Given a binary number as input, we have to write a solution to convert the binary number into an equivalent decimal number in C.

Wish to enhance your foundation skills, then why not check out our Foundation Course designed by experienced mentors at Prepbytes.

## What is a Binary Number?

A binary number is defined as a number that is expressed in the binary system or base 2 numeral system. It describes numeric values by two separate symbols; 1 (one) and 0 (zero).

## What is a Decimal Number?

Decimal is a term that describes the base-10 number system, probably the most commonly used number system. The decimal number system consists of ten single-digit numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The number after 9 is 10. The number after 19 is 20 and so forth.

**Example:**

**Input1:** 111

**Output1:** 7

**Explanation:** (1 * 22) + (1 * 21)+(1 * 20) = 4 + 2 + 1 = 7

**Input2:** 1010

**Output2:** 10

**Input3:** 110

**Output3:** 6

## Conversion of Binary to Decimal in C using Recursion

In this approach we are using the recursive function. BinarytoDecimal(strBinary, length) which takes input string and its length and for each character convert it to decimal and multiply it with 2i . Add previous results to it.

- Take the input string strBinary[] containing a binary number.
- Calculate its length using strlen(strBinary).
- Function BinarytoDecimal(strBinary, length) takes input and returns the number calculated using a recursive approach.
- If we are at last character which is LSB, then return its decimal as it will be the same. (multiplied with 1 i.e 20 )
- Otherwise set temp=binary[i] – ‘0’. Its decimal value.
- Now multiply temp with 2len-i-1 using temp << len – i – 1.
- Add the result of other digits to temp using temp = temp + BinarytoDecimal(binary, len, i + 1).
- At the end of recursion return temp.
- Print the calculated decimal in main.

** For Example**:

If the binary number is 111.

dec_value = 1

*(2 ^ 2) + 1*(2 ^1) + 1 * (2 ^ 0) = 7

The below diagram explains how to convert ( 1010 ) to equivalent decimal value:

### Code Implementation of Recursive approach for converting Binary to Decimal in C:

#include <stdio.h> #include <string.h> int BinarytoDecimal(char binary[],int len, int i){ if (i == len-1) return (binary[i] - '0'); int temp=binary[i]-'0'; temp=temp<<len-i-1; temp=temp+BinarytoDecimal(binary,len,i+1); return (temp); } int main(){ char strBinary[] = "111"; int length=strlen(strBinary); printf("Decimal Number of given binary number: %d",BinarytoDecimal(strBinary,length,0)); return 0; }

**Time Complexity:** The time complexity of this implementation of converting binary number into decimal number is O(logN).

**Space Complexity:** The space complexity of this implementation of converting binary number into decimal number is O(1).

## Conversion of Binary to Decimal in C using For Loop

In this approach we are using the for loop.

Let’s Discuss the algorithm for converting binary numbers into decimal numbers.

- Firstly, initialize the decimal_num variable with value 0, and add the binary number in the bin_num variable, and initialize rem.
- Now, start a for loop with condition i = 0, bin_num != 0, ++i.
- In the loop block,
- Update the rem value to bin_num % 10.
- Change the value of bin_num with bin_num / 10.
- Atlast change the value of decimal_num with decimal_num + (rem) * (pow(2, i)).

- At the end of the for loop, print the decimal_num variable which is having the value of the decimal number of the given binary number.

### Code Implementation of For Loop approach for converting Binary to Decimal in C:

#include <stdio.h> #include <math.h> int main() { int i, bin_num, decimal_num = 0, rem; bin_num = 111; for (i = 0; bin_num != 0; ++i) { rem = bin_num % 10; bin_num = bin_num / 10; decimal_num = decimal_num + (rem) * ( pow (2, i)); } printf ("\n Decimal Number of given binary number: %d", decimal_num); return 0; }

**Time Complexity:** The time complexity of this implementation of converting binary number into decimal number is O(logN).

**Space Complexity:** The space complexity of this implementation of converting binary number into decimal number is O(1).

## Conversion of Binary to Decimal in C using Function

Let’s Discuss the algorithm for converting binary numbers into decimal numbers.

- A binary number is stored in the bin_num variable, and one other variable dec_num is initialized for storing the decimal number.
- binaryTodecimal function will be called and bin_num is passed in it.
- In the function, decimal_num with 0, temp with 0 and rem is initialized.
- Then a while loop is started with a condition bin_num != 0.
- Inside the loop, following steps will be done:
- Change the value of rem to bin_num % 10.
- Change the value of bin_num to bin_num / 10.
- Change the value of decimal_num to decimal_num + rem * pow( 2, temp).

Change the value of temp to temp++.

- At last return the decimal_num variable.

### Code Implementation for converting Binary to Decimal in C using Function:

#include <stdio.h> int binaryTodecimal(int bin_num); int main() { int bin_num, dec_num; bin_num = 111; dec_num = binaryTodecimal (bin_num); printf (" Conversion of the binary number to decimal number is %d", dec_num); return 0; } int binaryTodecimal( int bin_num) { int decimal_num = 0, temp = 0, rem; while (bin_num != 0) { rem = bin_num % 10; bin_num = bin_num / 10; decimal_num = decimal_num + rem * pow( 2, temp); temp++; } return decimal_num; }

**Time Complexity:** The time complexity of this implementation of converting binary number into decimal number is O(logN).

**Space Complexity:** The space complexity of this implementation of converting binary number into decimal number is O(1).

This article tried to discuss different approaches to convert binary to decimal in C. Hope this blog helps you understand and solve the problem. To practice more problems you can check out MYCODE | Competitive Programming at Prepbytes.