### Combinational (Combinatorial) Circuits

(Text: Appendix C.2 and C.3)

#### Combinational circuits and gates

combinational circuits: no memory -- output is only a function of current inputs

gates are basic combinational circuits: AND gate, OR gate, inverter (complement), etc.

realization of gates from switches:

• OR gate from parallel circuit
• AND gate from series circuit

#### Representation of combinational circuits

• by Boolean formulas
• by truth tables
• by logic diagrams
• translating between these representations

#### Examples of combinational circuits

• NAND and NOR gates
• multiplexors
• decoders
• full adders (pg. C-27 to 28)

#### Canonical forms and PLAs

How can we systematically design a circuit given a truth table?
• 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:  see exercise C.1),
so two gate types (AND + NOT, or OR + NOT) are sufficient
• can we build everything from just one (universal) gate type?