Decimal to Binary in C Conversion Program with Explanation

Learning Number Systems

In our everyday life we follow the decimal system base 10, which includes 0 to 9 digits. Instead, computers are based on using binary numbers where there are only two values, 0 and 1 that correspond to off and on states in electronics respectively in a system known as base-2. Other number systems in computing exist besides decimal and binary:

Decimal Number System (Base- 10): The system incorporates 10 symbols (0-9) of which the position of each symbol enables it to be used to specify its value (i.e., 345 denotes 3 hundreds, 4 tens, and 5 ones). It is the most prevalent human system. C programming, decimal values could be represented using data types of float and double and each takes 4 and 8 bytes of storage respectively with different degrees of precision.

Binary Number System (Base-2): It is the basic language of computers with two digits namely 0 and 1. Every place position of binary notation is a power of two such that 101 in binary has the same value as 5 in decimal format (122+021+120=5). C In C, int or long int data types (32 or 64 bits) are usually used to represent binary numbers, and can be expressed using the prefix 0b (e.g., 0b1010).

Octal Number System (Base -8): Octal system has eight numbers (0-7) which are raised by the power of 8. It makes the long binary sequences easier to use since three binary digits could be rendered using one octal digit shortening there.

Hexadecimal Number Representation (Base-16): There are sixteen signs in this system 0-9 and A-F (A=10, B=11, etc.) All the place values are exponents of 16. Binary numbers are simplified by hexadecimal, whereby one hexadecimal represents four binary numeric values, and this is applicable in computing.

Dec 2 Binary Conversion Algorithm:

The division method is the essence of how the conversion of a decimal number to binary works. This is by continuously dividing the decimal number by 2 and noting down remainders. The result of the subsequent subtractions will always be 0 or 1 and these form the binary digits. This is repeated until one gets 0 as a quotient. The order of the stored remainders is used after wording the binary number in reverse order.

An algorithm of conversion looks like this:

° Declare integer variables of the decimal number, quotient, remainder and the binary number.

° Read the decimal number of a user.

° Set the quotient to the decimal number.

° Make the binary number initialize to 0.

° So long as the quotient isNon 0 loop

° Reduce the quotient with 2 (quotient % 2).

° Multiply the binary form by 10 and add the result to it.

° Bring down the quotient by dividing it with 2 ( quotient / 2 ).

° Reprint the binary number.

As an example to represent 13 in binary:

132=6 r 1

6/2=3 r 0

3b 2=1 remainder 1

1 2 = 0 1

Reading the remainders bottom-to-top (that is backward), the binary value of 13 is obtained: 1101.

Conversion methods of C

There are a number of ways to do decimal to binary conversion in C and each has its benefit:

For Loop Approach

Mechanism In this scheme, a decimal number is divided by 2 repeatedly and the remainder are kept in an array. It keeps repeating until the decimal number equals 0. Lastly, reversing the hardware array and printing the binary digits through iteration of the array is carried out.

• Set Initial Variables: define variables to hold the decimal number used, remainder value and the binary array (e.g. int binary in 32-bits).
• Input Decimal Number: Request the user by entering the decimal number.
• Binary: A for loop repeatedly divides by 2 and puts the remainder in the binary array and the quotient is updated.
• Output Binary Number: Print the elements of the binary array in reverse order in order to get the correct binary representation.
• Time Complexity: On log n because the number is divided by 2 again and again.
• Space Complexity: O(log n) as there is holding of binary digits in an array.

Implementing While Loop

Like in the for loop, the while loop repeatedly splits the decimal number with 2, finds the remainder and constructs the binary representation.

• Initialize Variables: Initialize variables of the decimal number, remainder and the binary number (initialized as 0).
• Input Decimal Number: Request input of the user.
• Conversion Process: The conversion is achieved by executing a whole loop that continues until a decimal number becomes less than 0. The inside of the loop is where the rest of the division by 2 is done and utilized to form the binary number with the decimal one being updated.
• Current Binary Number: The output is shown once the loop finishes.
• A complexidade é: O(log n).
• Space Complexity – O(log n)
•  

A User-Defined Function

When conversion logic is put in a function, the code becomes modular and reusable.

• Definition of the function: It could accept the decimal number as a parameter and perform the conversion in the body of the function (eg. with a while loop) and either print or send out the converted binary result.
• Function Call: This function is called by the main program and it receives the decimal input of the user.
• Code Structure: This method assists in breaking apart the issue into small manageable elements and makes it easier to read and streamline.

On a Stack

The binary digits (remainders) computed can then be stored in stacks. It is especially convenient since binary digits are bits generated most significantly last and the stack can easily be reversed by popping the elements.

Set Variables: Create an array of the stack (int) and the variable to indicate the top index.

Input Decimal Number: Get the user to give an input.

Remainders onto stack: In a loop (while or for loop) have decimal value divided by 2 and calculate the remainder and push it onto the stack (increment by 1) (top).

Pop and Print Binary Digits: Having exited the conversion loop, pop the values off the stack one at a time and print them so they are in correct order as a binary number.

Time: O (log n).

Space Complexity O( log n).

Bitwise Operators

It can be effectively done using bitwise operators such as the AND (&) and the right shift (>>) in converting decimal to binary since it operates on individual bits. The operation >> shifts bits to the right and operation & 1 retrieves the least significant bit. The advantage of this method is that this avoids divisions by arithmetic operations and hence is faster hardware wise.

Set Variables: make an integer to the decimal number and a variable to binary digits.

Input Decimal Number: Get the user to give an input.

Bitwise Operation Loop: A for or while loop performs a loop over every bit (e.g. by decreasing the most significant bit to the least significant bit). The >> moves the bits and & 1 gets the current bit.

Output Binary Number: One by one print the bits printed out. To skip leading zeros special handling might be required.

Time Complexity: O ( log n).

Space Complexity: O(1) since no additional array or stack to store the bits is used.

Of Non-Array Use

The purpose of this approach is to directly represent the decimal in its binary form, usually by printing digits at the moment they are computed, or by constructing the binary value as a number of decimal digits in order to skip storing it in an array.

Initialization Task: Define the variables of the decimal number and remainder.

Input Decimal Number: Request the input of the user.

Conversion Process: This is done with a while loop that computes the remainder and prints the remainder, but updates the decimal number by dividing by 2.

Output Binary Number: These digits are printed in such a way that the least significant bit appears first and thus some device that inverts the output or stores it in memory is required to correctly display the number. The method can be applied with the help of bitwise operators to be more efficient and prevent storing of the result in the array.

Time Complexity: O ( log n).

Complexity of space: O(1).

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