Computing the Full Quotient in Bi-Decomposition by Approximation
Anna Bernasconi1, Valentina Ciriani2, Jordi Cortadella3 and Tiziano Villa4
1Department of Computer Science Università di Pisa, Italy
anna.bernasconi@unipi.it
2Department of Computer Science “Giovanni Degli Antoni” Università degli Studi di Milano, Italy
valentina.ciriani@unimi.it
3Department of Computer Science Universitat Politècnica de Catalunya, Barcelona, Spain
jordi.cortadella@upc.edu
4Department of Computer Science Università degli Studi di Verona, Italy
tiziano.villa@univr.it
ABSTRACT
Bi-decomposition is a design technique widely used to realize logic functions by the composition of simpler components. It can be seen as a form of Boolean division, where a given function is split into a divisor and quotient (and a remainder, if needed). The key questions are how to find a good divisor and then how to compute the quotient. In this paper we choose as divisor an approximation of the given function, and characterize the incompletely specified function which describes the full flexibility for the quotient. We report at the end preliminary experiments for bi-decomposition based on two AND-like operators with a divisor approximation from 1 to 0, and discuss the impact of the approximation error rate on the final area of the components in the case of synthesis by three-level XOR-AND-OR forms.
