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Introduction
Published in Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski, Computer Arithmetics for Nanoelectronics, 2018
Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski
This can be accomplished through redesigning the flip-flops. This means to re-wire an available type to perform as a targeted flip-flop. We have already seen that a JK flip-flop with its J and K inputs connected to a logic 1 will operate as a T flip-flop. Converting a D flip-flop to T operation is quite similar; the Q‾ output is connected back to the D input. To convert a D flipflop into JK operation, some gates must be added to implements the logical truth that D=JQ‾∨K‾Q. CMOS flip-flops are typically constructed as D types because of the nature of their internal operation. Commercial CMOS JK flip-flops then add this circuit to the input in order to get JK operation. This approach eliminates the internal latching effect, that occurs with the general JK master-slave flip-flop: The J and K input signals must be present at the time the clock signal falls to logic 0, in order to affect the new output state.
FUZZY LOGIC
Published in Kumar S. Ray, Soft Computing and Its Applications, Volume One, 2014
Fuzzy Logic is not an appropriate tool for a complete formalization of NL. The aspect of vagueness and the relaxations of classical logical truth can only be handled by Fuzzy Logic. In the essay Vagueness: An Exercise in Logical Analysis (1937), Max Black first proposed the idea of vague sets and talked about three kinds of imprecision in NL: the generally, the ambiguity, and the vagueness. The generality is the power of a word to refer to a lot of things which can be very different each other. The ambiguity is the possibility of a linguistic expression to have many different meanings. The vagueness is the absence of precise confines in the reference of a lot of adjective and common names of human language, for example, "table", "house", "tall", "rich", "strong", "young", and so on. More precisely, vagueness is an approximate relation between a common name or a quantitative adjective and the objects of the world which can be referred by this name or predicated of this adjective. By the term "quantitative adjective" we mean an adjective which refers to qualities which have variable intensities, that is qualities which can be predicated of the subject more or less. Fuzzy Logic can completely handle the linguistic vagueness.
FUZZY REASONING
Published in Kumar S. Ray, Soft Computing and Its Applications, Volume Two, 2014
Fuzzy logic is an algebraic system < [0, 1], a, v,~, where the closed interval [0,1] is a set of truth values. The logical truth values are derived from the concept of multiple-valued logic. This concept can be extended to the linguistic truth values for the fuzzy linguistic variables.
A device of XOR logic gate and multiscale sensing based on layered topology
Published in Waves in Random and Complex Media, 2023
Jun-Yang Sui, You-Ming Liu, Hai-Feng Zhang
The transmission spectra of the positive and negative scales XOR logic gate are shown in Figure 2, with the two external magnetic fields B1 and B2 respectively applied to InSb1 and InSb2. When a magnetic field is present, it is denoted by a logic level (LL) ‘1’, otherwise LL is ‘0’ when a sharp TP exists, it is denoted by a LL of ‘1’, and vice versa as ‘0’. For a more intuitive embodiment, ‘In1’ indicates the state of existence of B1, ‘In2’ symbolizes the magnetic field B2, and ‘Ou1’ stands for the state of presence of TP. As can be seen from Figure 2(a), under the condition that EWs propagate in the positive direction when the applied magnetic field B1 is present and B2 is absent, transmissivity (T) is obtained and much greater than 0.9, the value of it is 0.9658, the NAFP corresponding to TP is 0.26496 α, and QF = 1379.98, forming a sharp TP. The states are ‘In1 = 1’, ‘In2 = 0’, and ‘Ou1 = 1’, related to the ‘1 XOR 0 = 1’ of the XOR logic gate. When B1 does not exist and B2 exists, T = 0.9301, much greater than 0.9, QF = 659.21. The states are ‘In1 = 0’, ‘In2 = 1’, and ‘Ou1 = 1’ cohering with the ‘0 XOR 1 = 1’ of the XOR logic gate. The TP of this case owns NAFP 0.26946 α, coinciding with ‘1 XOR 0 = 1’, which is convenient for detecting logical operations. When both B1 and B2 are subsistent, TP does not exist, then ‘In1 = 1’, ‘In2 = 1’, and ‘Ou1 = 0’, and T is much less than 0.1, correlating to the XOR logical operation ‘1 XOR 1 = 1’. When neither B1 nor B2 is not existent, TP is absent and T is much less than 0.1, then ‘In1 = 0’, ‘In2 = 0’, and ‘Ou1 = 0’ corresponding to the ‘0 XOR 0 = 0’ of the XOR logic gate. For EWs propagating in the opposite direction, as can be seen in Figure 2(b), the same logical relationship as when positive propagation, T = 0.9723, QF = 1110.03 at ‘1 XOR 0 = 1’, T = 0.9469, QF = 430.13 match ‘0 XOR 1 = 1’, and the NAFP of TP in both cases is 0.2645 α, it is worth noting that the difference between the NAFP belonging to the positive and negative TP is 0.00046 α, which reflects the non-reciprocity of PCLT. Similarly, for ‘1 XOR 1 = 0’ and ‘0 XOR 0 = 0’, T is much less than 0.1. It can be seen that the transmission spectra of the PCLT designed in our work strictly adheres to the XOR logic gate function on both the negative and negative scales under the regulation of the external magnetic fields B1 and B2, and due to its non-reciprocity, the two scales can orchestrate logic operations of different NAFP to obtain different QF values. The logical truth table is shown in Table 1.