Truth tables

Fig. 6.5 Schematic representations and truth tables for conventional AND and OR gates. Observe that both gates dissipate energy if the output of the AND gate equals 0 (or the output of the OR gate equals 1 ), there is no way of deducing the values of the respective inputs.

In order to construct an expression representing an arbitrary Boolean function J-, we must therefore j)erform two simple steps (1) construct expressions of the above form for each occurrence of a 1 in J- s truth table, and (2) join each such expression by the OR operator. Since each term is explicitly constructed so as to pick out a particular input configuration yielding the value 1 under J-, no more than one such term in the resulting OR expansion can yield the value 1 for a given input. All other configurations are identically zero. 

Fig. 6.7 Schematic representations and truth tables for the Fredkin gate and Reversible-AND gate. In the Fredkin gate, the c-line is the control line in the reversible-AND gate, lines gi and 92 are the garbage lines (see text).

Fig. 12.15 Schematic representations and truth tables for reversible primitives CONTROLLED NOT and CONTROLLED CONTROLLED NOT, used by Feynman in his construction of a reversible quantum computer [feyii85. ...

Hence, in order to specify the functionality of a grid of say N x N Sblocks with M-variable truth tables, each one requires N2 x 2M bits of information to... 

The truth tables of two Sblocks. (Haddow, P.C. and Tufte, G. [2001] Bridging the genotype-phenotype mapping for digital FPGAs. In proceedings of the Third NASA/DoDWorkshop on Evolvable Hardware, IEEE Computer Society.)... 

Fig. 22 (a) Model system able to perform six different logic functions depending on its structural parameters e and k. Current intensity passing through this system for e = k = 0 eV, v = 5 meV, and a and [1 going from 0 to 1 eV. The variation of the current respects the XOR truth table a strong current is obtained for = 0=1 and =1 = 0 and a weak one for = 0 = 0 and =1 = 1. Due to the stable plateaux at the comers of the map, this device naturally corrects small deviations in the inputs that lead to even smaller deviations in the output... 

Fig. 26 (a) The chemical structure of the molecular half-adder. The conformation of each N02 group encodes the logic input while the output status is encoded in the resistance between the drive and the output nano-electrodes. The complete truth table for the XOR and the AND outputs. Note the difference in magnitude between the XOR 1 and the AND 1 . (b) The T(E) spectra of the junction represented in Fig. 26 for all the logic inputs (solid line). Each inset emphasizes the modification of the conductance near the Fermi energy of the molecule. Each T(E) spectrum had been fitted in the active area to determine the minimum number of quantum levels required to reproduce it (dashed line)... 

Figure 22. Shown is the schematic outline of the four-terminal device in Figure 13 with its reduced logic profiles and subsequent truth table outputs where the electrostatic potential is varied through inputs V1in and V2,in. The central methylene is depicted as an electrical barrier. Monitoring of the electrostatic potential output is observed at Vout, and FI...

Keywords Luminescence m Fluorescence m Phosphorescence a Sensors a Switches a Logic Gates a Supramolecular Systems a Truth Tables a Photoinduced Electron Transfer a Molecular-Level Devices... 

Figure 2. (a) Electronic representation, (b) truth table, and (c) molecular implementation of YES (PASS) logic. 0 and 1 are digital representations of low and high signal levels respectively in all Figures. 

AND gate 4 differs from 3 in several aspects of performance and design. Experimentally, 4 produces a virtually perfect truth table The output logic 1 state has a fluorescence quantum yield (< >f) of 0.22 and the three logic 0 states do not rise above a cj>f value of 0.009. A fluorescence enhancement (FE) factor exceeding an order of magnitude such as this is a joy to work with since the switching phenomena are so clearly visible. 

Figure 5. (a) Electronic representation, (b) truth table and (c) molecular implementation of XOR logic. 

Logic gates are devices that can perform basic logic operations, depending on the nature of the input and output signals. The relation between the inputs and outputs is summarised in the truth table of the logic gate. 

For example, the AND logic gate has two inputs and one output. The truth table for the AND gate is shown in Table 12.4. 

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