NAND gate

Consider the NAND gate. The NAND gate yields a T unless both input values equal 1 . If the value of either one of input lines is fixed at 1 , the gate is equivalent to the NOT operator i.e. the gate yields an output of T if the free input-line equals 0 and a 0 if the free input-line equals T . If we now use the NOT operator to complement the NAND operator input line, we obtain the AND operator. Since we have already observed that the set AND, NOT is universal, we have thus also shown that the NAND operator is, by itself, universal. ... 

FAIRCHILD SEMICONDUCT CD4093BCN Quad 2-Input NAND Gate ... 

Fig. D.6. (a) A simple T-flip flop implemented using NAND gates (b) the symbol for a T flip-flop. Q is the output, Q is the inverse of the output. When a rising clock edge is applied to T, the state switches from on to off or vice versa. More sophisticated latches may be necessary to prevent race conditions depending on the transistors used.

Fig. D.8. Asimple decoder made using only inverters and NAND gates which can interface with the clock in figure Fig. D.7 to form a code generator. This arrangement will produce a 1 output for inputs of 0101, 1011, and 0100 and a 0 output otherwise.

All other flip-flops can also be implemented using the NAND gate as the building block. These state retention elements can be used to make memories and more complicated digital circuitry. 

Fig. D.9. (a) Inverter, (b) NAND gate, and (c) NOR gate designs using complementary transistor elements. Complementary devices can be fabricated using n and p-type OFETs, or by combining p-type OFETs with another material, such as amorphous silicon, which produces NFETs.

Fig. 9.10. The circuit diagram of a NAND-gate including two depletion mode transistors...

Thus, a Boolean expression can be written in the following manner for a NAND gate, saying that X = when the complement of (A AND S) = ... 

The most basic flip-flop is called a reset-set or RS flip-flop. It can be constructed from two cross-coupled NAND gates, as illustrated in Figure 23.12A. It has two inputs, labeled S for set and C for clear, and two outputs, labeled Q and Q. The Q output goes to a binary 1 and remains there when the S input momentarily goes from 1 to 0. In like manner, the Q output goes to a binary 1 and remains there when the C input momentarily goes from 1 to 0. Whenever g is a 1, Q is a 0 that is, they are always complementary. As a result, the C input will also clear the Q... 

Fig. 7.1 Chemical reaction mechanism representing a biochemical NAND gate. At steady state, the concentration of species 85 is low if and only if the concentrations of both species Ii and I2 are high. All species with asterisks are held constant by buffering. Thus, the system is formally open although there are two conservation constraints. The first constraint conserves the total concentration of S3 -F 84 -F 85, and the second conserves -F 87. All enzyme-catalyzed reactions in this model are governed by simple Michaelis-Menten kinetics. Lines ending in over an enzymatic reaction step indicate that the corresponding enzyme is inhibited (noncom-petitively) by the relevant chemical species. We have set the dissociation constants, Kp j, of each of the enzymes Ei-Eg, from their respective substrates equal to 5 concentration units. The inhibition constants, K i and K 2, for the noncompetitive inhibition of E1 and 7 by 11 and I2, respectively, are both equal to 1 unit. The Vmax for both Ej and E2 is set to 5 units, and that for E3 and E4 is 1 unit/s. The Vmax s for E5 and Eg are 10 and 1 units/s, respectively. (From [1].)...

Fig. 7.7 Mechanism composed of two different realizations of a chemical NAND gate. The first NAND-like suhmechanism is composed of species S3-S7 pins the inputs. The second is composed of Sg-Si4 plus the inputs. Both subsystems have the inputs as common causal antecedents. As in fig. 7.1, the concentrations of all species hearing an asterisk are considered to he held constant by buffering or external flows. (From [1].)...

Fig. 7.8 Two-dimensional projection of the classical MDS solution resulting from a CMC analysis of the mechanism in fig. 7.7. Note that, despite the fact that both NAND gate subsystems of the mechanism are driven by common inputs, the different subsystems group on different half-planes of the diagram. The placement of the inputs of the diagram is due to the choice of rate constants (see text). The reasons for the connection drawn between (S13, S14) and S5 and for the lack of connection between Sn, S12 and the other subsystem or inputs are described in the text. For this diagram, 02 4 > 99.8%. (From [1].)...

Certain metabolites, such as those of lactose, bind to the repressor protein, change its shape, and cause it to loosen its grip on the DNA. mRNA and proteins can then be formed. However, there may be promoter snbstances also necessary to this process. The result is that proteins are formed only if both inputs allow it. A genetic NAND gate is illustrated in Figure 8.2.5. The NAND gate is a basic unit of computers, so genetic computers can, in theory, be formed from simple bacterial DNA. 

FIGURE 8.2.5 Formation of a NAND gate from bacterial DNA can lead to construction of a genetic computer. (From Hayes, B., Am. Sci., 89, 204, 2001. With permission.)... 

Baytekin H.T. Akkaya E.U. A molecular NAND gate based on Watson-Crick base pairing. Org. Lett. 2080. 2, 1725-1727. 

Figure 3 Layout of the logic function / = 5 (a + (6 + c) (e / + c )) a) using two-input NAND gates b) using a complex gate.

In RUMBLE, a set of movable gates is selected, which must include fixed gates or input/output ports to terminate every path. Fixed gates and I/Os help formulate timing constraints and limit the locations of movables. In Fig. 3.6a, we assume that new locations have to be computed for the latch and the two OR gates, while all NAND gates are kept fixed. 

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