1. Gates and Low Level Digital Logic
Copyright 2005 Curt Hill

2. 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

3. Boolean Algebra
A B
A or B
A and B
A xor B
Nand
Nor
0 0 1
0 1
1 1
We are interested in these because they may be implemented electronically
Not just reverses a single value
Copyright 2005 Curt Hill

4. 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

5. 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

6. 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

7. 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

8. 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

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

10. 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

11. 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

12. 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

13. 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

14. 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

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

16. 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

17. 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

18. Vacuum Tube Problems Generate substantial heat Low reliability Slow
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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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
Copyright 2005 Curt Hill