LSP 121
Activity 11
Number Systems and Logs

1. If a computer or device wishes to send or receive data over the Internet, the device has to have an IP address.  It is through this address that other devices know where to send the data.  It works very much like your home address.  If you want to receive U.S. mail, you have to provide someone with a street address, city, state, and probably zip code.

a. Currently the Internet uses a 32-bit addressing scheme.  How many address are possible using 32 bits?  Recall, since we are dealing with binary values, or bits, and bits have only 2 possible values – 0 and 1 – then you have to calculate the value of 232.

b. While this number seems pretty large, there is some concern that we are starting to run out of IP addresses (due to earlier poor Internet address management and now the proliferation of new technologies that send telephone calls over the Internet).  The group that controls all things official concerning the Internet has asked all Internet users to start to convert their systems to 128-bit addresses.  How big is the value 2128?

c. Most people can’t grasp the size of the value 2128.  Let’s put it another way.  If the Internet governing body assigned 1 million Internet addresses every picosecond, how long would they be able to assign addresses (give your answer in years).  Recall how we set up this equation in the lecture slides.  Let me get you started:

	2128 addresses x 1 picosecond / 1,000,000 addresses x …

d. Does this number seem like overkill, or is this reasonable?  State why the Internet governing body might have chosen such a large number.

2. The fastest spaceships launched to date are traveling away from Earth at speeds of about 50,000 kilometers per hour (or 50,000,000 meters per hour).  How long (in years) would such a spaceship take to reach Alpha Centauri?  (Alpha Centauri is 4.3 light years distant.)   Is this doable?  What would have to change to make this doable?  (1 light year = 9.4605284 x 1015 meters.)  Take the light year distance and multiply it by 4.3.  This is your distance.  Then divide your distance by your velocity of 50,000,000 meters per hour.  Finally, convert to a longer term such as years.)

3. Convert the binary value 100101 to decimal without using a calculator.  Show your work.

4. Convert the decimal value 89 to binary without using a calculator.  Show your work.

5. When you opened a Word document to complete this activity, you probably entered LSP 121 at the top of the document.  Using the ASCII code chart on the back of this page, show the binary values that Word will use internally in place of “LSP 121”.

Space	0100000	0	0110000	@	1000000	P	1010000	‘	1100000	p	1110000	
!	0100001	1	0110001	A	1000001	Q	1010001	a	1100001	q	1110001	
“	0100010	2	0110010	B	1000010	R	1010010	b	1100010	r	1110010	
#	0100011	3	0110011	C	1000011	S	1010011	c	1100011	s	1110011	
$	0100100	4	0110100	D	1000100	T	1010100	d	1100100	t	1110100	
%	0100101	5	0110101	E	1000101	U	1010101	e	1100101	u	1110101	
&	0100110	6	0110110	F	1000110	V	1010110	f	1100110	v	1110110	
‘	0100111	7	0110111	G	1000111	W	1010111	g	1100111	w	1110111	
(	0101000	8	0111000	H	1001000	X	1011000	h	1101000	x	1111000	
)	0101001	9	0111001	I	1001001	Y	1011001	i	1101001	y	1111001	
*	0101010	:	0111010	J	1001010	Z	1011010	j	1101010	z	1111010	
+	0101011	;	0111011	K	1001011	[	1011011	k	1101011	{	1111011	
‘	0101100	<	0111100	L	1001100	\	1011100	l	1101100	|	1111100	
,	0101101	=	0111101	M	1001101	]	1011101	m	1101101	}	1111101	
.	0101110	>	0111110	N	1001110	^	1011110	n	1101110	~	1111110	
/	0101111	?	0111111	O	1001111	_	1011111	o	1101111		1111111	

6.  Open the file logs.xls (found on the QRC website under Excel Files).
The Richter scale is used to measure the intensity of earthquakes.  It is a logarithmic relationship with the following formula:
 R = log(I)
 I is the intensity of the earthquake and R is the number on the Richter scale.  
(Remember that if there is no base written with the log it is base 10).  
Don’t be scared off by logs.  Think of them as a short-cut way of writing large numbers.  For example, let’s say the intensity of an earthquake is 100,000,000.  Can you imagine if the papers published that big number?  What would people think?  Most people cannot handle well numbers with large amounts of zeros (unless those people work for the government ;-).  Instead of writing 100,000,000, let’s just write how many zeros there are.  In this case, there are 8 zeros.  That’s exactly what log10 is asking.  10 to what power equals 100,000,000?  10 to the 8th power.  So the log(100,000,000) equals 8.  Thus, the Richter value for an earthquake with intensity 100,000,000 is 8.
Let’s say it another way.  Let’s remove the log. Converting the above formula from log form to exponent form would give us:
10R = I
(Note: 10 was raised to the R power, which cancels the log function.)  Which version you use depends on which variable you are given.  If you are given the Richter value (R) and want to calculate the intensity, then use 10R = I.  If you are given the intensity and want to calculate the R value, use R = log(I).
Since the Richter scale is logarithmic, an increase of 1 on the Richter scale translates to 10 times increase in intensity.  An R of 2 means an intensity of 100 while an R or 3 has an intensity of 1000 which is 10 times larger than the previous intensity.
 a) Open the Richter worksheet in the Excel file.  For the first 9 earthquakes, calculate the Richter number and for the remaining calculate the intensity using the formulas above.  Paste this worksheet into your Word document. 
 b) Which earthquake had the highest Richter number? 
 c) Is there a correlation between Intensity and number of deaths?  That is, as the intensity of the earthquakes increased, did the number of deaths increase?  Why do you think that is?
 d) If one earthquake had a Richter number of 5 and another had a Richter number of 7, how many times more intense would the second one be than the first?
 e) If one earthquake had an intensity of 8,000,000 and another had an intensity of 80,000,000 how, specifically, would their Richter numbers compare?