Binary to Decimal - Problem

Given a binary number as a string, convert it to its decimal equivalent without using any built-in conversion functions.

A binary number consists of only 0 and 1 digits. Each digit represents a power of 2, starting from the rightmost digit as 2⁰.

Example: Binary "1101" = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13

Input & Output

Example 1 — Basic Binary

$ Input: binary = "1101"

› Output: 13

💡 Note: 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13

Example 2 — Single Bit

$ Input: binary = "1"

› Output: 1

💡 Note: Single bit 1 in position 0: 1×2⁰ = 1

Example 3 — All Zeros

$ Input: binary = "000"

› Output: 0

💡 Note: All bits are 0, so the decimal value is 0

Constraints

1 ≤ binary.length ≤ 30
binary consists of only '0' and '1' characters

Visualization

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Asked in

G Google 25 M Microsoft 20 A Amazon 18

The key insight is that binary-to-decimal conversion can be done efficiently by processing bits from left to right, doubling the running result and adding each bit. The optimal approach uses the formula result = result × 2 + bit for each digit. Time: O(n), Space: O(1)

Common Approaches

✓ Left-to-Right Doubling

⏱️ Time: O(n) Space: O(1)

Iterate from left to right, maintaining a running result. For each bit, double the current result and add the bit value. This naturally computes the decimal equivalent.

Position-Based Calculation

⏱️ Time: O(n²) Space: O(1)

Iterate through each digit from right to left, calculate 2^position for each digit, multiply by the digit value (0 or 1), and sum all contributions.

Left-to-Right Doubling — Algorithm Steps

Start with result = 0
For each bit from left to right: result = result × 2 + bit
Return final result

Visualization

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Step-by-Step Walkthrough

Start Left

Begin with result = 0, process from left

Double & Add

For each bit: result = result × 2 + bit

Final Value

Result accumulates the decimal value

Code -

solution.c — C

#include <stdio.h>
#include <string.h>

int solution(char* binary) {
    int result = 0;
    int n = strlen(binary);
    
    for (int i = 0; i < n; i++) {
        result = result * 2 + (binary[i] - '0');
    }
    
    return result;
}

int main() {
    char binary[100];
    fgets(binary, sizeof(binary), stdin);
    binary[strcspn(binary, "\n")] = 0; // Remove newline
    
    int result = solution(binary);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single loop through n digits with constant work per digit

⚠ Quadratic Growth

Space Complexity

O(1)

Only using a single variable to track running result

✓ Linear Space

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Medium Frequency

~8 min Avg. Time

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Binary to Decimal - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Left-to-Right Doubling — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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