Assignment 2

To Make the Assignment Unique

(1) According to my student number, I will be doing 2(0), 3(2) and 6(0).

Bit Strings and Logic

(1)

0 = Y AND (NOT Y)
1 = X AND Y
2 = X AND (NOT Y)
3 = X
4 = Y AND (NOT X)
5 = Y
6 = [Y AND (NOT X)] OR [X AND (NOT Y)]
7 = X OR Y
8 = (NOT X) AND (NOT Y)
9 = [NOT X AND NOT Y)] OR [X AND Y]
10 = NOT Y
11 = X OR [NOT (X AND Y)]
12 = NOT X
13 = Y OR (NOT X)
14 = NOT (X AND Y)
15 = X OR (NOT X)

(2)

While working on #1, I discovered that some of the expressions could be written equivalently with AND or OR in combination with NOT. In class we discussed DeMorgan’s Law that shows that any AND or OR can be replaced with the other in combination with NOT, as shown below:


NOT (A AND B) = (NOT A) OR (NOT B)
NOT (A OR B) = (NOT A) AND (NOT B)

Therefore, all or the binary functions can be written in terms of AND and NOT using the above rules to replace the OR function.

(3)

According to my student number with mod 16, I will be doing the binary operation of OR.

I found that OR is commutative, associative and idempotent.

The following chart, with f = OR, illustrates that OR is associative. (I have been unable to import the table from WORD, I will scan it and post it ASAP.)

(4) When working in trinary, things grow exponentially with a base of 3, instead of exponentially with a base of 2 as in binary. Therefore, with 2 binary input arguments, there are 9 different arrangements of the input arguments. For the output operations, there are 3 possible output values for each of these 9 arrangements. This means that there are output operations.

(5)

(6) Using pic1 and pic2 as given in class, here are the images that I created in GIMP.

pic1 AND pic2

pic1 OR pic2

pic1 XOR pic2

(7)

A – Poison caused the victim’s death.
B - There was a change in blood pressure.
C – There is a residue of poison in his stomach.
D – There were puncture marks on the body.
E – Poison was injected by a needle.

A IFF (B OR C)
B NOR C BUT D
E IFF D
A OR (NOT D)

Order of Magnitude

(1)
Commodore 64: 64KB

1GB = 1024 MB
= 1024 x 1024 KB

= 2^20 KB

2^20 divided by 64 (2^6) equals 2^14 (16384)

Therefore, a computer with 1GB has 16384 times the memory of a Commodore 64.

(2)

Double sided floppy disk: 800KB

DVD: 4.7GB = 4.7 x 1024 MB

= 4.7 x 1024 x 1024 KB

= 4.7 x 2^20 KB

(4.7 x 2^20) divided by 800 = 6160.384

Therefore, the DVD is equivalent to about 6160 floppy disks.

(3)

The first commercial PC, the Altair 8800 (1975) had a clock rate of 2MHz (2 million cycles per second).

Modern computers (2002) with an Intel Pentium 4 have a clock rate of 3GHz (3 billion cycles per second).

(3 x 10^9) / (2 x 10^6) = 1.5 x 10^3 (1500)

Therefore, a modern computer is about 1500 times as fast as a computer from 1975.

My sources for information on clock rates:

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

http://www.islandnet.com/~KPOLSSON/comphist/comp2006.htm

Most new computers sold are in the 2 to 3 gigahertz (2,000 to 3,000 Mhz) range.

http://mindprod.com/bgloss/cpu.html