Spectral Logic and Its Applications for the Design of Digital Devices

CHAPTER 8

HARDWARE IMPLEMENTATION OF SPECTRAL METHODS

In this chapter we discuss some methods for implementation of logic networks by using memories as basic modules.

In general, synthesis with memories has advantages that the design time and efforts are minimal, since design in this case is reduced to the programming of a memory structure (449). The optimization is possible in the case of two-level addressing of Read-Only Memories(ROM), and simplification of the related multiplexer network at the output. For more details, see Reference 41. This approach to the synthesis is efficient when a given system of functions f is represented by the truth vectors that are directly stored in the ROM, and there are no minimzation of f in the sense of reduction of the product terms in Sum-of-Product (SOP) expressions. Since the complete truth vectors are stored, it follows that the method is inefficient when f has many values 0 or 1, and unspecified values. In these cases, specification by cubes or analytical expressions may provide more compact representations. The method is efficient, if f has many product terms in SOP as the arithmetic functions. It is also efficient when it is required a frequent change of functionality (adaptivity) of the produced network.

In the case of representation of functions by spectral expressions, the memory, which is the core part of the implementations by spectral representations is used to store the spectral coefficients.

The considerations in this chapter ...