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# C Program to Convert Decimal Numbers to Binary Numbers

Last Updated on April 25, 2023 by Prepbytes The decimal to binary in c program initiates the user to enter a decimal number and then converts it to its equivalent binary representation using a while loop.

## 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
In conclusion, converting decimal to binary in c involves dividing the decimal number by 2 and noting down the remainder. The binary number can be represented using the int or long int data type in C and overflow/underflow can be handled using a larger data type or modulus operator.

Q1. How do you convert a decimal to binary in C?
Ans: To convert decimal to binary in c, you can use the "itoa" function which converts an integer value to a string of characters in a specified base, such as 2 for binary.

Q2. How can I print a binary number in C?
Ans: To print a binary number in C, you can use the "printf" function with the "%d" format specifier and the binary prefix "0b" to indicate the base. For example, printf("The binary equivalent is 0b%d", binary_num);

Q3. How can I convert a binary number to a decimal number in C?
Ans: To convert a binary number to a decimal number in C, you can use the "atoi" function which converts a string of characters to an integer value in base 10. However, you need to first convert the binary number to a string using the "sprintf" function with the "%d" format specifier and the binary prefix "0b".

Q4. What is the range of values that can be represented in binary using the data type "int" in C?
Ans: The range of values that can be represented in binary using the "int" data type in C is -2147483648 to 2147483647.

Q5. How do you handle overflow or underflow when working with binary numbers in C?
Ans: Overflow or underflow can occur when working with binary numbers in C if the result of an arithmetic operation exceeds the range of values that can be represented in the allocated memory. To handle this, you can either use a larger data type with more memory or use the "modulus" operator to obtain the remainder of the operation within the range of the data type.

Q6. How many bits are required to represent a decimal number in binary form?
Ans: The number of bits required to represent a decimal number in binary form depends on the size of the decimal number. A decimal number can be represented in binary form using as many bits as needed to represent the decimal number’s value. For example, the decimal number 7 can be represented in binary form using 3 bits (111), while the decimal number 1024 requires 11 bits (10000000000).