IEEE Circuits and Systems Magazine - Q1 2021 - 28

on the outputs but are orders of magnitude faster than
the alternatives for invertible operations. This observation also demonstrates the ability to design circuits capable of invertible operations for more complex behaviors.
E. DNA-Based Computing
The DNA found in living cells is composed of four bases:
Adenine (A), Cytosine (C), Guanine (G), and Thymine
(T). Each base is attached to its neighbor base in the
sequence via phosphate bonding. Two DNA sequences
bond with each other between complementary base
pairs (A-T and C-G), forming the DNA double helix. During the formation of a DNA double strand, two complementary single strands bond with each other in antiparallel fashion.
The first proposals for representing binary numbers with DNA and performing arithmetic operators
emerged in the nineties [108]. However, the first addition algorithms provide output in a different form than
the input, thus preventing the iterative application of
operations to implement arithmetic systems. Moreover,
earlier DNA computing models do not support addresses and operations on single strands, thus not allowing
arithmetic operations to be performed through parallel
processing [109].
More recently, models such as the Sticker-based DNA
model have been proposed [110]. The sticker-based DNA
model is used to represent fixed-point and floating-point
numbers, overcoming the limitations of the previous
models and allowing iterative and parallel processing to
be carried out [111]. With the DNA sticker, a binary number is represented through two groups of single-stranded DNA molecules: i) the memory strand, a long DNA
molecule that is subdivided into nonoverlapping segments and ii) a set of stickers, i.e., short DNA molecules,
each with the length of a segment of the memory strand.

Bit i

Bit i + 1

G T C A

C A T T

Bit i + 2

G G C C

Each one of the nonoverlapping segments represents a
bit, and a sticker is complementary to one and only one
of the nonoverlapping segments. As depicted in Fig. 19 a
segment on the memory strand annealed to the matching sticker represents a " 1 " ; otherwise, the value of the
bit is " 0 " .
Test tubes contain sets of strands representing binary numbers, either the operands or the results of
arithmetic operations. The functional formulation of the
operations on the Sticker-based DNA model allows the
setup of algorithms for performing DNA-based computing [111]. Three main operations are essentially considered to implement logic and arithmetic operations: Combine, Separate and Set.
■ Combine ^ Td, Ts1, f, Tsn h - pour the contents of
tubes Tsi into Td and then empty Tsi; formally, using the set theory, Td / ' i Tsi ; Tsi / 4.
■ Separate ^ Ts, i, B [1], B [0] h - Separate the contents of
Ts based on the value of the ith bit: the DNA strands
with an ith bit equal to " 1 " are inserted into tube
B [1] , while the other DNA strands, into tube B [0] .
■ Set ^ Tsd, i h - Set the ith bit of all DNA strands in tube
Tsd, which serve as the source and destination in
this operation.
Several logic and arithmetic operations on the
Sticker-based DNA model have been proposed [111];
the bitwise AND operation over two n bit vectors is
presented in Algorithm 1, and the n-bit integer ADD, in
Algorithm 2. In Algorithm 1, the output of the AND operation over the operands represented by the strands
in source tubes Ts1 and Ts2 is made available in the
destination tube Td . After pouring the contents of
tubes Ts1 and Ts2 into the auxiliary tube Ta (line 1),
the strands in this tube are separated according to the
value of the bits in each of the n positions in tubes
B [1] and B [0] (line 3); whenever the value of the ith bit

Bit i + 3

G T C T

G T A A

Memory
Strands
C A G T

G T C A
1

C A G T

C C G G

C A T T
0

G G C C
1

G T C T
0

C C G T

Stickers

Figure 19. Memory strands, stickers and DNA-based number representation.
28

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