Binary Vs. Decimals

In order to convert binary numbers to decimals you must start from the end and multiply where there is a 1 by an exponent of 2. For the number 110010101 for example:
2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0=
1 1 0 0 1 0 1 0 1
256 + 128 + 0 + 0 + 16 + 0 + 4 + 0 + 1 = 405

So the answer is 405.

Converting decimals to binary is similar, but not the same. In order to do this, u must divide your starting number by two, recording if there is a remainder or not as a 1 or a 0 until you divide all the way through the number. For the number 529 for example:
(529/2) (264/2) (132/2) (66/2) (33/2) (16/2) (8/2) (4/2) (2/2) (1/2)
(264 R. 1) (132) (66) ( 33) (16 R. 1) (8) (4) (2) (1) (0 R. 1)
1 0 0 0 1 0 0 0 0 1

So the answer is 1000010001.

Positional vs. Non- Positional
Positional and Non-Positional number systems are very simple to understand. A positional number system consists of numbers where each position is related to the next by a constant multiplier. A non-positional number system does not have a constant multiplier for each position. Rather, in a non-positional number system, the numbers are represented as symbols to convey their purpose. For example, writing numbers in roman numerals is a specific way to write using a non-positional numbering system.

Modelling the World (part deux)

Modelling funds our knowledge in so many ways. It has so many uses in mathematics, physics, and many other of the sciences. It makes remembering infomation and computing information much easier by allowing our thoughts to correspond to some observable entity in the world. A model breaks down and reduces an apparent complexity into ideas that we can better understand. Such models as the Fibonacci sequence and different branching systems have made understanding and remembering information a much simpler task.

DOS vs. Unix

The Dos and Unix operating systems have very similar workings. The reference manual page (man man) in the steel directory, allows you to better understand how to get around the directory itself. It gives you commands that allow you to access different things in the database. The Dos counterpart could possibly be their directory or dir. In order to delete files in Unix, one must type in rm and the file that needs to be removed. However, the much easier to remember prefix for Dos is DEL and then the file needed to be removed. So far, Dos seems a much easier operating system to work with. But, once one gets into the much easier commands such as those that make and remove directories, Dos and Unix are exactly the same, mkdir in order to make the directory and rmdir to remove the directory. In Dos however, there is a different command besides rmdir and mkdir in order to perform these actions. One could also utilize the RD (remove directory) and MD (make directory). So personally, I find that the Dos operating system is much more user friendly and much easier to use.

Modeling the World

Pretty much everything around us can be modeled in order to understand things better. In the natural sciences, models are used as tools for dealing with reality. They can be formal and quantitative, allowing us to gain a better understanding of reality. According to the lecture notes, "to understand the World in scientific terms it is necessary to build models." In this way, it is possible to elucidate new concepts and describe phenomena through the use of mathematics or computational rules. Basically, models make it possible to understand information. Models are created to test unknown knowledge and help make theories into fact. We work with information to create models in order to create more information.