🔄📚Intermediate

Binary to Decimal Conversion

Convert binary to decimal

Convert binary to decimal by multiplying each bit by its position value (power of 2). Each position from right to left represents 2⁰, 2¹, 2², etc.

📐 Formula

For binary number b₃b₂b₁b₀:

Decimal = b₀×2⁰ + b₁×2¹ + b₂×2² + b₃×2³ + ...

🔢 Step-by-Step: Converting 11001 to Decimal

Binary: 1 1 0 0 1

Position: 4 3 2 1 0

= 1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰

= 1×16 + 1×8 + 0×4 + 0×2 + 1×1

= 16 + 8 + 0 + 0 + 1

= 25

📊 Powers of 2 Reference

2⁰	2¹	2²	2³	2⁴	2⁵	2⁶	2⁷
1	2	4	8	16	32	64	128

Program Code

binary_decimal.c

1#include <stdio.h>
2#include <math.h>
3
4int main() {
5    long long binary;
6    int decimal = 0, i = 0;
7    
8    printf("Enter a binary number: ");
9    scanf("%lld", &binary);
10    
11    long long original = binary;
12    
13    while (binary > 0) {
14        int digit = binary % 10;      // Get rightmost digit
15        decimal += digit * pow(2, i); // Add position value
16        binary /= 10;                 // Remove rightmost digit
17        i++;                          // Move to next position
18    }
19    
20    printf("Decimal of %lld: %d\n", original, decimal);
21    
22    return 0;
23}