Paradigms underlying digital computation
The functional abstractions:
- Transistors afford gain and nonlinearity
- Gain and nonlinearity afford switching and signal restoration
- Switching enables logic
- Logic implements discrete mathematics
The physical abstractions:
- Binary-valued symbols approximate analog (real world) values
- Voltages are huge compared to the underlying noise
- Voltages are restored at every logical step
- Flawless representation ? flawless mathematics
- Dynamic range is exponential in the number of bits