Logically Determined Design: Clockless System Design with NULL Convention Logic

CHAPTER 9

Multi-value Numeric Design

2NCL is an inherently multi-valued logic. Variables can be constructed from any number of values with any assigned meaning. These heterogeneous variables can be directly combined by appropriately combining their values. For instance, Section 4.4 of Chapter 4 presents a 2NCL expression adding a binary variable to a trinary variable producing a quaternary variable. This generality allows many conceptual conveniences in design specification. The question of this chapter is whether multi-value representation provides conveniences for expressing numeric processes.

9.1 NUMERIC REPRESENTATION

Multi-value variable representation allows the consideration of radices and encodings other than binary for numeric representation. This section will focus on cost of representation of numeric values, both for transmission and functional combination. The costs will be considered in terms of quantity of paths and operators to characterize physical resources and in terms of quantity of path transitions to characterize power and speed.

9.1.1 Resource Cost of Transmission

The total cost of transmitting a numeric representation is the cost of representing the values per digit times the cost of representing each digit. For the familiar electronic representation where ...