Logically Determined Design: Clockless System Design with NULL Convention Logic

CHAPTER 2

A Sufficiently Expressive Logic

Another approach to overcoming the expressional insufficiencies of Boolean logic is to search for a practical logic that is expressionally sufficient. While the previous chapter defined the conceptual form of an expressionally sufficient logic, it did not define a practical instance of such a logic.

2.1 SEARCHING FOR A NEW LOGIC

The search is conducted by first enhancing Boolean logic to expressional sufficiency in terms of pure function operators. This results in a 4 value logic, which is impractical to implement. This 4 value logic is then evolved to a practical 2 value logic.

2.1.1 Expressing Discrete Data Presentation Boundaries

To the data values TRUE and FALSE is added the value NULL, to represent the state of ‘no data’. This will be referred to as the NULL convention. The input presented to a combinational logic expression will monotonically transition between ‘complete data’ and ‘no data’ or all NULL. These monotonic transitions shown in Figure 2.1 will be referred to as wavefronts. The monotonic transition from ‘complete NULL’ to ‘complete data’ is a data wavefront and the transition from ‘complete data’ to ‘complete NULL’ is a NULL wavefront. Each successive data wavefront is separated by a NULL wavefront.

2.1.2 Logically Recognizing ...