How do you perform binary conversion using loops?

Binary conversion, whether from decimal to binary or vice-versa, can be efficiently achieved using loops in various programming languages. Below, we will explore how to perform both types of conversions using loops.

1. Decimal to Binary Conversion using Loops:

The core idea is to repeatedly divide the decimal number by 2 and store the remainders. These remainders, when read in reverse order, form the binary representation. Here's how it can be implemented using a loop in a conceptual example:

function decimalToBinary(decimalNumber) {
  if (decimalNumber === 0) {
    return "0";
  }
  let binaryString = "";
  while (decimalNumber > 0) {
    let remainder = decimalNumber % 2;
    binaryString = remainder + binaryString; // Prepend remainder
    decimalNumber = Math.floor(decimalNumber / 2); // Integer division
  }
  return binaryString;
}

//Example usage:
const decimalNum = 25;
const binaryNum = decimalToBinary(decimalNum);
console.log(`The binary of ${decimalNum} is: ${binaryNum}`); // Output: The binary of 25 is: 11001

Explanation:

- We handle the edge case where the decimal number is 0.

- A while loop continues as long as the decimal number is greater than 0.

- Inside the loop, we get the remainder when the number is divided by 2, which is either 0 or 1.

- We prepend this remainder to our binary string, building it in reverse order.

- We then update the decimal number by integer dividing it by 2.

2. Binary to Decimal Conversion using Loops:

The process involves multiplying each binary digit by 2 raised to the power of its position (starting from right to left, with the rightmost digit having the power of 0). The results are then summed up. Here is a conceptual example using a loop:

function binaryToDecimal(binaryString) {
  let decimalNumber = 0;
  let power = 0;
  for (let i = binaryString.length - 1; i >= 0; i--) {
    if (binaryString[i] === '1') {
      decimalNumber += Math.pow(2, power);
    }
    power++;
  }
  return decimalNumber;
}

//Example Usage
const binaryNum = "11001";
const decimalNum = binaryToDecimal(binaryNum);
console.log(`The decimal of ${binaryNum} is: ${decimalNum}`); // Output: The decimal of 11001 is: 25

Explanation:

- We initialize our decimal number to 0 and the power to 0.

- We iterate through the binary string from right to left using a for loop.

- If the current binary digit is '1', we add 2 raised to the power of its position to our decimal number.

- We increment the power for each position.

Conclusion:

These loop-based methods provide a clear and efficient way to perform binary conversion. Whether you are converting from decimal to binary or vice versa, loops allow you to effectively manipulate the digits and derive the correct output.

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