# C Program to Convert a Binary Number to a Decimal Number

Last updated on September 24, 2020

The following is a C program to convert a binary number to a decimal number.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
/*******************************************************
* Program to convert a binary number to decimal number
********************************************************/
#include<stdio.h> // include stdio.h
#include<math.h> // include stdio.h
int main()
{
long int bin, remainder, decimal = 0, i = 0;
printf("Enter a binary number: ");
scanf("%d", &bin);
while(bin != 0)
{
remainder = bin % 10;
decimal += remainder * (int)pow(2, i++);
bin = bin / 10;
}
printf("Decimal: %d", decimal);
return 0;
}
``` |

**Expected Output:** 1st run:

1 2 | ```
Enter a binary number: 100
Decimal: 4
``` |

2nd run:

1 2 | ```
Enter a binary number: 1000011
Decimal: 67
``` |

## How it works #

Here are the steps to convert a binary number to a decimal number:

**Example 1**: Convert binary number `100`

to its decimal equivalent.

1 2 3 | ```
=> ( 1 * 2^2 ) + ( 0 * 2^1 ) + ( 0 * 2^0 )
=> 4 + 0 + 0
=> 4
``` |

**Example 2**: Convert binary number `1001`

to its decimal equivalent.

1 2 3 | ```
=> ( 1 * 2^3 ) + ( 0 * 2^2 ) + ( 0 * 2^1 ) + ( 1 * 2^0 )
=> 8 + 0 + 0 + 1
=> 9
``` |

The following table shows what happens at each iteration of the loop (assuming `bin = 10101`

):

Iteration | remainder | decimal | bin |
---|---|---|---|

After 1st iteration | `remainder = 10101 % 10 = 1` |
`decimal = 0 + 1 * (2^0) = 1` |
`bin = 10101 / 10 = 1010` |

After 2nd iteration | `remainder = 1010 % 10 = 0` |
`decimal = 1 + 0 * (2^1) = 1` |
`bin = 1010 / 10 = 101` |

After 3rd iteration | `remainder = 101 % 10 = 1` |
`decimal = 1 + 1 * (2^2) = 5` |
`bin = 101 / 10 = 10` |

After 4th iteration | `remainder = 10 % 10 = 0` |
`decimal = 5 + 0 * 2^3 = 5` |
`bin = 10 / 10 = 1` |

After 5th iteration | `remainder = 1 % 10 = 1` |
`decimal = 5 + 1 * (2^4) = 21` |
`bin = 1 / 10 = 0` |

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