Wireless World Logic Display Aid / Wireless World, May 1969

1: Introduction

The current methods of teaching logic design are lacking in some respects as there is a gulf between the practical and theoretical aspects of tuition. The normal procedure is to introduce the student to a ‘logic tutor’ after some initial training has been done in the elements of Boolean algebra. Representative circuits are ‘patched-up’ and the outputs are interpreted from lights, meters or in fact from anything that is capable of a two-state indication.

Excellent ways of representing logic functions graphically already exist, in the form of Venn diagrams, Karnaugh maps and Truth tables, and these have the advantage of presenting the abstract functions in ways that can be easily visualized. This latter point is important, as the student who can visualize logic combinations will soon reach a much deeper understanding of the underlying fundamentals. It is almost certain that during the theoretical instruction at least one of the above methods of representation, more likely all three, was employed.

As soon as practical work is started the method of display is reduced to flashing lights and other two-state
indicators. These types of indicators have to be interpreted by the student and, since they are not graphically
representative it is most unlikely that he will be able to visualize the function being demonstrated and, therefore, he may miss the point.

The Wireless World Logic Display Aid combats this problem by producing, on a standard oscilloscope, the Venn diagram, Karnaugh map or the Truth table of any gate or logic circuit that is connected to the display aid.

For instance, if a binary adder circuit were connected to the display aid, and if the instrument were switched to the Truth table mode, the rules of binary addition, which is the adder Truth table, would be displayed on the oscilloscope. In other words the hardware itself produces exactly the same display as was used by the instructor on the blackboard during the theoretical sessions and, as a result, the problems confronting the instructor and the student are much reduced.

Some applications of the instrument are listed below: others will suggest themselves to readers as they become more acquainted with the device.

Applications
1. Teaching Boolean algebra.
2. Introducing and explaining the properties of Venn diagrams, Truth tables and Karnaugh maps.
3. Demonstrating the basic logic functions: AND, OR, NAND, NOR, etc.
4. Showing how gates can be combined to satisfy complex Boolean equations.
5. Explaining the difference between positive and negative logic and demonstrating the relationships between AND – OR – NAND - NOR and the effects on the hardware of a change in logic convention.
6. Explaining what minimization is and how it is accomplished.
7. As an aid to minimization of logic systems.
8. Shows how binary arithmetic can be performed with logic.
9. As an aid to teaching modern mathematics.
10. Quickly tests the results of practical work carried out by students.
11. Can be used as check-out equipment on production lines manufacturing logic sub-assemblies.
12. As a bench test equipment for rapid fault finding on logic assemblies.
13. Can be built into equipment for monitoring purposes.

By way of an experiment the writer introduced the instrument to his seven- and five-year old daughters who had no prior knowledge of the Venn diagrams. The ‘lesson’ was treated as a game. The square on the oscilloscope screen which contains the three interlocking circles of the Venn diagram (universe) was called a garden. The three circles representing the variables were called the areas where plum, apple and orange trees grow. Within five minutes both children could recognize all the individual areas of the Venn diagram. Encouraged, the writer introduced the children to the Karnaugh map and Truth table In turn. In a very short time they could interpret the meanings of both.

Captions that go with the attached pictures:

The form which the display takes can be clearly seen in the accompanying photographs which show the instrument operating in its various modes. The completed prototype incorporates all the extra facilities mentioned on page 198.The four sets of function control switches, one set for each display area, can be clearly seen. Two input sockets for the external logic circuits are provided. The two push-buttons on the right of each set select either external circuit 1 or 2 for the appropriate display area; pressing both of these buttons results in the difference between the two circuits being displayed. The set of terminals on the left are for the variable outputs (A, B, C, D), the set in the centre are for the outputs of the external logic circuits (Z1, Z2) and the terminals on the right are power supplies for external logic circuits and for the extra variables (E, F) when the instrument is used in the 6-variable Karnaugh map mode



Photographs of the oscilloscope screen showing the display in operation. It is stressed that these patterns were produced by the prototype which has all the additions mentioned on page198. The basic Logic Display Aid will only produce one of the four maps shown in each photograph at any one time. In photograph (a) the instrument was connected to a full binary adder and the SUM output is displayed. The whole left-hand part of the photograph is the Truth table for the SUM output of the binary adder; the first column is A, the second B, the third C and the fourth the result or SUM. The top right-hand display (still photograph (a)) is the Karnaugh map for the function and below it is the appropriate Venn diagram. In photograph (b) the external logic circuit was an AND gate connected to the Not A, Not b, Not C terminals, the positions of the Venn diagram and Karnaugh map are reversed when compared to (a).

Photographs (c) shows how two different circuit functions can be displayed simultaneously, the Venn diagram and Karnaugh map for A and Not A being displayed. For photograph (d) two binary adders, one of which was not functioning correctly, were connected to the display aid. The left side of the picture shows the Venn diagram for each of the two adders; the top right display is the Venn diagram, and the bottom right is the Karnaugh map,for the difference between the two adders showing that the term not A, Not B, C is missing in one adder.


Block Diagram