MCS-170 The Nature of Computer Science

Fall 2006

Lecture 17

1. Review - Logic Circuits and Switches

Logic Circuit -- circuit that controls the flow of electricity

Flow "ON" - represents a binary value of 1, or a logical value of TRUE
Flow "OFF" - represents a binary value of 0, or a logical value of FALSE
Logical Circuit is essentially a sophisticated Switch

A switching circuit can be as simple as a switch connected in series with a lamp.

Earliest computer (~1930) Electric relays as switches.
Generation 0 Computers (1940's) - Vacuum Tubes as switches.
Generation 1 Computers (1950's-1960's) - Transistors as Switches.

Two Types of Transistors-- NMOS and PMOS. Type is dependent on material added to silicon.

n-type silicon: phosphorus impurities added which makes material more negative (majority of free electrons)
p-type silicon: boron impurities added which makes material more positive

NMOS Transistor-

Source and Drain are n-type and sit on a positively charged well of p-type silicon.

When positive voltage (green arrow) is applied to the gate, electrons in the p-type silicon are attracted to the area under the gate, forming an electron channel between the source and the drain.

This opens the flow from the drain to the source.

In this state the transistor is on.

transistor-c

transistor-d

Example - Transistor simulator at http://www.prenhall.com/reed/Chapter16/logic.html

2. Transistors as Building Blocks of Logic Gates

Combinations of NMOS and PMOS transistors can be used in sequence (connecting output of one to input of another) to produce signals that are functions of the input.

Demonstration - Simulator (http://www.prenhall.com/reed/Chapter16/logic.html)

Three Basic Gates: NOT, AND, OR
Symbols:

not

and

NOT AND OR

Logic Tables

3. From Gates to Complex Circuits

AND, OR, and NOT gates form the building blocks of more complex logical and arithmetic circuits.

Adding two 1-bit numbers:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 with a carry of 1

A circuit that would implement this addition would have two input lines, representing the two numbers to be added, and would need two output lines, representing the sum of the inputs (as a bit) and a possible carry bit.

Logical Table -- Overhead

How can we use NOT, AND, OR gates to implement this table?

The carry output is a simple AND of the two inputs.
The sum output is more complex.

Half-Adder Circuit

half

Full-Adder: Handles a carry-in from a previous addition

full

Demonstration - Simulator (http://www.prenhall.com/reed/Chapter16/logic.html)

4. Exclusive OR

The Exclusive-OR, or XOR function can be described verbally as, "Either A or B, but not both."

This is logically the same as (Not A AND B) OR (A AND NOT B) (Use a table to show equivalence)

In Class -- design a circuit with 2 NOT gates, 2 AND gates and one OR gate that will implement an XOR function