Shannon & Hartley's Measures

Shannon's measure of Entropy is the average shortest average message in bits that a certain amount of information can be conveyed with out any information loss. The Entropy measures how much information is lost in data compression and uses specific Algorithms to measure this.

Hartley's Function is actually a special case of Shannon's entropy so it's extremely similar to Shannon's. The only difference is that Hartley's equation takes into effect the a log of a varying base in a set of information. While Shannon only takes the log of base 2. Hartley's function is more rare and typically only happens in certain situations of measuring information. Shannon's measure is applicable to a much wider array of information.

Data Analysis

Data Analysis and Inductive Modeling is a wonderful tool to use for anybody involved with statistics and predicting upcoming events. With data analysis skills anybody can take a seeming random set of data and turn it into something with real meaning. For example, the 1st set of data we received for Lab 9, may have just seemed like a weird array of sea level changes, but after using data analysis and figuring out the linear regression, the data showed that the sea level is increasing at an alarming rate and will continue to grow at this rate in the foreseeable future. With data analysis, people can actually predict future problems and attempt to stop them before they actually occur. Although it's not a perfect science, using data analysis can find out trends that will help solve problems that some may have never seen coming, which is an extremely valuable tool in today's world.

In Lab 9, I learned several methods that can be used for data analysis, the main method being Linear Regression. This method allows you to take a set of data and actually put a line of best fit to a seemingly random scatter plot, so that you can infer any growing trends that the specific data is telling you. There is some error, but by using the Analysis Tools in Microsoft Excel, you can see how much error occurs and whether or not this is a viable trend or not. This skill will be very valuable in the future if I need to analyze any other sets of seemingly random data.

My Histogram

Lab 7 Task 3

For Task 3, we must prove through Logic Gates that DeMorgan's Law is true. For this I was able to create the following circuit in the Logic Gate Simulator:



After running different values of A and B on the circuit I was able to form the following truth table, proving DeMorgan's Law true:

A	B	NOT A	NOT B	A AND B	NOT (A AND B)	NOT A OR NOT B
0	0	1	1	0	1	1
0	1	1	0	0	1	1
1	0	0	1	0	1	1
1	1	0	0	1	0	0

As you can see from the red numbers, NOT (A AND B) is the equivalent of NOT (A OR B), therefore proving that DeMorgan's Law is true.

Lab 7 Task 2

For this task the final result for the logic gate is NOT (A XOR B), for this expression I came up with the following image in the Logic Gate Simulator:



After viewing the result of this expression at different values of A and B, I came up with the following Truth Table:

A	B	A XOR B	NOT (A XOR B)
0	0	0	1
0	1	1	0
1	0	1	0
1	1	0	1

This expression is only true when both A and B are the same value, if they differ in value then the expression is false. It is the opposite of the Exclusive-OR or XOR expression, and this is the result of the NOT being placed in front of the XOR expression. So the function of this circuit is to only allow for a "True" result when the values are equivalent, if they aren't then there is a "False" result.

Converting Binary and Decimal

I found the easiest way to convert the binary number 110010101, was to create the table below where each place has a different power of 2 assigned to it. Then if there is a 1 below a specific power of 2, you find what that power is and place it in the 3rd row of the table. Once you have found all the values of the "1s" in the number, you add those values together and come up with the decimal value of the binary number.

28	27	26	25	24	23	22	21	20
1	1	0	0	1	0	1	0	1
256+	128+			16+		4+		1

256+128+16+4+1 = 405

So the value of the Binary number 110010101 is 405

To convert the Decimal number 529 to its Binary form, all you need to do is divide the number by 2 until you can no longer divide it. Although you don't need to organize it into a table I feel its best to make it look clear and concise. As you can see you start with dividing 529 by 2, which is 264 with a remainder of 1, so the first place in the new binary number is 1. Then you divide 264 by 2, which is 132 with a remainder of 0, so the second place in the new binary number is 0. You do this continuously until you reach zero.

Decimal	Quotient	Remainder	Binary
529	264	1	1
264	132	0	01
132	66	0	001
66	33	0	0001
33	16	1	10001
16	8	0	010001
8	4	0	0010001
4	2	0	00010001
2	1	0	000010001
1	0	1	1000010001

As you can see once you reach 0 and can no longer divide the number by 2, you have the final binary number.

In this case the decimal number 529 is 1000010001 in Binary.

Positional vs. Non-Positional
The difference between Positional and Non-Positional number systems is very simple to understand. A positional number system is one where each position is related to the next by a constant multiplier. For example the decimal systems constant multiplier is 10, so if you find the number 6 in the "hundreds place," it is multiplied by 10^3 or 100.

A non-positional number system does not have a constant multiplier for each position, instead a new symbol is usually created to convey the newest number position. An example of this would be the Roman Numeral System, each position is not related to the one next to it. The number XLI has no constant multplier to tell you that it means 41 in decimal form, you just have to have a specific understanding of what each symbol means.

Andy Clark and Search Engines

While reading an excerpt from Andy Clark's book Natural-Born Cyborgs I found his opinions about search engines to be very interesting. Clark's views are that newer search engines like Google search for the structure of links between pages instead of strictly looking at the content of the pages. He uses the example of searching for a word like "Harvard" and the Harvard homepage not being one of the top pages in that search for early search engines like Yahoo or Excite, however with engines like Google it's the very first page in the search. By performing searches like this it connects the web more than anyone could have thought.

When search engines are able to bring together these "soft assembled" information packages that Clark outlines, users are able to access any information at any time of day. This has seemed to revolutionize society's ability to give and receive information at any time. The user also has all the control in what information he or she wishes to access. This is basically the opposite of a book or newspaper where the reader is being force fed information, an online search allows for total user control. All of this work has allowed information to be accessible to anybody in the world and also brought the world closer together. Somebody in Paris, France can be accessing the same information that someone in rural Indiana, and I feel its all for the best. With information being so easily accessible due to the capabilities of these search engines, and this can only help people collaborate to come up with newer ideas that can improve the world around us.