Assignment 2

First 4 digits of my student ID - 2087

2087 mod8 = 7 2087 mod3 = 2 2087 mod 7 = 1


corresponding questions from assignment 2 are (2) -7......(3) - 2........ (6) -1

Bit Strings and logic

1. The 16 binary functions expressed using binary operations AND/OR and NOT with inputs

X = 0011 and Y =0101


Notation used to represent operators in brackets AND (^) OR (V) NOT (\)


0000 Y^ \Y
1000 \(X V Y)
0001 X^Y
1001 \((XVY) ^(X^Y))
0010 \(\X^Y)
1010 \Y
0011 \ \X
1011 \(Y^\X)
0100 Y^\X
1100 \X
0101 \\ Y
1101 \X^Y
0110 (X^Y) ^\(X^Y)
1110 \(X^y)
0111 X V Y
1111 \(Y^\Y)

2. All of the 16 possible binary functions can be represent using only compostions of { NOT, IMPLY}. This is true because IMPLY is composed of NOT and OR and using De Morgan's Laws one can obtain AND statement. Therefore aremed with NOT, OR, AND one can generate all 16 functions.

3. Indepotence describes properties of operators that yield the same result after the operation is applied a multiple of times. ex NOT (NOTX) = X. The binary operators that exhibit this property include: AND, OR and NOT and all operators that build on these fundamental operators.

4. Given trinary inputs (0,1,2) the number of possible binary operations is 3^3^2 = 19683

5. There are 3 binary operators required to represent every possible two argument function on trinary operations are NOT, OR, AND and IMPLY

6. Using GIMP to create the following

(pic1 AND pic2)

(pic1 OR pic 2)

(pic 1 IMPLY pic 2)

7. Let C = change in blood chemistry, R= residue poisin in stomach, P = death by poisin through needle, M = puncture marks

Corresponding operations to statements listed in assignment in order.

P IFF ( C OR R )

NOT ( C OR R ) AND M

M IMPLY P

NOT P IMPLY NOT M

Orders of Magnitude

1. Commodore 64 had 64 K memory = 2^6 K. A computer with 1 GB memory = 2^10 x 2^10 K= 2^20 K

Therefore a 1 GB memory has 2^20/2^6 = 2^14 = 16384 times more storage than a 64 K.

2. A 51/4 disk -> 800K, A DVD --> 4.7 GB = 4.7 x 2^20 K

Therefore 1 DVD is equivalent to 4.7 x 2^20 / 800 = 6160.384 disks

3. Promoting clock speed ( or CPU speed ) used to be a major selling feature in computer advertisements in the 1990's. One such computer; the Apple's 'Power Macintosh 8100/110" had a clock rate of 110 MHz which beat the fastest Intel processor at the time of 100 MHz.

Today's computer clock speeds are as high as. One such model available to the general public is the Dell Precision T7400 has a CPU speed of 3.4 GHz. This turns out to be just over 3oX faster than the 1990 models.

It should be noted that comparison of clock speed between different CPU families is not uselful since certain families of chips are faster in certain tasks and slower than other. One comparison of CPU speeds within the same family gives an accurate picture.

Source

http://en.wikipedia.org/wiki/Clock_rate

http://www1.ca.dell.com/content/products/productdetails.aspx/precn_t7400?c=ca&cs=calca1&l=en&s=biz