### V22.0436 - Prof. Grishman

### Lecture 3: Logic Design -- Combinational Circuits: canonical forms and
propagation delay

Text: Appendix B.3

#### Combinational circuits, cont'd

#### Canonical forms and PLAs

- sum-of-products representation
- universality of this representation (as shown by conversion from truth
table)
- reflected in PLAs (programmable logic arrays) as universal logic elements

#### How many types of gates do we need?

- sum of products form means AND, OR, and NOT gates together are sufficient
- can build AND from OR and NOT, or OR from AND and NOT (DeMorgan's theorems),
so two gate types (AND + NOT, or OR + NOT) are sufficient
- can we build everything from just one (universal) gate type? (your
challenge in Assignment 1)

#### Propagation delay *(note: not covered in text)*

- delay of individual transistor -- how fast it can switch -- determined
by physical factors (e.g., size); now below 1 ns
- speed of transistor determines speed of gate
- the
*propagation delay* (speed) of a combinatorial circuit is
the length of time from the moment when all input signals are stable until
the moment when all outputs have stabilized
- propagation delay of a combinatorial circuit can be determined as longest
path (in number of gates) from any input to any output