5: Add the Results of All Multiplications

Sum up the results of all the multiplication to get the decimal equivalent of the binary number.

That was a brief overview of the algorithm used to convert binary numbers to decimal format. Now, let us delve deeper into the two methods that can be used to carry out the conversion.

Method 1: Convert Using Loop and Integer Variables

This method involves using either a while loop or a for loop. Here are the steps involved in this method.

## Use while Loop

Step 1: Declare an Integer Variable

Declare an integer variable and initialize it to zero.

Step 2: Obtain the Remainder and Quotient

Divide the binary number by 10 to obtain the remainder and quotient.

Step 3: Multiply the Remainder with 2n-1

Multiply the remainder by 2n-1, where n is the position of the binary digit in the number.

Step 4: Add the Result to the Variable

Add the result from step 3 to the integer variable declared in step 1.

Step 5: Update the Binary Number

Update the binary number by making the quotient the new binary number.

Step 6: Repeat Steps 2 to 5 Until the Binary Number Becomes 0

Carry out steps 2 to 5 continuously until the binary number becomes 0.

## Use for Loop

Step 1: Declare an Integer Variable

Declare an integer variable and initialize it to zero.

Step 2: Count the Number of Bits in the Binary Number

Count the number of bits in the binary number.

Step 3: Loop Through Each Bit in the Binary Number

Using a for loop, loop through each bit in the binary number from the right.

Step 4: Obtain the Power of 2 for Each Bit

For each bit, obtain the power of 2 by using the pow() function.

Step 5: Calculate the Product of Each Bit by its Power of 2

Calculate the product of each bit by its power of 2.

Step 6: Add all the Products to the Variable

Add all the products obtained in step 5 to the integer variable declared in step 1.

These two methods are the most commonly used methods for converting binary numbers to decimal format. Now that you know how to carry out the conversion, you are on your way to becoming a master in the digital world!

Method 2: Use a Procedural Approach

Another approach to convert binary numbers to decimal is by using a procedural approach.

This method involves creating a user-defined procedure or function to carry out the conversion. Here is how you can use a modular code to make the conversion.

## User-defined procedure or function

The first step in using a procedural approach is to create a user-defined procedure or function. You can give it a name that specifies the purpose of the code.

For instance, you can name the procedure or function “binarytodecimal ()”.

This is how to create the user-defined procedure or function:

Step 1: Declare the Function

Start by declaring the function by specifying its return data type and arguments.

Step 2: Get the Binary Number

Within the function code, calculate the decimal equivalent by following the formula discussed earlier. The function should take a binary number as an argument.

Step 3: Return the Decimal Equivalent

Return the decimal equivalent of the binary number.

By creating a user-defined procedure or function, you can use it in multiple parts of your program, making it easier to manage and reuse your code.

Method 3: Use the char Array to Store Binary Number

In this method, you convert the binary number to its decimal equivalent by storing the binary digits in a character array. This is how you can carry out the conversion using this approach.

## Storing binary numbers in integer encoding

When storing binary numbers in integer encoding, the maximum size of the integer should be considered. For instance, for a 32-bit compiler, the maximum size that an integer can hold is 2 – 1.

By converting a binary number to its decimal equivalent, the size of the integer can increase, exceeding 2 – 1. Therefore, this method is not suitable when working with large binary numbers.

## Using a char array

To use a char array, you need to allocate dynamic memory to the array. This is how you can do it:

Step 1: Declare a Dynamic Char Array

Declare a dynamic char array using the malloc() function.

The number of elements in the array should be equal to the number of binary digits in the binary number.

Step 2: Enter the Binary Number

Ask the user to enter the binary number.

Step 3: Store the Binary Digits

Store the binary digits in the dynamic char array.

Step 4: Calculate the Decimal Equivalent

Calculate the decimal equivalent of the binary number using the atoi() function.

Step 5: Free Memory

Free the memory allocated to the dynamic char array using the free() function.

Using a char array to store binary numbers can be useful when working with small binary numbers. However, when working with larger binary numbers, it may be more practical to use the formula or loop methods discussed earlier.

## Conclusion

In conclusion, converting binary numbers to decimal format is a crucial task in the digital world. There are different approaches you can use to carry out the conversion.

The methods discussed in this article include using a formula, using loops, using user-defined procedures or functions, and using a char array to store binary numbers. Each method has its advantages and disadvantages.

Therefore, it is important to choose the most appropriate method depending on the size and complexity of the binary number being converted. By using these methods, you can become a master in binary to decimal conversion, making your digital life a lot easier.

In conclusion, converting binary numbers to decimal is a fundamental task in the digital world. This article presented four methods to transform binary digits to their decimal equivalent: using a formula, using loops, using a procedural approach, and using a char array.

The choice of method depends on the complexity and size of the binary number. By using these methods, one can become a master in binary to decimal conversion and navigate the digital world with ease.

Understanding how to convert binary to decimal is vital for anyone working or studying in computer science and related fields.