How They Really Work

Osher Lifelong Learning Institute
University of Illinois, Urbana-Champaign

Scott Badman, Instructor

Simple Logic

Logical AND, OR, Exclusive OR (XOR), and NOT

Core concept: All computing is based on simple logic.

This Logic only works in situations where there are only two possible choices, such as "true or false", "yes or no", or "on or off"

Multiple choices are handled by mathematical probablilites.

AND: Intuitive meaning -- both, not just one or none.

Inclusive OR: "What can I have in my coffee?" "Milk or sugar" (with both usually implied).

Exclusive OR: "What can I have for dessert?" "Cake or Pie" (but not both usually implied)

NOT: intuitive negation

Truth tables, very similar to the addition and multiplication tables

NAND and NOR are just negations of AND and OR

Implementation of Logic using switches

Any type of switch that can actuate the next switch could theortically be the basis of a computer.

A computer could be made out of many technologies.

The only reasons they are made from electronics are electronic's incredible speed, huge capacities, and and low cost.

They could be made from mechanical wheels and levers, electromechanical relays, water pipes and values, or a few thousand students sitting in chairs in Memorial Stadium.

Old fashioned electronic tubes can be amplifiers or electronic switches.

Electric current flows from the filiment, through the grid, to the positively charged annode at the top.

A negative charge on the grid could decrease or stop the electron flow.

Small variations of electric charge on the grid causes similar, but much larger variations in the current flow, making the tube an amplifier.

If all you need is an on/off switch, the tube can be a lot smaller and use a lot less current.

Transistors are very similar to tubes.

Uses a sandwich of silicon layers that have metallic impurities mixed in so they can conduct electricity, but they don't burn up from too much conduction.

Using the right formulas of different impurities in the middle layer versus the outer layer allows the transistor to function very similar to a tube.

Transistors used as amplifiers can be as big as the nail on your little finger.

If transistors are only used as on/off switches, the engineers can currently fit over 1 billion on a chip of silicon the size of your thumb nail.

Implementation of Logic Gates using transistors

AND, OR, and NOT gates

XOR gate is more complicated

NAND or NOR gates are actually easier to implement, and logically more useful.

In practice computer engineers do lots of tricks to reduce the transistor count while still performing the same logic in complicated circuits.

NAND can implement every other gate.

Logic is the basis of arithmetic.

"Principia Mathematica".

Online Version of "Principia Mathematica"

Principia Mathematica Page 362 (look at the bottom)