V22.0436  Prof. Grishman
Lecture 3: Logic Design  Combinational Circuits: canonical forms and
propagation delay
Text: Appendix B.3
Combinational circuits, cont'd

multiplexors

decoders

full adders
Canonical forms and PLAs
How can we systematically design a circuit given a truth table?

sumofproducts 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
Spring 1999