# 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 // include stdio.h #include // 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