Decimal to Binary Conversion Program

Given a non negative number n, the task is to convert the given number into an equivalent binary representation.

Examples:

Input: n = 12
Output: "1100"
Explanation: the binary representation of 12 is "1100", since 12 = 1×2³ + 1×2² + 0×2¹+ 0×2⁰ = 12

Input: n = 33
Output: "100001"
Explanation: the binary representation of 33 is "100001", since 1×2⁵ + 0×2⁴ + 0×2³ + 0×2² + 0×2¹ + 1×2⁰ = 33

[Approach - 1] Division by 2 - O(log₂(n)) Time and O(log₂(n)) Space

To convert a decimal number to binary, repeatedly divide it by 2 and record the remainders. Reading these remainders in reverse gives the binary representation.

1100

[Approach - 2] Using Head Recursion - O(log₂(n)) Time and O(log₂(n)) Space

The idea is same as the previous approach, but we will use recursion to generate the binary equivalent number.

1100

[Approach - 3] Using Bitwise Operators - O(log₂(n)) Time and O(log₂(n)) Space

Using bitwise operators, we can extract binary digits by checking the least significant bit (n & 1) and then right-shifting the number (n >> 1) to process the next bit.
This method is faster than arithmetic division and modulo, as bitwise operations are more efficient at the hardware level.

1100

[Approach - 4] Using Built-in Methods - O(log₂(n)) Time and O(log₂(n)) Space

The main idea is to leverage built-in functions provided by programming languages to directly convert a decimal number to its binary form. These functions abstract away the underlying logic and return the binary representation as a string, making the process quick, concise, and error-free.

1100