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# C Program to Convert Decimal Numbers to Binary Numbers

Last Updated on July 8, 2024 by Abhishek Sharma

Converting decimal numbers to binary numbers is a fundamental concept in computer science and digital electronics. Decimal numbers are base-10 numbers, which we use in our daily lives, whereas binary numbers are base-2 numbers, used internally by almost all modern computers and digital systems. Understanding how to convert decimal numbers to binary is crucial for various applications, such as computer programming, networking, and data processing. In this article, we will discuss a C program that converts decimal numbers to binary numbers, explaining the logic, implementation, and frequently asked questions about the process.

## Decimal Numbers in C

Decimal numbers in C are represented using the data type float or double depending on the required precision. Float uses 4 bytes and has a precision of 6-7 decimal digits, while double uses 8 bytes and has a precision of 15-16 decimal digits.

## Binary number in C

Binary numbers in C are represented using the data type int or long int which allocate memory in the form of 32 or 64 bits respectively. Binary numbers are written using the prefix 0b followed by a sequence of 0’s and 1’s.

## Algorithm to Convert a Decimal to Binary in C

Here’s a simple algorithm to convert a decimal to binary in c:

• Declare integer variables to store the decimal number, quotient, remainder, and binary number.
• Read the decimal number from the user.
• Initialize the quotient to the decimal number.
• Initialize the binary number to 0.
• Loop until the quotient is 0.
• Calculate the remainder by taking the modulus of the quotient with 2.
• Multiply the binary number by 10 and add the remainder to it.
• Update the quotient by dividing it by 2.
• Repeat steps 6-8 until the quotient is 0.
• Print the binary number

Example Code for Decimal to Binary in C

```#include <stdio.h>

int main() {
int decimal_num, binary_num = 0, i = 1, remainder;

printf("Enter a decimal number: ");
scanf("%d", &decimal_num);

while (decimal_num != 0) {
remainder = decimal_num % 2;
decimal_num /= 2;
binary_num += remainder * i;
i *= 10;
}

printf("Binary number: %d\n", binary_num);

return 0;
}```

The explanation for decimal to binary in c:
The program reads a decimal number from the user and then uses a while loop to convert the decimal number to binary. Inside the loop, the program calculates the remainder when the decimal number is divided by 2, adds the remainder to the binary number in the correct position, and updates the position by multiplying a counter by 10. Finally, it converts a decimal to binary in c the program prints out the binary number. The time complexity of the provided C program to convert a decimal number to a binary number is O(log n). The space complexity of this program is O(1).

Conclusion
Converting decimal numbers to binary numbers is an essential operation in computer science, enabling effective data representation and manipulation in digital systems. By understanding and implementing a C program for this conversion, one gains valuable insights into binary arithmetic and the foundational principles of computer operations. The discussed program and its variations demonstrate the practical application of bitwise operations and loops, which are crucial for efficient programming. Mastery of such conversions equips developers and engineers with the tools necessary for tasks ranging from low-level hardware programming to high-level software development.

## Frequently Asked Questions(FAQs) on C Program to Convert Decimal Numbers to Binary Numbers

Here are some FAQs on C Program to Convert Decimal Numbers to Binary Numbers:

1. What is the difference between decimal and binary number systems?
Decimal Number System: Uses base-10, consisting of digits 0-9. It is the standard system for denoting integer and non-integer numbers.
Binary Number System: Uses base-2, consisting of digits 0 and 1. It is used internally by almost all modern computers and digital systems.

2. Why is it important to convert decimal numbers to binary?
Converting decimal numbers to binary is important because computers use binary numbers to perform all their operations. Understanding this conversion helps in designing algorithms, understanding computer architecture, and debugging low-level code.

3. Can you explain the division by 2 method for conversion?
The division by 2 method involves repeatedly dividing the decimal number by 2 and recording the remainders. The binary number is formed by the remainders read from bottom to top (last remainder to first).

4. How does the provided program work?
The program uses a while loop to divide the decimal number by 2, storing the remainders in an array. After the loop, the array contains the binary digits in reverse order. A for loop then prints the binary digits in the correct order.

5. What is the maximum decimal number that can be converted using this program?
The maximum number depends on the size of the integer type used. For a 32-bit integer, the maximum is 2^31 – 1. For larger numbers, you would need to use a larger integer type, such as long long int.

6. How can you handle negative decimal numbers in conversion?
For negative numbers, you can use the two’s complement method to represent them in binary. This involves inverting the bits of the positive equivalent and adding 1.