24 votes
Accepted

How should floating point inaccuracies be explained and justified?

If your students can understand why: $$\frac{1}{3} = 0.\dot{3}$$ then you can explain simply why floating point calculations are "broken". When you divide one by three on a simple calculator, you ...
Aurora0001's user avatar
  • 3,516
23 votes

How should floating point inaccuracies be explained and justified?

In my experience, the most confusing aspect here is not that there are rounding errors. Students should already have an understanding that there are physical limits that keep us from calculating with ...
ComicSansMS's user avatar
11 votes
Accepted

The use of the Octal system

The value might not be in knowing octal itself (although as noted in the comments, there is inherent relevance to it). Rather, it might be what learning different bases teaches about abstraction and ...
Peter's user avatar
  • 9,102
9 votes

How should floating point inaccuracies be explained and justified?

A few points: Do not call the discrepancies rounding errors Do not confuse students with epsilon math Do not obsess on teaching them exactly how IEEE floats are stored Do not show them examples of ...
candied_orange's user avatar
9 votes

How should floating point inaccuracies be explained and justified?

Even fairly early coders need to understand some limited form of why double a = 1.000001; double b = 0.000001; System.out.println((a-b)==1.0); ...
Ben I.'s user avatar
  • 33.6k
8 votes

The use of the Octal system

Sometimes you just want to group your bits 3 at a time instead of 4. Octal groups 3 bits per digit. Hexadecimal groups 4 bits per digit. For example Unix file permissions are written in octal ...
TomOnTime's user avatar
  • 371
4 votes

How should floating point inaccuracies be explained and justified?

Here are a few more ideas: Point out that that only $2^{32}$ values can be represented in 32 bits (or $2^{64}$ values in 64 bits), while there are an infinite number of real numbers. Therefore, not ...
Ellen Spertus's user avatar
4 votes

The use of the Octal system

It's necessary to know about octal because some compilers and tools will interpret multi-digit numbers with leading zeros differently to how many people will read them. Tracking down this sort of bug ...
Sean Houlihane's user avatar
3 votes

The use of the Octal system

An octal representation is shorter, in characters, than a binary representation for data with any number of bits greater than one. Unlike hexadecimal, an octal representation can be displayed using ...
hotpaw2's user avatar
  • 1,905
2 votes

How should floating point inaccuracies be explained and justified?

As a student myself, I had a course about how processing and encoding works where we had a detailed part about operations in different bases and how floats and <...
Romain Bernard's user avatar
1 vote

Creating a rubric for computer arithmetic

I missed this question! I will attempt to provide feedback in parts: I am concerned that there are too many critiera. I don't understand the reason for this concern, so I cannot comment upon it. The ...
Ben I.'s user avatar
  • 33.6k
1 vote

How should floating point inaccuracies be explained and justified?

There are plenty of good answers here, so I'll just add the extremely simple example I concocted to show why addition is not associative. Suppose your have a decimal floating point system with one ...
Victor Eijkhout's user avatar
1 vote

The use of the Octal system

One vestige of octal notation is in UNIX (includes macosx) file permissions. You can say ($ is your system prompt) $ chmod 644 file.txt and change all rings (...
ncmathsadist's user avatar
  • 2,329
1 vote

The use of the Octal system

One lesson that hasn't been mentioned yet is that the basic (manual) algorithms that students use for addition, subtraction, etc. are independent of base. In Octal, you just "carry" when you get to "...
Buffy's user avatar
  • 36.3k
1 vote

The use of the Octal system

3 bits per octal digit was convenient on old time machines which used words of 12, 18, 36 bits words. Easier to do mental calculations than with hexadecimal. For example, you have the PDP family : ...
Michel Billaud's user avatar

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