Copyright 2005 Curt Hill Gates and Low Level Digital Logic

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill Boolean Algebra A BA or BA and BA xor BNandNor We are interested in these because they may be implemented electronically Not just reverses a single value

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill Gate Symbols We use a variety of symbols to diagram gate networks NOT AND OR NAND (Not And) NOR (Not Or) 

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill Common characteristics Speed Resistance Current required to drive Current produced

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill Technologies: Vacuum tubes Discrete transistors Small integrated circuits Large and very large integrated circuits

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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 years ago The law of diminishing returns works with it as well

Copyright 2005 Curt Hill 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

Copyright 2005 Curt Hill 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