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/