Computer Number Systems

Computer number systems is the first of three topics in the December ACSL contest. In this short post, I’ll go through the training material we used in our 9/28/2018 and 10/5/2018 meetings.

Upon first glance, number systems are wonky. To make their importance more clear, we ask the following questions:

1. Why does ACSL care so much about them in the first place?
2. Why don’t we all use base 10 for everything? Wouldn’t it be more convenient to have one standard way of counting?

To answer some of these questions, I’ll refer to this article, which provides a good historic overview. Overall, the key takeaway is that number systems are the solution to one of the fundamental human skill: counting things. As such, they have been around for a long time, and different methods of counting have evolved over time. Right now, while we use base 10 in everyday life, we also use other bases for different applications. For example, computers use base 2 because the two states per digit are naturally expressible in circuits. Clocks use base 60 because 60 seconds make a minute and 60 minutes make an hour.

Now that we have a good foundational understanding of why we need a topic, we move on to understanding specific problem-solving techniques. Specifically, the two key techniques to solve most number system problems are converting from base 10 to base n, and vice-versa. Both are described in further detail in the problem set.

For practice, try solving the problems linked here. Think about the process rather than applying memorized techniques: jot down any information you see or patterns you observe, and view exploring the problem in any manner as progress.

The above method actually has a name: Computational Thinking. In our training we’ll embrace this idea more, approaching tough problems together and building these important skills.

Recursion

I’m still in the process of writing solutions for the recursion problems. Consequently, I’ve attached the two TJ ICT problem sets here and here.

Stay tuned for the solutions and official write-ups of training material. As for now, we’ll just go over this stuff verbally in our training.