An interesting question came up from a few of my students while teaching my class. Some of them discovered a bug in their programs which they did not understand. They were writing a program which was doing some calculations on currency.
Computer Programmers commonly use floating point numbers, but I am sure that not all of them really understand what is going on underneath the hood. As I am sure everyone reading this knows, all data is stored in binary format on computers. In base 10 as with all numbering systems with a base, each digit is a round number in the base. The fractional amounts are what is interesting and specific to floating point numbers and not to integers.
When using floating point numbers they aren't stored in a way which is intuitive to base 10 users. As an example I will use the fractional amount 1/4. To make seeing the conversion easier I'll say that it is also 25/100 or really 2/10 + 5/100.
In a base 10 floating point number we may represent this number as the following.
If we were to write that same number in binary format we should note that it is 1/4 or really 0/2 + 1/4.
You'll want to notice here that those two numbers are not similar, and as you can probably guess, some examples would not come out quite so cleanly.
The problem which the students came across stemmed from subtracting 10 cents from some amount of money. I'll use $100.00 as my example. When the students did the calculation it worked in the following way:
100.00 - 0.1 = 99.900000000000006
That seems to not make sense, but it does make some sense. There are numbers which in base 10 will have decimal places which will extend on, and we have to round them at some point. A good example of this is 1/3 which can be written roughly as any of the following
All of those are approximations of that fractional amount. In binary we have the same type of problem, because 0.1 cannot be represented correctly in binary. This causes a problem; it will round at a certain point, and because the number isn't represented correctly, the calculation is done incorrectly. In many other languages it hides away that inaccuracy, but Python allows you to see it.
It is important to know how your floating point numbers are working underneath. Be careful. The computer doesn't speak our language.
I recently started teaching a course for the Computer Science Department at Kent State University. I am teaching a course called Introduction to Computer Programming. It is a course teaching non-computer science majors the basics of programming.
In this course the students learn simple concepts and ideas behind programming, and along the way will learn to develop simple applications. The students who take this course come from many different areas: Technology, Education, Art History, Visual Communication Design, etc.
I am enjoying teaching the course, and it is beneficial not just to the students but to me as well. As I am teaching this course I am refreshing my memory on a lot of different areas of computer science which I believe are very important to software development.
Python is the programming language of choice for this class. It has been chosen for many reasons, but a few choice ones are: Python's being a very high level language, ease of use, quick development, works with Windows, Linux, and Mac OS. We have Mac, Linux, and Windows users in the class so it is nice to use a language which is easy to develop in and works well in each of the operating systems.
In an effort to start posting more to my blog perhaps I can post a few of the interesting concepts which are applicable to all programming not just Python.
Update (24 March 2008): Steve Smith found a more reliable solution to install the SQL Server Client Tools. Once in the tools folder open the setup folder and in there is a SqlRun_Tools.msi file. If you run that it should actually install SSMS.
When I recently installed SQL Server 2005 and SQL Server Management Studio on my computer it did not install SSMS or any of the other Client Tools. When running the installation of SQL Server 2005 I followed along with the instructions. I individually selected each component to install including the Client Tools for SQL Server. When the installation finished there was no SQL Server Management Studio.
Figuring this might be a difficult thing to Google for, I asked Steve Smith if he knew how to get the client tools. He told me that just about the only way to get SSMS to install was to sacrifice a chicken and hope for luck, because there is something weird which has to be done in order to get the program to install.
Upon scouring the folders on the disc, I discovered that the default setup file is coming from a servers folder. I tried using the setup file from the tools folder. This should have worked, but I had a slight problem. Since I had told SQL Sever to install the client tools from the wrong setup file it now believed I had them installed already and would not install them.
Since the installation defaults to the Servers setup file, I never even saw the tools install. There was also no reason to even suspect one since the primary setup file claimed to be able to install the client tools.
I had to uninstall and reinstall SQL Server without the Client tools and then the setup file from the client tools would install SQL Server Management Studio. This was quite a pain, and I don't understand why the client tools are listed as options in a setup file which cannot install them. I think this is a bit crazy, but at least now when I install it I don't have this problem anymore.
I recently needed to convert hexadecimal numbers into integer numbers. So for your benefit, and for mine when I forget how to do this, I will tell you a couple of ways to convert numbers of these types. Both methods are quite simple and easy to use.
string myHexNumber = "C4FFB716";
int myIntNumber = Int32.Parse(myHexNumber, System.Globalization.NumberStyles.HexNumber);
This will convert a hexadecimal number in string format into an integer number. You could also do the following.
string myHexNumber = "C4FFB716";
int myIntNumber = Convert.ToInt32(myHexNumber, 16);
In this case you have easily converted from a hexadecimal string into an integer. If you want to convert from a base other than 16 into an integer you can pass either 2 or 8 instead of 16 to this method.
(Yes, I am aware that those are terrible variable names. This is merely an example.)
I read every blog post Scott Guthrie writes, and I intend to keep it that way. In his most recent blog post he let me know about Silverlight's 1.0 release as well as the announcement that Silverlight will be formally supported for Linux. Silverlight has seemed quite impressive so far, and I had been disappointed about Microsoft's not supporting Linux as well. I am happy to learn that the project called "Moonlight" will be able to run on 3 different browsers in Linux; Firefox, Opera, and Konqueror. As a Linux user myself I am always disappointed in the lack of Linux support given by larger companies. Flash is not very compatible with Linux, so it is quite impressive to see Microsoft assisting in the development of Moonlight.
For those of you who do not know there is an implementation of the .NET Framework referred to as Mono. It is a project in the Linux world which allows .NET code to run in Linux. I've done some development using Mono, and I've even written ASP.NET pages in Mono. So far they've done well in replicating the features provided by for .NET developers.
I think many people are eagerly anticipating the Silverlight 1.1 release which has also been mentioned as the current project Scott Guthrie's team is working on.
I am happy to know that when I write code in Silverlight anyone on any of the main 3 Operating systems should be able to see the Silverlight. If Microsoft can get some big websites using Silverlight, most people across the Internet will have Silverlight very quickly.
I recommend checking out a lot of Microsoft's webpages. I've seen a few of them, and these new Silverlight sites are quite amazing.