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 ...
- 3,506
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 ...
- 631
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 ...
- 9,082
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 ...
- 1,063
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);
...
- 32.7k
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 ...
- 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 ...
- 7,630
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 ...
- 1,652
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 ...
- 1,895
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 <...
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 ...
- 32.7k
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 ...
- 1,433
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 (...
- 2,319
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 "...
- 35.8k
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 : ...
- 937
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