CSCI 255, ENGR 274, ECE 212 -- 31 August, 2000
Announcements
Gates
Gates in CMOS
The power of NAND
- 1913, Henry Sheffer proposed the NAND (really, NOR) as the basis of
Boolean algebra
- 197?, 7400 is the
first integrated circuit on a chip
- x|y = (x y)'
- x' = x|x
- x y = (x|y)'
- x+y = (x'|y')'
Boolean equations to/from gates
Boolean functions
| x |
y |
functions |
| 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 |
Truth functions to Boolean equations
| Sum of products |
disjunctive normal form |
F = Σ(...) |
| Product of Sums |
conjunctive normal form |
F = Π(...) |