Introduction
Chips (or more precisely: integrated circuits) are found in your PC, MacBook, Android Phone and microwave oven where they perform a diversity of functions, ranging from timekeeping and motor control to arithmetic and logic. Basically a small plate of silicon, chips are usually designed logically and subsequentially transformed to a list of connectable gates. This list, commonly known as a net list is finally transformed into a 2-dimensional design on a silicon base.
This last step however, the physical real-world process of connecting the gates, is highly volatile. Good arrangements on the base lead to short connections, leading to faster circuits, whereas poor arrangements lead to slower circuits. It leads to no doubt that a good arrangement of logical gates and good wiring between them is of vital essence to the performance of the IC as a whole.
To make things easier, we will consider the wiring problem only. The gates have already been arranged, and all it takes is finding very short wiring patterns.
Assignment
This is an arrangement of gates on a base, and all it takes is to wire the appropriate gates together. There are three net lists for difference functionalities. Each net list needs to be implemented.
30 gates
50 gates
100 gates
Advanced
For each of the three arrangements, try to determine the relation between the number of wires and the required number of layers.