# C++ Program to Convert Decimal to Binary

January 31, 2023, Learn eTutorial
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In this C++ program, we convert the decimal number entered by the user to its corresponding binary number.

## Decimal number

In algebra, a decimal number can be defined as a number that has the base 10. means the numbers from 0 to 9.

## Binary number

A number system where a number is represented by using only two digits (0 and 1) with a base of 2 is called a binary number system. For example,112 is a binary number.

## How to convert a decimal number into a binary number?

To convert a decimal number into its equivalent binary number, we divide the decimal number by 2 each time, till we get 0 as a dividend. Let us take an example to convert 13 into a binary number.

• 13 ÷ 2: 6 and remainder 1
• 6 ÷ 2: 3 and remainder 0
• 3 ÷ 2: 1 and remainder 1
• 1 ÷ 2: 0 and remainder 1

Now we take the bits of the remainder from the last to the first, i.e.(MSB to LSB). Hence, 1310 = 11012.

## How to write a C++ program to convert a decimal number into a binary number?

display a message for user to enter input. The program has to convert this decimal input into its binary value. Here we are using three variables decimalnum, binarynum[20], and i. initially the value of i is set to 0. When the user enters the decimal number, it gets stored in decimalnum. Now a` while loop` is evaluated with the condition decimalnum!=0.

``````
while(decimalnum!=0)
{
binarynum[i] = decimalnum%2;
i++;
decimalnum = decimalnum/2;
}

```
```

Here, when the condition evaluates true, the program flow goes inside the loop and decimalnum%2 gets initialized to binarynum[i]. The value ofgets incremented. decimalnum/2 is initialized to decimalnum. Now decimalnum = decimalnum/2; The control flow goes back and evaluates the `while loop` again and the process repeats until the condition of the `while loop` evaluates to be false. After ending the` while loop, `we use another` for loop `for printing the binary number in reverse order.

### Algorithm

Step 1: Call the header file iostream.

Step 2: Use the namespace std.

Step 3: Open the main function; int main().

Step 4: Declare two integer type variables decimalnum, binarynum[20], i=0;

Step 5: Ask the user to enter a number;

Step 6: Get the number into the variable decimalnum;

Step 7: Evaluate a while loop with condition decimalnum!=0

Step 8: If true then compute decimalnum%2 and store the value to binarynum[i];

Step 9: increment the value of i;

Step 10: Update the variable decimalnum by decimalnum/2;

Step 11: Continue step 7 to step 10 until the condition goes wrong;

Step 12: Print the binarynum[] by using a for loop;

Step 13:Exit;

## C++ Source Code

```                                          ```#include<iostream>
using namespace std;
int main()
{
int decimalnum, binarynum[20], i=0;
cout<<"Enter the decimal Number: ";
cin>>decimalnum;
while(decimalnum!=0)
{
binarynum[i] = decimalnum%2;
i++;
decimalnum = decimalnum/2;
}
cout<<"\nEquivalent Binary Value: ";
for(i=(i-1); i>=0; i--)
cout<<binarynum[i];
cout<<endl;
return 0;
}```
```

## OUTPUT

```Enter the decimal Number: 125
Equivalent Binary Value: 1111101
```

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