Copyright 2005 Curt Hill Gates and Low Level Digital Logic.

Copyright 2005 Curt Hill

Gates and Low Level Digital Logic


Boolean Algebra Introduction• Digital signals will represent one of two values

– Used to be +5 and 0 or 0 and -5• This will be used to represent True and False or

1 and 0 respectively• Most of the work with logic was done by

George Boole in the late 19th century• He came up with the four operations: NOT,

AND, OR, XOR (Exclusive OR)• We need to know precisely what these do,

which is made easier by the fact that these are patterned after our usage in English

• Not is unary and merely reverses the value• The rest are binary and are given in following

table


Boolean Algebra

A B A or B A and B A xor B Nand Nor

0 0 0 0 0 1 1

0 1 1 0 1 1 0

10 1 0 1 1 0

1 1 1 1 0 0 0

• We are interested in these because they may be implemented electronically

• Not just reverses a single value


Gates• At the lowest level the building blocks of

computers are gates or switches• A CPU is a collection of gates• The fact that we can implement these in

a rather straightforward matter makes the construction of computers possible

• Typical gates can be constructed with just a transistor or few diodes

• From there we will see that things like an adder can be constructed from gates


Gate Symbols

• We use a variety of symbols to diagram gate networks

• NOT• AND• OR• NAND (Not And)• NOR (Not Or)


Why these?

• And, Or and Not are sufficient to generate anything

• There are subsets that also work• Both NAND and NOR or sufficient

by themselves• When these were discrete chips

then a manufacturer could just stock one type


How?

• A NOT is a signal inverter• Usually a single amplification stage

– A tube or transistor will reverse the phase– Unity gain– Single stage is an inverter

• An AND or OR can be constructed with one diode per input


Electrical properties

• The gates that are used are bistable

• Fancy way of saying that they produce one of two electrical outputs

• They remain in that state until moved on to their next state

• Often this state is only allowed to change during a certain portion of the clock cycle


Common characteristics

• Speed• Resistance• Current required to drive• Current produced


Speed

• How fast can we clock it• How fast can it change from one

state to next• This is usually a function of the

underlying implementation• EG: Transistors are faster than

tubes– Smaller is better with transistors


Resistance

• We have more to consider than how to arrange the gates

• We must also consider the electrical resistance

• In regard to gates this also becomes important in fan in fan out

• Fan in is how many inputs a device may have


Current needed to drive the gate

• Since each input device requires current to drive and the driving device has limits on how much current it can produce– There is a limit how many devices can

be driven

• Fan out describes how many output lines this device can drive


Current Problems

• Resistance to electrical current produces heat

• The amount of heat affects the operating temperature of the device

• Some things are very heat sensitive, such as transistors

• We can reduce both heat and increase speed by reducing size


Observation

• Seymour Cray observed that the limit on the speed of his supercomputers was the speed of light across wires

• Hence first Cray was shaped like a love seat to minimize wire distances– Cylinder housed logic boards– Bench was power supply

• Microprocessors have very much exploited this


Technologies:

• Vacuum tubes• Discrete transistors• Small integrated circuits• Large and very large integrated

circuits


History of computer gate technology

• Vacuum tubes– Invented in the first decade of the

century by Lee deForest

• The principle is that a heater warms the cathode, which emits electrons– This must be in a vacuum to be effective

• The anode catches these• The voltages must be relatively high

for these to work at all


Vacuum tube workings

• If the anode is positively charged it attracts the electrons and the current flows

• If the anode is negatively charged it repels the electrons and the current stops

• Hence it functions as a switch• If you put a grid between the anode

and cathode that has an analog signal on it, then it will function as an amplifier


Vacuum Tube Problems– Generate substantial heat

• This heat is destructive on a lot of other components

• It also requires substantial electrical requirements

• They say that Philadelphia dimmed when they first turned on ENIAC

– Low reliability– Slow– Bulky– High voltages are potentially

dangerous


Transistors• Based on semiconductors• Discovered by Bell labs in 1947• Silicon with small amounts of impurities

– These impurities can cause the material to have less or more electrons (N or P)

• The action occurs at junctions between two different impurities

• The amount and polarity of the voltage determines whether current can flow from across the junction or not

• So a transistor has three pieces, PNP or NPN


Transistors• The middle layer is the base and that is

where the signal to be amplified is put• The other two are the emitter and

collector, where current flows from the emitter to the collector in a PNP and from the collector to emitter in an NPN

• Advantages– Transistors lack the heater that tubes have

so they are much cooler devices, it fact they die when they get too hot

– They are much smaller– They are much faster

• From here on it is evolution not revolution


Integrated circuit

• In discrete transistors we have one transistor per package

• In an integrated circuit, we put more than one transistor or diode in a package

• Small scale, large scale and very large scale integration are just matters of degree


Fabrication• If you consider the traditional

components of a circuit in the 1940s there were the following:– Tubes (usually for amplification, but also as

rectifiers)– Resistors– Capacitors– Connecting wires

• A transistor can perform the function of the tube

• We have techniques for fabricating resistors and very small capacitors and connecting wires on our integrated circuits


Therefore

• What used to be a whole board is now a chip

• The hardest thing is medium or larger size capacitors, which are usually external

• By the time we hit the Pentium, there is approximately 3 million transistors on this chip


Now where?

• Silicon is nearing the end of the line

• We are far out on the learning curve

• The gains we have seen in the past are not going to be repeated– Hence the move to multi-core CPUs

• There are too many quantum physics theoretical problems to continue for much longer


Gallium arsenide• A favorite as a replacement

– It has a very high switching speed• It has become dominant in very

high frequency applications• However, we are at about the

same level in making integrated circuits with this stuff as we were with silicon in 20-30 years ago

• The law of diminishing returns works with it as well


Optics

• Bell Labs has already demonstrated an optical computer

• However, with light technology we are about in the same condition as we were with electricity in the 30s or 40s

• The law of diminishing returns works with it as well


Light Advantages• Resistance to interference• Many things can disrupt electrical

signals• I am not aware of anything that will do

the same with light• Lack of media• Nothing in electrical technology is

analogous to a laser• We can transmit our signal without

media for enormous distances, with no resistance or power dissipation

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Copyright 2005 Curt Hill Gates and Low Level Digital Logic.

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