Assignment 2

first four digits 2064

2064 = 0(mod 8)
2064 = 0(mod 3)
2064 = 6(mod 7)

Question 1.

x - 0011
y- 0101

Possible ways of getting 16 binary functions using AND/OR and NOT
(not x) and x - 0000
x and y - 0001
x and (not y) - 0010
x and x - 0011
(not x) and y - 0100
y and y - 0101
(x or y) and [(not x) or (not y)] - 0110
x or y -0111
not(x or y) -1000
not[(x or y) and {(not x) or (not y)}] - 1001
not y - 1010
not[(not x) and y ] - 1011
not x -1100
not [ x and (not y)] -1101
(not x) or (not y) - 1110
x or (not x) -1111

Question 2. (0) All 16 binary functions can be represented using {AND,NOT}

Question 3 (0)

Commutative functions are

0000

0001

0110

0111

1000

1001

1110

1111

Question 4. When working in trinary with two input arguments and one output argument there are 19,683 possible binary operations.


Question 5. I think that only 2 binary operations are necessary to express every possible two argument function on trinary operations. I also think that in http://www.aymara.org/ternary/ternary.pdf the author is not getting the right

truth table for impl(x,y).

Question 6-6 Setting Black = 1 and White = 0
It seems that both images are the same.
(pic1 AND pic 2) and (pic1 OR pic2) is the same as
pic1 AND (pic1 IMPL pic2)

Question 7.

A - Poison caused the victims death

B- There was a change in victim's blood chemistry

C- There was a residue of poison in the stomach

D-There were puncture marks on the body

E- Poison was injected by a needle

IFF - if and only if

IF - only if

A IFF (B OR C)

NOT(B OR C)

D

E IF D

A OR (NOT D)

Orders of Magnitude

Question 1.

The computer with 1GB of memory has 16384 times more memory than a computer with 64K.

Question 2.

6160.4 floppy disks with 800K are equivalent to a 4.7GB DVD.

Question 3.

The first mass marketed PC cpu was Intel 8080 with a clock speed of 2MHZ

Computers now have clock speeds of up to 4GHZ. This has an increase factor of 2000, although

it is actually much higher than this due to more work done in todays processors per every cycle.

http://www.intel.com/technology/timeline.pdf