The negation device used in computer circuitry is called an inverter, since it changes its input from a 1 to a 0, or vice versa. The usefulness of such an element is obvious when we remember the computer trick of subtracting by adding complements. The inverter circuit used with a code like the excess-3 readily forms these complements.
Further sophistication of the basic Boolean forms leads to units other than the AND and OR gates. Possible are NOT, NOR, and exclusive-OR forms. In the latter, there is an output if one and only one input is present. The NOR circuit is interesting in that it was made possible with the introduction of the transistor; the vacuum tube does not permit this configuration.
Computer Control Co.
The functions of two binary variables.
Present-day symbolic logic is not the pure Boolean as presented back in 1854. Boole’s OR was the exclusive, one and only one, type. Today the logician generally assumes the either-or connotation. The logic has also been amplified, using the commutative, associative, and distributive laws much like those of conventional algebra. We are indebted to De Morgan for most of this work, showing that A and B equals B and A; A and (A and B) equals (A and B) and A; and so on. While these seem intuitively true, the implications are nonetheless of great importance both in pure logic and its practical use in circuitry.
A graphic representation of the metamorphosis from symbolic to actual implementation of Boolean equations follows: The implication of importance is that logic applies equally well whether we are making a qualifying statement such as “A man must have strength and courage to win a barehanded fight with a lion,” or wiring a defensive missile so that it will fire only if a target is within range and is unfriendly.
In the early period of computer design the engineer was faced with the problem of building his own switches and gates. Today many companies offer complete “packaged” components—AND gates, OR gates, and the other configurations. This is the modular approach to building a computer and the advantages are obvious. The designer can treat the components simply as “black boxes” that will respond in a prescribed way to certain input conditions. If he wants, the engineer can go a step further and buy a ready-built logic panel consisting of many components of different types. All he need do to form various logic circuits is to interconnect the proper components with plug-in leads. This brings us to the point of learning what we can do with these clever gates and switches now that we have them available and know something about the way they work.
We talked about the computer adder circuit earlier in this chapter. It is made up of two half-adders, remember, with perhaps an additional OR gate, flip-flop, etc. Each half-adder is composed of two AND gates and an OR gate. So we have put together several basically simple parts and the result is a piece of equipment that will perform addition at a rate to make our heads swim.
There are other things we can do with Boolean logic besides arithmetic. A few gates will actuate a warning signal in a factory in case either of two ventilators is closed and the temperature goes up beyond a safe point; or in case both vents are closed at the same time. We can build a logic computer that will tell us when three of four assembly lines are shut down at the same time, and also which three they are.
