Half-adder

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)... 

In order to reveal the mechanism of this molecular half-adder, the T(E) spectra of the molecule are presented in Fig. 26b. When perpendicular to the plane of the molecule, each NO2 contributes a very sharp resonance which does not participate in the overall conductance. When rotated by 90°, an NO2 introduces a supplementary resonance in the gap of the molecule. Due to its asymmetrical delocalization over the atomic orbitals, this resonance increase the conduction between the drive and the XOR electrode, but not between the drive and the AND electrode. This insures a 1 output for the former and a 0 for the latter. When the two NO2S are rotated, the two resonances they introduce create a deep interference between the drive and the XOR electrode. Located on the Fermi energy of the molecule, this interference leads to a low conductance state and a 0 logical output for the XOR gate. In contrast, the two resonances do not interfere destructively between the drive and the AND electrode, leading to a high conductance state and a 1 logical output. 

Fig. 27 (a) Optimized graphene sheet for the realization of a half-adder. Each logical input noted a and [i controls the photoisomerization state of one of the two stilbene groups. Depending on this isomerization state, the overall conductance of the molecule between the three electrodes is modified, (b) Current intensity calculated in the two output electrodes depending on the conformation of the stilbene groups... 

Pei-li L, De-xui H, Xin-Liang Z, Guang-xi Z (2006) Ultrahigh-speed all-optical half adder on four-wave mixing in semiconductor optical amplifier. Opt Express 14 11840... 

Duchemin I, Renaud N, Joachim C (2005) A quantum digital half-adder inside a single molecule. Chem Phys Lett 406 167... 

A valuable analysis from Credi [205], from Balzani s Bologna laboratory shows how ideas underlying the XOR gate system 106.107 can be combined with EET-based AND-type systems [209] to give a half-adder capable of arithmetic functions. The practical realization of this analysis would be most welcome. 

XOR is a particularly interesting type of double-input logic, for two reasons. Firstly, it achieves a high output only if the two inputs are digitally different i.e., 1 and 0, or 0 and 1 (Figure 11). Secondly, it is a vital half of the half-adder, from which arithmetic is performed in current computers and calculators. The other vital half is the AND operation, which has a longer history of emulation at the molecular scale (Section 11.4). So the achievement of molecular XOR logic is likely to cause a domino effect in the movement towards molecular scale arithmetic. 

Fig. 11. A full adder for the addition of multi-digit numbers. The three inputs are II and 12 -the digits to be added - and Cl - the carry digit from the previous pair of inputs. Through a combination of two half adders and a further XOR gate, connected in both series and in parallel, the sum and carry outputs of the addition are produced...

Figure 60 A photo-driven molecular shuttle acts as a half adder. ...

Although many relatively complex logic systems are now available, we wiU only consider one arithmetic processor—the half-adder—in this review. Many interesting molecular-scale arithmetic systems have come to light in recent years. Since nnknown molecular processes in the brain have allowed hnmans to be numerate, it was important to demonstrate nnmeracy with synthetic molecules. The simplest semiconductor-based arithmetic device is the half-adder, which has two inputs and two ouqrut channels. 

Figure 8 Graphical description of a network with maximal molecnlar information. An XOR gate in T3 is formed and the network simnltaneonsly produces an INHIBIT in T1 and an AND in T2, allowing the construction of a half adder and a half subtracter.

Name AND OR NOR NAND INHIBIT XOR XNOR Half-adder Half-subtractor ... 

The first expression of molecular numeracy was special because people become (and remain) numerate via mysterious, but molecular, processes in their brains. An electronic half-adder circuit has two inputs and two output channels which is the basis of number processing in most electronic computers. Addition needs an AND logic gate for the carry digit and an XOR logic gate for the sum digit (Fig. 2) [ 129,130]. 

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