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MIXED-LOGIC NOTATION

A Tool for Concise Expression
by Bob Perrin

Start • Physical vs. Logical Truth Tables • Logical Interpretation of Physical Truth Tables • Logic Incompatabilities • Drafting and Reading Mixed-Logic Notation • The Terminal State • Sources and PDF

Recently, I’ve come across a number of engineers who have trouble clearly expressing logic equations as part of a schematic. Although most of these folks have only been out of school for a few years, some have been engineers for many years but are primarily self-taught and don’t have a degree in electrical engineering.

Upon investigating one case, I found that the textbook used at my colleague’s university settled on a positive-logic system [1]. Although I’m sure the author felt this approach was less confusing, all he accomplished was dumbing down the material and short-changing the student. Homologic is the digital equivalent of training wheels—suitable for beginners but cumbersome in the long run.

Mixed-logic notation is a method for expressing logical equations in schematic form. It takes advantage of DeMorgan’s theorems to enable engineers to express the Boolean equations that govern the system’s operation clearly and concisely on the schematic.

Schematics are often thought of simply as graphical net lists used by our autorouters while they generate Gerber files for PCBs. Some "forward-looking" engineers consider schematics a temporary encumbrance, an anachronism to be tolerated until the world migrates entirely to VHDL.

Well, for now at least, schematics are the primary medium for communicating circuit topology in most areas outside of VLSI design. The schematic that is created today will be referred to countless times by other engineers, technicians, customers, and (God help us) managers.

With this in mind, I decided that a short explanation of the mixed-logic system might be useful to have around. This article is not a review of Boolean algebra; it simply explains how to create logic schematics that are effective communication tools.

Given the constraints of HTML, I can’t use the overbar (indicating "complement of") in this article. Therefore, when you see a word or variable preceded by an asterisk in this article, you should interpret it the same as you would a bar completely across the word or variable.

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