Multi-Valued Sub-Function Encoding in Functional Decomposition Based on Information Relationships Measures

• Authors: Artur Chojnacki;Lech Józwiack
• Venue: ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
• Year: 2000

Functional decomposition is becoming increasingly popular, because it is more general than all other known logic synthesis approaches and it seems to be the most effective approach for LUT-based FPGAs, (C) PLDs and complex CMOS-gates. The multi-level functional decomposition can be seen as a recursive splitting of a given function, into two sub-functions: the predecessor (bound-set) function and successor function. Initially, the bound set function is a multi-valued (symbolic) function, where a certain value (symbol) is assigned to each particular input-cube compatibility class of the function being decomposed. To be implemented with binary logic, the multi-valued bound-set function must be expressed as a set of binary functions. This transformation is called the multi-valued sub-function encoding. It can be performed by the binary code assignment to each particular input-cube compatibility class. It determines the resulting binary predecessor and successor sub-functions and therefore influences the quality of the resulting circuit to a high degree. In this paper, a new method of the multi-valued sub-function encoding is presented. The method is based on the information relationship measures. Experimental results from the prototype CAD-tool that implements the method demonstrate that it is able to efficiently construct extremely effective circuits for symmetric functions. Results for asymmetric functions are also very good.