Assignment #2

The first digits of my student number are 2007.
2007mod8 = 7 (Q. 2h.)
2007mod3 = 0 (Q. 3a)
2007mod7 = 5 (Q. 6f)

1. The 16 binary functions can be expressed as a composition of the binary operations AND/OR and NOT.
0. Y and not Y
1. X and Y
2. X and not Y
3. X
4. Y and not X
5. Y
6. (X and not Y) and (Y and not X)
7. X or Y
8. Not X or Y
9. Not (X or Y) and not(X and Y)
10. Not Y
11. X and not (X or Y)
12. Not X
13. Y and (X and not (X or Y))
14. Not (X and Y)
15. Not (Y and not Y)

2. I cannot find any combinations of (NOT,IMPL) for the following binary functions 1,2,3,5,6,7,9,10,11.

3.a) 2007mod16 = 7
Is (X or Y) commutative?

x 0 0 1 1
y 0 1 0 1
f(x,y) o 1 1 1
f(y,x) 0 1 1 1 Therefore, (X or Y) is commutative because f(x,y) = f(y,x).

4. As there are 3 possible outputs and 9 possible binary arguments, there are 3^9 = 19683 possible binary operations.

5. Since the operations IMPL, OR, AND, and NOT can generate all 16 binary functions, these same four can generate every possible two argument function on trinary operations.

6. Downloading GIMP has been a nightmare. What would happen if I threw my laptop out the window?

7. Death caused by poison - D
Change in blood chemistry - C
Residue of poison - R
Puncture marks on body - M
Poison injection - I
Poison - P
[P AND (C OR R)] OR [NOT P AND NOT C AND NOT R]
NOT C AND NOT R AND M
NOT [I AND NOT M]
P OR NOT M


Orders of Magnitude

1. A computer with 1 GB of memory has [ 1024 MB x 1024 KB / 64 KB] 16,384 more memory than a Commodore 64 with 64 KB of memory.

2. [4.7 GB x 1024 MB x 1024 KB / 800 KB] 6160 floppy disks that hold 800 KB of storage is equivalent to one DVD which has 4.7 GB of storage.

3. The Mac Plus has a Motorola 68000 CPU which runs at a speed of 8MHz. The AMD has an Athlon 64 X2 4800+ with two cores, each running at 2.4GHz. When measuring and comparing speed, AMD's combined 4.8GHz is 600 times faster than the Motorola. However, the AMD is a far more advanced processor, thus performing much faster than the old 68000 per Mhz. So it's very safe to say that the AMD is at least 1,000 times faster than the Mac Plus. (http://hubpages.com/hub/_86_Mac_Plus_Vs_07_AMD_DualCore_You_Wont_Believe_Who_Wins)