assignment 2

9338 = 2(mod 8)


= 2(mod 3)


= 0(mod 7)





Question 1


0011 - x


0101 - y


0100 -y and not x


0010 -x and not y


0001 -x and y


1000 - not x or y


1100 - not x


1010 - not y


1001 - not x and not y


0011 - x


1110 - not (x and y)


1101 - not (x 0r y)


1011 - not x and not y


0111 - x or y


0000- y and not y


0110 - (x or y) and not (x and y) and (not x)


0101 - y


1111 - x and (not x)





Question 2b



I was able to represent some of the 16 binary function using AND, XOR, however I wasn't able to represent the ones below

- 1000

- 1001

- 0000

- 1111

- 1011

- 1110

-

Question 3

Associative Law

xyz = z(xy) = x(yz)

or

x+y+z = z+(x+y) = x+(y+z)

x y z xy zy z(xy) x(yz)

0 0 0 0 0 0 0

0 0 1 0 0 0 0

0 1 0 0 0 0 0

0 1 1 0 1 0 0

1 0 0 0 0 0 0

1 0 1 0 0 0 0

1 1 0 1 0 0 0

1 1 1 1 1 1 1



Ques 4

When n = 3 we have three-variable functions f(1, 2, 3), therefore there are 3^3^3 different output argument that is equal to 19 683



Ques 5

There are four necessary properties needed to express every possible two argument. The operations are (IMPL), (DISJUNCTION-operation "or"), (CONJUNCTION-operation "and") and (NEGATION-operation "not")

reference

http://www.fw.uri.br/~arpasi/artigos/ternary.pdf



Ques 6.

pic1) AND (pic2), (pic1) OR (pic 2), pic 1 XOR pic 2

Ques 7
let P represent poison caused the victims death

Let C represent the change in blood chemistry

Let R represent residue of poison in the stomach

let X represent puncture marks on the body

let Y represent the poison was injected
Let D represent the victim's death

Statements

(P IMPL C) IFF (C or R)

((Not C) and (not R)) and X

Y IF X

(P IMPL D) and (Not X)

Order of Magnitude

1) If a computer has 1 GB of memory then this is approximately 1048576 K of memory. If compared with the Comodore which had 64 K it would have 16384 times more memory.

2) Converting 4.7 GB to K gives 4.7 x 1024 x 1024 = 4928307.2 K dividing 4928397.2 K by 800 K = 6160.384. Hence, we can imply that it would take approximately 6 161 floppy disks to be equivalent to one 4.7GB DVD (since there is no fractional disk).

3) The 1986 Mac Plus computer has Motorola that runs at 68000 CPU running at 8MHz when compared to a 2007 AMD that has a Athlon 64 X2 4800 + with two cores, with each core running at 2.4GHz. The processing speed the the AMD's with 4.8GHZ is 600 times faster than the Mac Plus http://hubpages.com/hub/

computers revolution

It has been suggested that the history of computers can be traced back to about 2000 years ago starting with the birth of the abacus and the different calculation machines that were invented. It is believed that computers were invented to solve complex problems in mathematics and problems related to science. While this might be true for some areas of mathematics and science, where the computer is sometime used as a calculating machine, the computers often serves other purposes for the general population for example e-mailing, researching, banking, shopping etc. Dorothy Derringer argues that computing is the least important thing that a computers do.

The computers of the past were relatively large and had slow processing speed, that is they were able to process 50 - 200 cards each minute. The memory and storage capacity of past computers were also limited in comparison to todays computers which possess a more efficient operating system and a larger memory, coupled with faster processing speed. However, after the completion of the ENIAC in 1945 more research went into improving the computer to the network of personal computers we have in our homes today.

On the other hand, in 1642 Blaise Pascal was credited with the invention of the first digital computer. This computer had eight digit. Since then, computers have continued to changed and modernize to meet the needs of our ever changing society. According to Dorothy Deringer "computers through their use in a variety of communication, information, and manufacturing systems... have the most potential for being the most powerful intellectual tools that mankind has ever invented". That is, computers and computer technology prevades several aspects of our daily lives within North America. This is also true for other developed countries and developing countries in the world. In these countries the computers serves various functions such as banking, making reservations at the airports, filing tax returns, credit card, automobile and for tracking purposes etc. Today we continue to rely on computers to scan bar codes at the checkout and for personal banking, entertainment, medical administration, research, military planning, tax collection, social networking etc.

It was believed that with the advent of computers, people would have more time off work and would be required to work less hours. However, people continue to work even longer hours as companies expand and become even more reliant on computers. While computers continue to become advance it is only a tool and need people to input, retrieve and store and analyze data.

I believe that in the future computers will continue to get smaller, and will continue to be use in all aspects of our lives. Computers will also have larger RAM for data storage and data retrival. I also believe that computers will also have faster processing speed as people become more reliant on them for business and pleasure. Whatever the future of computer holds, mankind will continue to be reliant on them for daily operational purposes, for example, social networking, banks, research, tracking files, e-mailing etc. Financial institutions will become overly dependent on computer to maintain personal databases for credit cards, mortgages, and personal banking and for tracking purposes, as the population increases and applies for more credit and bank cards.