NAND GATE |
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Logic
The NAND gate is an electronic circuit that performs alternative denial (i.e. “not both”). The output of
the NAND Boolean operator is false only when both of the inputs are true. Otherwise, the output is true.
Although the word NAND is not used in everyday communication, it is not difficult to see that it is the
complement of the word AND. The following analysis clarifies the meaning of the NAND operator. Consider the statement not both math and biology are tested on the final board. We could say neither math nand biology are tested on the final board, but such is not a currently acceptable English usage of the word NAND; so bear with not both. It is typical in engineering to use 1 instead of TRUE and 0 instead of FALSE. Hence, we rewrite Table 2 as Table 3 below.
Table 3: Truth Table of complete evaluation Physical ImplementationIn 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. The next most basic logic gate is the NAND gate, which is effectively two Inverters as shown in Figure 2. Hence, we only need four transistors to build a NAND gate.
Figure 1: Interactive transistor circuit of the NOT logic operator
Figure 2: Interactive transistor circuit of the NAND logic operator
TransistorsThe 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 circuits in figures 1 and 2, for example, use 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 DesignBelow we show two additional typical constructions of the NAND 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. 
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