convertHexadecimalToBinary()

Step 1: Understanding Hexadecimal and Binary

Before we jump onto the code, it's necessary to understand the logic behind hexadecimal and binary conversions. A hexadecimal digit can take a value from 0 to 15 (0-F). On the other hand, a single binary digit (bit) can take one of two values, 0 or 1.

To translate from hexadecimal to binary, we can map each hexadecimal digit to its four-digit binary equivalent.

Let's take an example; the hexadecimal digit 7 translates to 0111 in binary, and D translates to 1101 in binary.

let hex = "7D";

Step 2: Loop over Each Hexadecimal Digit

Now, we can loop over each hexadecimal digit in the string. Let's try doing this.

for(let i = 0; i < hex.length; i++){
    console.log(hex[i]);
}

Step 3: Translating Hexadecimal to Decimal

Currently, our hexadecimal number is still in string format. So we will convert it to a decimal number. We use the parseInt() function to do that. The parseInt() function takes two arguments: the number and the base of this number. Since hexadecimal is base 16, we use 16 as the second argument.

for(let i = 0; i < hex.length; i++){
    let decimal = parseInt(hex[i],16);
    console.log(decimal);
}

Step 4: Translating Decimal to Binary

As we now have decimal numbers, we can easily convert them to binary using the toString() method.

The toString() method can convert numbers from decimal to binary, octal, or hexadecimal. It takes one parameter, the base to convert to. Since we want to convert to binary (base 2), we use 2 as the argument.

for(let i = 0; i < hex.length; i++){
    let decimal = parseInt(hex[i],16);
    let binary = decimal.toString(2);
    console.log(binary);
}

Step 5: Combining All Steps into a Function

Finally, we put everything together into a function. We introduce a binaryStr variable to store all of our binary digits. Also, as binary format requires 4 digits per hexadecimal digit and toString() will sometimes return less than 4 digits, we will use padStart() to fix this issue.

And this is how we can implement the function convertHexadecimalToBinary():

function convertHexadecimalToBinary(hex){
    let binaryStr = '';
    for(let i = 0; i < hex.length; i++){
        let decimal = parseInt(hex[i],16);
        let binary = decimal.toString(2);
        binaryStr += binary.padStart(4, "0");
    }
    return binaryStr;
}

console.log(convertHexadecimalToBinary("7D")); // Expected output: 01111101

This convertHexadecimalToBinary() function takes a hexadecimal string as a parameter, converts each hexadecimal digit to binary using decimal as a bridge and returns the binary string equivalent. We can now easily do any hexadecimal to binary conversions in our code by calling this function.