Example 1: C++ Program to Convert Binary Number to Decimal
Output
Enter a binary number: 1101 1101 in binary = 13 in decimal
In the program, we have included the header file cmath to perform mathematical operations in the program.
We ask the user to enter a binary number and pass it to the convert() function to convert it decimal.
Suppose n = 1101. Let's see how the while loop in the convert() function works.
| n != 0 | rem = n % 10 | n /= 10 | i | dec += rem * pow(2, i) |
|---|---|---|---|---|
| 1101 != 0 | 1101 % 10 = 1 | 1101 / 10 = 110 | 0 | 0 + 1 * pow (2, 0) = 1 |
| 110 != 0 | 110 % 10 = 0 | 110 / 10 = 11 | 1 | 1 + 0 * pow (2, 1) = 1 |
| 10 != 0 | 11 % 10 = 1 | 11 /10 = 1 | 2 | 1 + 1 * pow (2, 2) = 5 |
| 1 != 0 | 1 % 10 = 1 | 1 / 10 = 0 | 3 | 5 + 1 * pow (2, 3) = 13 |
| 0 != 0 | - | - | - | Loop terminates |
So, 1101 in binary is 13 in decimal.
Now, let's see how we can change the decimal number into a binary number.
Example 2: C++ Program to convert decimal number to binary
Output
Enter a decimal number: 13 13 in decimal = 1101 in binary
Suppose n = 13. Let's see how the while loop in the convert() function works.
| n != 0 | rem = n % 2 | n /= 2 | i | bin += rem * i | i * = 10 |
|---|---|---|---|---|---|
| 13 != 0 | 13 % 2 = 1 | 13 / 2 = 6 | 1 | 0 + 1 * 1 = 1 | 1 * 10 = 10 |
| 6 != 0 | 6 % 2 = 0 | 6 / 2 = 3 | 10 | 1 + 0 * 10 = 1 | 10 * 10 = 100 |
| 3 != 0 | 3 % 2 = 1 | 3 / 2 = 1 | 100 | 1 + 1 * 100 = 101 | 100 * 10 = 1000 |
| 1 != 0 | 1 % 2 = 1 | 1 / 2 = 0 | 1000 | 101 + 1 * 1000 = 1101 | 1000 * 10 = 10000 |
| 0 != 0 | - | - | - | Loop terminates |
Thus, 13 in decimal is 1101 in binary.