THE NOT GATE
by Isai Damier

The NOT gate is an electronic circuit that performs negation. The output of the NOT Boolean operator is true when the input is false, and the output is false when the input is true. Hence, all NOT does is take an operand and negate it. For the sake of argument let us analyze a sentence that uses the word NOT: Good is NOT evil.

A philosopher will tell us the absence of good does not necessitate the presence of evil. However that may be, our concern here is not meaning. Our concern is the statement. As we show in Table 1, the operand Good can be in two possible states: either it is present or it is not present. As such, we must evaluate the statement for two possibilities. We show the complete evaluation in Table 2.

Possibilities	Good	COMMENT
Case 1	False	Good is absent
Case 2	True	Good is present

Table 1: possible input conditions

Good	Evil	COMMENT
FALSE	TRUE	Good is absent
TRUE	FALSE	Good is present

Table 2: Truth Table of complete evaluation

It is typical in engineering to use 1 instead of TRUE and 0 instead of FALSE. Therefore we rewrite the data from Table 2 in Table 3 accordingly.

Good	Evil	COMMENT
0	1	Good is absent
1	0	Good is present

Table 3: Truth Table of complete evaluation

For greater detail on the logic significance of the word NOT, read the Boolean Algebra article.

Physical Implementation

In order to apply the principles of Boolean algebra to create real machines that can think and make decisions, we have had to find ways to physically implement the logic operators AND, OR, NOT, etc. To that end, modern day engineering uses transistor networks called logic gates. Hence, a logic gate is actually a group of transistors so arranged as to behave as a Boolean operator.

From a circuit complexity perspective, the most basic logic gate is the NOT gate (aka the Inverter). The NOT gate is made of two transistors, as shown in Figure 1. In theory a NOT gate is really just one transistor. But in practice microchip manufacturers use a pair of transistors to construct the NOT gate.

Figure 1: Interactive transistor circuit of the NOT logic operator

Transistors

The use of transistors to build logic gates is quite modern. Before transistors we used other devices, such as vacuum tubes (aka thermionic valves). And very soon we may use DNA, or some other abundant material. There are many types of transistors. Our circuit in Figure 1, for example, uses complementary metal–oxide semiconductor (CMOS) technology. Our choice of CMOS is arbitrarily based on the fact that CMOS is by far the dominant technology in use today. The dominance is due to how well CMOS performs in all the important categories: fabrication cost, packing density, loading capacity (i.e. fan–out), operational speed (i.e. propagation delay), noise margin, and power dissipation (i.e. green technology).

There is of course more to transistors than can be presented here; especially since transistors are used for more than just digital systems. And so we refer you to any good micro-electronics textbook.

Alternate Design

Below we show three additional typical constructions of the NOT gate. Each of the constructions presents specific conveniences to designers. If you are very new to digital systems design, you may not understand the importance of the figures below. Still, we include them in this article for the people who may need them.