Page 6 - Surface-Confined Assemblies and Polymers for Molecular Logic

Surface-Confined Assemblies and Polymers de Ruiter and van der Boom

TABLE 4. Truth Table for the Combinatorial Logic Operations of the
Os-Based Monolayer Operating with Three Chemical Inputs and Two
Different Starting States: Output A and Output B 32
chemical inputs
entry Cr 6þ Co 2þ Ir 3þ output A a output B b
1 0 0 0 1 0
2 0 0 1 0 0
3 0 1 0 1 1
4 0 1 1 1 1
5 1 0 0 0 0
6 1 0 1 0 0
7 1 1 0 1 1
8 1 1 1 1 1
b
a Output A: output generated with Os 2þ as the starting state. Output B: output
generated with Os 3þ as the starting state. FIGURE 9. Relative memory increase, compared to binary memory, by
increasing the radix (N). Adapted with permission from ref 40. Copyright
2010 American Chemical Society.

technology, as the first reliable devices were bistable. Ac-
cording to Keyes, only current binary transistor technology is
feasible for computing, since transistors exhibit a large gain,
can separate inputs from outputs, and act as amplifiers,
so errors are nonaccumulative. 33 Moreover, they are self-
correcting since the input potential range is much larger than
their output range, which eliminates undesirable noise le-
vels and small variances introduced by device fabrication. 10
FIGURE 8. (A) Combinatorial circuit operating with three chemical inputs What is the advantage of using a different base? Informa-
2þ
(Table 3) with a static current state (1, Os ). (B) Sequential circuit generated
tion processing occurs with a certain information density
with a dynamic current state (Os 2þ or Os ). Adapted with permission from
3þ
that is determined by the base (or radix). If the information
ref 32. Copyright 2010 Wiley-VCH Verlag GmbH & Co. KgaA.
density is low, or the information is processed inefficiently,
combinatorial logic circuit shown in Figure 8A. However, if
one needs simply more space to achieve a certain computa-
Os 3þ (logic 0) is used as the starting state, a YES gate is
tional level. In this regard, a higher-valued radix is beneficial
generated with respect to input-two (Co 2þ ). Therefore, a logic
as it raises the information density per single logic operation.
circuit and a gate can be mimicked with the same system, by
The most efficient radix for information processing is Euler's
changing the oxidation state of the system at the beginning 34
number 2.718. Since integer numbers are used, ternary
of each entry. By doing so, all the possible combinations of
(base-3) is the most efficient. The number of digits required
inputs and previous states (whether the starting state is Os 2þ /
to represent any given number is ∼1.6 less in ternary than
Os 3þ ) were tested, which are required for sequential logic.
in binary, resulting in a significant increase in memory
Interestingly, for the input string 0 0 0, the output is depen- d
capacity. Changing from binary memory 2 to multistate
dent whether the starting (previous) state was Os 2þ or Os 3þ . d d
memory N leads to an exponential increase of (N/2) , where
This reveals the sequential logic element that is present in
N is the radix and d is the amount of digits (Figure 9).
this system, and the corresponding sequential logic circuit is
Within the framework of molecular logic, multivalued
depicted in Figure 8B. This circuit operates according to the
logic and data storage with molecule-based systems are
combination of outputs A and B generated by the combina-
relatively rare. In 2006, de Silva et al. utilized the principles
torial logic circuit and the YES gate. Although this is fundamen-
of multivalued digits for molecular computational identifica-
tally one sequential logic circuit, it consists of two individually 35
tion (MCID). Combinations of dyes attached to polymer
addressable combinatorial logic scenarios. 32
beads respond to different chemical environments, enabling
multiple fluorescent states, that, when combined, operate
V. Multistate Logic and Memory similarly to radio frequency identification (RFID). Ternary
The above molecular logic gates and circuits are exclusively logic gates were reported by Remacle and Levine who
binary in nature. Base-2 has historically been used in silicon showed that three coupled quantum dots can be used to
568 ’ ACCOUNTS OF CHEMICAL RESEARCH ’ 563–573 ’ 2011 ’ Vol. 44, No. 8