In this example, you will learn to convert binary to decimal numbers. Here we write a C program that takes a binary number as input and converts it into an equivalent decimal number. Converting a binary number to decimal means converting the number with base value 2 to base value 10.

The base value of a number system determines the number of digits used to represent a numeric value. For example, a binary number system uses 2 digits 0-1 to represent any numeric value.

Given a binary number n, you need to convert to a decimal number.

Example,

Input: 101
Output: 5


Input: 1001
Output: 9

To understand this code, you must have knowledge of the following C programming topics:

• Understanding of function in C.
• C Operators.

Binary to Decimal Conversion Formula:

The following formula is used to convert binary numbers to decimal numbers.

(Decimal Num)₁₀ = ( d ₀ × 2⁰ )+ ( d ₁ × 2¹ )+ ( d ₂ × 2² )+ ….. + ( d _{n − 1} × 2^n-1)

where “d” is a binary number containing “n” digits and d ₀ , d ₁ , d ₂ , …, d_n-1 are the individual digits of the binary number starting from the right-most position.

Example,

Let us convert (1001)₂, from binary to decimal using the formula. We start doing the conversion from the rightmost digit, which is ‘1’ here.

(Decimal Number)10 = (d₀ × 2⁰ )+ (d₁ × 2¹ )+ (d₂ × 2² )+ ….. (d_n−1 × 2^n-1)

= (1 × 2⁰) + (0 × 2¹) + (0 × 2²) + (1 × 2³)

= (1 × 1) + (0 × 2) + (0 × 4) + (1 × 8)

= 1 + 0 + 0 + 8

= 9

The binary to the decimal conversion of the first 20 decimal numbers is displayed in the chart given below.

C Program to Convert Binary Number to Decimal:

Method 1: Using math.h library function

#include <stdio.h>
#include <math.h>


// function definition
int convertBinaryToDecimal(long long n)
{
    int dec = 0, i = 0, rem;

    while (n!=0)
    {
        rem = n % 10;
        n /= 10;
        dec += rem * pow(2, i);
        ++i;
    }

    return dec;
}



int main()
{
    long long n = 1001;

    const int dec = convertBinaryToDecimal(n);

    printf("%lld in binary = %d in decimal\n", n, dec);

    return 0;
}

Output:

Method 2:

#include <stdio.h>


// function definition
int convertBinaryToDecimal(long long n)
{
    int num = n;
    int dec_value = 0;

    // Initializing baseValue value to 1, i.e 2^0
    int baseValue = 1;

    int temp = num;
    while (temp)
    {
        int last_digit = temp % 10;
        temp = temp / 10;

        dec_value += last_digit * baseValue;

        baseValue = baseValue * 2;
    }

    return dec_value;
}



int main()
{
    long long n = 10011;

    const int dec = convertBinaryToDecimal(n);

    printf("%lld in binary = %d in decimal\n", n, dec);

    return 0;
}

Output:

10011 in binary = 19 in decimal

Note: Above mentioned C program works only with binary numbers in the range of integers.

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