Binary logic

Fuzzy sets and fuzzy logic. Fuzzy sets differ from the normal crisp sets in the fact that their elements have partial membership (represented by a value between 0 an 1) in the set. Fuzzy logic differs from the binary logic by the fact that the truth values are represented by fuzzy sets. 

Benioff introduced a series of Hamiltonians describing the evolution of a system consisting of spin-1/2 particles (spins up/down corresponding to binary logical states 0/1) occupying the sites of a lattice. The initial. state of the system I (t = 0) corresponds to the input state of a computation. Benioff s systems evolve, under the action of a Hamiltonian, in such a way that the quantum states (0),... 

It is very important that such molecular-level motions are accompanied by changes of some chemical or physical property of the system, resulting in a readout signal that can be used to monitor the operation of the machine. The reversibility of the movement ie, the possibility to restore the initial situation by means of an opposite stimulus, is an essential feature of a molecular machine. Since such induced motions correspond to a binary logic systems of this kind could also prove useful for information processing. 

In a chiral photochromic system (Figure 1), A and B represent two different chiral forms of a bistable molecule, and a reversible change in chirality occurs upon light irradiation. The left-handed (S or M) and right-handed (R or P) forms of a chiral compound 91 represent two distinct states in a molecular binary logic element. 

The data in a computer are fundamentally digital bits, requiring binary logic, but they are organized for convenience in a large number of computer... 

Safety interlocking and shutdown systems require detailed test procedures based around the design docmnentafion (e.g., cause-and-effect charts, binary logic diagrams) that must be formulated and agreed on in advance. 

AND gate gives a positive output and the XOR gate a negative output, which is a combined output of 10. This binary logic is summarized below ... 

In interlocked compounds such as rotaxanes and catenanes, electron-donor and -acceptor units not only cause the presence of CT interactions, but are also responsible for the occurrence of intercomponent and intermolecular oxidation and reduction processes. Such processes weaken or even destroy the CT interactions that stabilize the structure of the compound, with a consequent change in its coconformation. External inputs, like electrons or photons, can be used to cause the redox processes and the structural rearrangements that follow. Suitably designed rotaxanes and catenanes can therefore exhibit machine-like movements that correspond to a binary logic behavior. 

Rabi oscillations are periodical transitions of a two-state quantum system between its stationary states in the presence of an oscillatory driving field, see e.g. [1], Besides the fundamental interest, the effect of Rabi oscillations is promising for realization of binary logic and optical control in quantum informatics and quantum computing. 

Control is exercised by binary logic gates. These will prevent steps from being set in motion until the conditions under which they should become operative have been established. Thus, for example, the chemical dispense tanks cannot be opened until a specified temperature has been reached, irrespective of the time called for in the programme. 

It can be noted that in all cases (Fig. 7) the machine-like behavior consists in the reversible change of the state of the system (from state 1 to state O , and then back to state O ). This shows that such molecular-level machines behave according to binary logic. Therefore, they could be used, in principle, for information processing at the molecular level [22]. 

Life, as we will explain, runs on base 4 the DNA bases A, G, C, and T. Computers (except analog computers, now rarely used) run on base 2. That is, they are digital and use binary logic for digits, based on two symbols typically expressed as 0 and 1. Deep down, the work in binary logic, such as 1 = true, 0 = false, and binary arithmetic on binary numbers 0 = 0,1 = 1,10 = 2,11 = 3, 110 = 6, 111 = 7,..., blocks of 8 bits a time (e.g., a byte), could also represent a machine code instruction such as add or jump to another part of the calculation. ... 

In order to develop methods for fuzzy logic deductions, Baldwin recast the methods of binary logic into a new form, i the statement A is true in binary logic is represented as a set on the space (C, i) then it has the element 0 with an indicator function of 0 and the element 1 with an Indicator function of 1. Using the notation previously used for fuzzy sets with v(A) denoting the truth of A then v(A) = true = Ttwe = 0 0, 111. 

This formulation of the problem illustrates a feature of modus tollens deduction. In order to understand this it is perhaps easiest to look at the truth table for implication in ordinary binary logic Table 2,1. U AD B and if B is true, then A may be true 01 false but if B is false then A is false. This means that the best information one can obtain concerning the truth of B can at best only leave you undecided about the truth of A. If the truth of B is somewhere between false and true, then A will be correspondingly somewhere between false and undecided. Thus in fuzzy logic, if the truth of B is between unrestricted and absolutely true, then we will still be undecided about the truth of A. If the truth... 

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