Multilevel Synthesis

When there are too many inputs to a gate, fan-in becomes an issue. I.e we are limited to the number of inputs per gate.

Fan in problems can be addressed using factoring and functional decomposition.

Factoring

Example

Consider the function , and suppose we have a maximum fan-in of 4.

We could write , but this costs too much.

We can factor common terms however, and write which is better.

Example

Consider the function

Using factoring, we get .

Now, let .

We find that:

Thus, .