Recall the truth tables for two binary propositions from your discrete mathematics
course, there are 
distinct combinations
of output:
Truth
Tables on Two Propositions
|
p |
q |
t |
Ú |
¬ |
p |
® |
q |
« |
Ù |
Ø (pÙ q) |
Å |
Ø q |
Ø (p® q) |
Ø p |
Ø (q® p) |
Ø (pÚ q) |
c |
|
T |
T |
T |
T |
T |
T |
T |
T |
T |
T |
F |
F |
F |
F |
F |
F |
F |
F |
|
T |
F |
T |
T |
T |
T |
F |
F |
F |
F |
T |
T |
T |
T |
F |
F |
F |
F |
|
F |
T |
T |
T |
F |
F |
T |
T |
F |
F |
T |
T |
F |
F |
T |
T |
F |
F |
|
F |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
T |
F |
|
col. # |
15 |
14 |
13 |
12 |
11 |
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |
|
Now we extend the above truth table to micoroperations on a computer. For the sake of consistency with our text, see table 4-5, Computer System Architecture, Third Edition by M. Morris Mano, 1993, Prentice Hall, we consider the inputs from 00 to 11 (in reverse order).
Truth Tables for 16 Functions of Two Variables
|
x |
y |
F0 |
F1 |
F2 |
F3 |
F4 |
F5 |
F6 |
F7 |
F8 |
F9 |
F10 |
F11 |
F12 |
F13 |
F14 |
F15 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
0 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
|
1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
|
1 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
We replace x with the binary content of register A and y with the binary contents of register B to achieve the microoperation for a given Boolean function. Some functions are used repeatedly and given special names.
|
Boolean Function |
Microoperation |
Name |
|
F0 = 0 |
F ¬ 0 |
Clear |
|
F1 = xy |
F ¬ A Ù B |
AND |
|
F2 = xy' |
F ¬ A Ù B' |
|
|
F3 = x |
F ¬ A |
Transfer A |
|
F4 = x'y |
F ¬ A' Ù B |
|
|
F5 = y |
F ¬ B |
Transfer B |
|
F6 = x Å y |
F ¬ A Å B |
Exclusive-OR |
|
F7 = x + y |
F ¬ A Ú B |
OR |
|
F8 = (x + y)' |
F ¬ (A Ú B)' |
|
|
F9 = (x Å y)' |
F ¬ (A Å B)' |
Exclusive-NOR |
|
F10 = y' |
F ¬ B' |
Complement B |
|
F11 = x + y' |
F ¬ A Ú B' |
|
|
F12 = x' |
F ¬ A' |
Complement A |
|
F13 = x' + y |
F ¬ A' Ú B |
|
|
F14 = (xy)' |
F ¬ (A Ù B)' |
NAND |
|
F15 = 1 |
F ¬ all 1`s |
Set to all 1`s |
