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[Solved]: Algorithms for logical synthesis of multiple output bits?

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Problem Detail: 

Karnaugh maps and the Quine–McCluskey algorithm can be good choices for coming up with fairly minimal logical expressions that match the requirements of a truth table.

What if I have a situation where I have $M$ input bits and $N$ output bits though?

A naive way to deal with it would be to solve each output bit independently and come up with $N$ logical expressions. The problem with that is that in circuitry or in CPU implementations, you can do multibit operations which can potentially handle a more optimal logical expression which takes into account several, if not all, of the bits at once.

Are there any algorithms to come up with a fairly minimal logical expression when you have $M$ input bits mapping to $N$ output bits?

Asked By : Alan Wolfe

Answered By : vzn

as you realize, while universal, Quine-Mcclusky is only a "bitwise" construction method (single bit output) that does not recognize/ exploit common subpatterns for multibit outputs. multibit function construction optimization is a very broad area handled by EE type papers/ applications/ algorithms, there are very many published. the general topic is "logic synthesis". there is also a very broad array of software built for this purpose both commercial and public domain. here is an example of a relatively recent survey of algorithms and also a technique of using known/ previously computed circuits in a library-like context. this paper is useful here in that it refs many of the top systems in use and gives a consolodated view that you seem to be asking for in particular.

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