Step 1: Understanding the Process

Converting a number from Octal to Hexadecimal involves converting the Octal number to a decimal number first and then converting the decimal to hexadecimal. In JavaScript, the built-in Number constructor can be used to convert the octal to decimal and then the toString() method can be used to convert the decimal to hexadecimal.

Here is how to convert Octal to decimal:

let octalNumber = '567';
let decimalNumber = Number.parseInt(octalNumber, 8);
console.log(decimalNumber);  // Outputs: 375

Step 2: Converting Decimal to Hexadecimal

Next we will convert the decimal value to a Hexadecimal. The toString() JavaScript method takes an argument where you can specify the base for the conversion. If you pass 16, it will convert the decimal to hexadecimal.

let hexadecimalNumber = decimalNumber.toString(16);
console.log(hexadecimalNumber);  // Outputs: 177

Step 3: Creating Convert Function

Now consolidate these two steps into a single function. This function will accept an octal number as input and return the equivalent hexadecimal number.

function convertOctalToHexadecimal(octalNumber) {
    let decimalNumber = Number.parseInt(octalNumber, 8);
    let hexadecimalNumber = decimalNumber.toString(16);
    return hexadecimalNumber;
}
console.log(convertOctalToHexadecimal('567'));  // Outputs: 177

Step 4: Error Handling

While the function above works, it does not currently handle any input errors. In JavaScript, isNaN function can be used to check if the conversion from octal to decimal was successful or not. If the conversion fails, the function would return NaN. In that case, the function can be updated to return an error message.

function convertOctalToHexadecimal(octalNumber) {
    let decimalNumber = Number.parseInt(octalNumber, 8);
    if(isNaN(decimalNumber)) {
        return 'Invalid Octal Number';
    }
    let hexadecimalNumber = decimalNumber.toString(16);
    return hexadecimalNumber;
}

console.log(convertOctalToHexadecimal('5678'));  // Outputs: Invalid Octal Number

Step 5: Simplifying the Function

Since we are using arrow functions in ES6, the function can be simplified even further. If octalNumber can't convert to decimalNumber, it'll throw an error message, else it'll return the required hexadecimalNumber.

const convertOctalToHexadecimal = octalNumber => {
    let decimalNumber = Number.parseInt(octalNumber, 8);
    return isNaN(decimalNumber) ? 'Invalid Octal Number' : decimalNumber.toString(16);
}

console.log(convertOctalToHexadecimal('567'));  // Outputs: 177

Conclusion

In conclusion, we have created a function using JavaScript which converts an Octal number into hexadecimal. Also added an error handling mechanism into convertOctalToHexadecimal function to catch invalid octal numbers.