### V22.0436 - Prof. Grishman

### Lecture 2: Trends; Introduction to Logic Design

#### Technology Trends

We continue to learn, at a steady pace, how to fabricate smaller and
smaller transistors. This allows for

- a higher level of integration (currently, millions of gates on a chip)
- faster circuits (compare the initial PC of 5 Mhz with current PCs of
200 Mhz)

The cost of a chip has remained (very roughly) constant, so price/performance
has been rapidly decreasing. How should this extra circuitry and extra performance
be used? We shall return to this issue after discussing processor design.

### Logic Design: Combinatorial Circuits

*(Text: Appendix B.2 and B.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
- exclusive-OR gate (half-adder)
- multiplexors
- decoders