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Base 3 to Base 10 Conversion Lab

The goal of this lab is to write a JavaScript program that converts a trinary (base-3) number to a decimal (base 10) number. Note that we'll be using first principles, meaning we won't be using the built-in parseInt function that JavaScript provides.

Steps

1. What is a Trinary number? The trinary number system, also known as base-3, uses three digits -- 0, 1, and 2. It's similar to the familiar decimal (base-10) number system that we use every day, only it's based on powers of 3 instead of powers of 10. The right most position in a trinary number represents 3 to the power of 0, the next position to the left represents 3 to the power of 1, and so on.

2. Understanding the JavaScript parseInt method Before we begin, it's important to understand that JavaScript provides a built-in function, parseInt, which can perform base conversion for us. For example, parseInt('102012', 3) would convert the base-3 number '102012' into its base-10 equivalent which is 302 . However, in this lab, to understand base conversion at a deeper level, we're going to ignore that this function exists and do the conversion ourselves.

3. Creating our Custom Conversion Function We're going to write a function that takes a string representation of a trinary number as input (e.g. '102012'). If the input string is not a valid trinary number, the function will return 0.

Here's a breakdown of how we'll compute the conversion manually:

For example, a string '102012':

• Multiply each digit by 3 raised to the power of its position, counting from 0 from right to left.
• For example, the rightmost 2 is at position 0, so you multiply it by 3^0. The next digit to its left, 1, is at position 1, so you multiply it by 3^1.
• Repeat this process for each digit and then sum the results.

The calculation would look something like this:

# "102012"
    1       0       2       0       1       2    # the number
1*3^5 + 0*3^4 + 2*3^3 + 0*3^2 + 1*3^1 + 2*3^0    # the value
  243 +     0 +    54 +     0 +     3 +     2 =  302

Following the steps you've learned, implement them programatically in JavaScript to achieve the same results as the parseInt() method, you should be able to convert any valid trinary number into its decimal counterpart.