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A Molecular Analog-to-Digital Converter
Stefan Angerbauer1, Franz Enzenhofer1, Michael Gattringer1, Andreas Springer1, and
Werner Haselmayr1
1Institute of Communications Engineering and RF Systems, Johannes Kepler University
Linz
June 07, 2024
1
A Molecular Analog-to-Digital Converter
Stefan Angerbauer, Franz Enzenhofer, Michael Gattringer, Andreas Springer, and
Werner Haselmayr
Johannes Kepler University Linz, Institute of Communications Engineering and RF Systems
Abstract—The Internet of Bio-Nano Things (IoBNT) is an
envisioned extension of the Internet of Things (IoT), which aims
to connect natural and synthetic biological systems and networks
to the Internet. Due to the access to new domains (e.g., human
body) this concept may help to enable transformative applications
in healthcare and nanomedicine. However, it also faces several
challenges, such as suitable interfaces and appropriate commu-
nication methods. Synthetic Molecular Communications (MC), a
molecule-based bio-compatible communication concept, is among
the most promising solution, which also defines the requirements
for the respective interfaces. Typically, MC systems require
a digital representation of the information to be transmitted
and, thus, the development of devices for the conversion of
analog biological signals to digital signals is crucial, but not well
investigated. Thus, in this paper we propose a novel Molecular
Analog-to-Digital converter (MADC). The MADC is based on
a new neural network representation of the electronic flash
ADC concept. This representation enables the implementation of
the MADC using the recently proposed Molecular Nano Neural
Networks (M3N). In particular, the proposed MADC consists of
two matrix multiplication layers that are connected via a ReLU
and threshold layer. We derive general design guidelines for the
MADC and successfully validate it through computer simulations.
Index Terms—Artificial Neural Networks, Flash Analog-to-
Digital Converter, Internet of Bio-Nano Things, Molecular Com-
munications
I. INTRODUCTION
Communications plays a vital role in modern society span-
ning various sectors of every day life: Social networks and
communication apps connect cultures and people around the
globe, smart devices and processes are enabled by the Internet
of Things (IoT) [1] and the value of virtual currencies is
validated by mutual agreement of multiple interconnected
computers distributed across the world [2]. In addition to
these established concepts, researchers explore different op-
portunities in medicine, agriculture and other life sciences.
In this context, the Internet of Bio-Nano Things (IoBNT),
an envisioned extension of the IoT to the bio-molecular
domain (e.g., the human body) provides a holistic approach
to accessing, controlling and coordinating the individual en-
tities (i.e., Bio-Nano-Things (BNTs)) of the network [3], [4].
This concept connects two entirely different domains: In the
classical communications domain, information is stored and
transmitted using electromagnetic (EM) signals. These signals
propagate with velocities close to the speed of light and hence
data-rates are extremely high and latencies are extremely low.
However, the ability of those signals to penetrate through the
human body and be received by BNTs is limited by physical
and biological constraints. On the other hand, the concept
of Molecular Communications (MC) was developed for in-
formation transmission in the biological domain. Molecular
signals can propagate well through biological tissue and re-
ception by BNTs is plausible. The downsides of this approach
are low data-rates and high propagation delay. The central
proposition of the IoBNT is the combination of EM-based
MC
IoT
Interface
Device
Downlink Uplink
BNT
BNT
Environment
Biological Domain
Cyber Domain
MC
MC
Interaction Interaction
Fig. 1: Overview of the communication in the IoBNT: Cyber
domain and biological domain are connected by an Interface
Device (ID) converting between electrical and molecular sig-
nals. In the biological domain, information is exchanged by
MC among BNTs and between BNTs and the IoT (via ID).
Based on the received information, the BNTs interact with
their environment and possibly report the results back to the
IoT (via ID).
communication and MC, to connect biological systems to the
IoT, harnessing the advantages of each approach. MC is the
enabling technology for communication over biological sys-
tems, while EM-based communication ensures the connection
to the IoT. The communication in the IoBNT is illustrated in
Fig. 1. The BNTs interact with the environment, based on the
information they receive from other BNTs and the IoT (via the
Interface Device (ID)). This interaction includes, for example
data collection, delivery of substances or phagocytosis. The
communication among BNTs and between BNTs and the IoT
(via ID) is realized by MC. Since biological entities typically
encode information in the continuous concentration of one or
multiple substances, but MC relies on a digital representation
of information, analog-to-digital conversion is required in
almost all communication links in the biological domain:
When the environment is sensed and signal processing within
the BNT is digital [5], an ADC is required. Furthermore,
if the BNT does its computations in an analog manner [6],
an analog-to-digital converter (ADC) is required to convert
the respective concentrations into a digital representation, that
−
+
R
K2
−
+
R
K3
−
+
R
K4
−
+
R
K5
−
+
R
K6
−
+
R
K7
1.5R
−
+
0.5R0.5R
K1
U0
Uin
Encoder
B3
B2
B1
Fig. 2: Schematic of an electronic 3-bit flash ADC.
can be modulated onto a molecular signal [7]. Since both
the input and output of such an ADC must be molecular,
we call it a Molecular ADC (MADC). Even though some
chemical digitalization concepts exist [8], [9], to the best of
our knowledge none of them realizes an actual N-bit analog-
to-digital conversion. Therefore, the objective of this work is
to close this gap and present the first concept of a MADC. The
contributions of this paper can be summarized as follows:
•We present a novel neural network representation of a
electronic flash ADC, based on a matrix multiplication
and threshold layer.
•The neural network representation enables the implemen-
tation of an ADC in the molecular domain, based on
the recently proposed Molecular Nano Neural Networks
(M3N) [6]; so-called Molecular ADC (MADC).
•The proposed MADC is validated by computer simulation
using the example of a 3-bit MADC.
II. ELECTRONIC FLAS H ADC
Fig. 2 shows a schematic of a electronic 3-bit flash
ADC [10], which works as follows: The resistors divide the
constant voltage U0into multiple voltage levels Ui, which can
be computed according to
Ui=i−0.5
MU0, i ∈ {1, . . . , M −1},(1)
with M= 2Nand Nis the bit width of the ADC. Each voltage
level Uiis the threshold of one comparator. In the first step,
the input voltage Uin to be converted into a digital form is
feed to the non-inverting input of each comparator. Hence,
the i-th comparator outputs Ki= 1, if the input voltage is
larger than the i-th threshold voltage Uiand Ki= 0 otherwise.
The signals Kiare already digital signals, but contain some
redundancy, i.e., 2N−1comparator signals encode a N-bit
number. In a second step, the encoder is used to remove
this redundancy and compress the information to Nbits. The
concept introduced in this paper is inspired by the electronic
flash ADC, but does all computations in a molecular way. This
requires various adaptions, which will be discussed in Sec. IV.
III. MOL EC UL AR NA NO NEURAL NE TWORKS (M3N)
In our previous work [6], we developed a reaction-diffusion-
based Neural Network (NN), so-called Molecular Nano Neural
A
Vin,1
A
Vin,2
A−−→ B
V1,1
A−−→ B
V1,2
A−−→ B
V2,1
A−−→ B
V2,2
B
V
B
V
A
B
A
Fig. 3: System architecture of a 2×2matrix multiplication.
Network (M3N). Similar to classical (artificial) NN, a M3N
consists of multiple layers, which are stacked to form a
network. Since the proposed MADC is based on stacking M3N
layers, we provide a brief summary in the following.
A. Matrix Multiplication Layer
For illustration purposes, the structure of a molecular matrix
multiplication layer1realizing a 2×2matrix multiplication
is shown in Fig. 3. Compartments (indicated by circles) are
connected by channels (indicated by lines). The compartments
have a certain volume Vand contain a certain concentration C
of a specific type of molecule (written in sans-serif). They are
named inlets, intermediates and outlets from top to bottom.
The indices for the volume and concentration identifies the
compartment, where ”in, k”and ”out, j”refers to the k-th
inlet and j-th outlet compartment, respectively, and ”k, j”
corresponds to an intermediate compartment connected to the
k-th inlet and j-th outlet. Moreover, for the concentration the
superscript indicates the molecule type and whether it refers
to the initial (”init”) or final (”fin”) concentration.
The working principle of the structure is as follows: At
the beginning of the calculation, the input vector Cin =
[CA,init
in,1, . . . , CA,init
in,I ]T, is encoded in the initial Amolecule
concentrations of the Iinlet compartments. Since the size of
the structure is assumed on the micro/nano-scale, diffusion
can be considered to be a fast process. Hence, the initial
concentration in one inlet is quickly spread among an inlet
and its connected intermediates. In the intermediates, a slow
reaction A+C+k1
−−→ B+or A+C−k1
−−→ B−, with reaction
rate k1, takes place. The molecules B+and B−realize positive
and negative matrix weights, which is implemented by initially
filling the intermediates with C+and C−molecules. Since
diffusion is assumed to be much faster than the reactions, the
concentration in an inlet and its connected intermediates is the
same, even in the case of an ongoing reaction. In this case,
the number of B∈ {B+,B−}molecules generated per unit
time in all intermediates connected to the same inlet differs
only by the volume of the individual compartments, i.e., a
larger compartment will produce a larger overall amount of
Bmolecules than smaller compartments. Hence, the ratio of
intermediate volumes can be used, to control the amount of
molecules propagating from an inlet to an outlet. It is impor-
tant to note, that all Bmolecules generated in the intermediates
1Please refer to [11] for a detailed discussion.
will eventually end up in the respective outlet and cannot
return from there (see Fig. 3). The final concentration in the
outlets is a linear combination of the inlet concentrations, with
weights determined by the intermediate volumes.2In each
outlet the reaction B++B−k2
−−→ ∗, with reaction rate k2,
takes place, where ∗indicates a molecule type that is not of
interest for the computation output. After this reaction has
finished, only the molecule type, that were in excess remain the
respective outlet. Hence, the final concentration of B+an B−
molecules refer to positive and negative numbers, respectively.
Based on the discussion above, the initial concentration of A
molecules in the inlets, Cin and the final concentration of B
molecule in the Joutlets Cout = [CB,fin
in,1, . . . , CB,fin
in,J ]Tcan be
written as [11]
Cout =MCin,(2)
where the entry in the k-th row and j-th column of matrix M
is given by
Mj,k =sk,j
Vin,k
V
Vk,j
PJ
j=1 Vk,j
.(3)
The sign of the respective compartment is denoted by sk,j
and the volume of the outlet compartments is chosen Vout,j =
V. Hence, the weights Mj,k of the matrix Mcan be chosen
arbitrarily by choosing the volumes and content (i.e., C+or
C−) of the structure appropriately.
B. Threshold Decision Layer
The second type of layer, that is needed to realize an MADC
is the threshold decision layer. The threshold decision layer
has as many compartments as the previous layer has outlet
compartments. Each threshold compartment is connected via
a channel to exactly one outlet compartment of the previous
layer and one inlet compartment of the next layer. The
molecule transfer between the compartments is controlled by
switchable membranes. The computation in each threshold
compartment starts, when the membrane connecting it to
the previous outlet becomes unidirectional permeable and,
thus, B+molecules of the previous outlet compartment are
transferred into the threshold compartment3. This process,
which is dominated by diffusion is again fast compared to
the reaction in the threshold compartment on the micro/nano-
scale. Hence, the initial concentration of B+molecules in
the threshold compartment at the beginning of the threshold
operation is CB+,init
th . The threshold compartment uses these
molecules as a catalyst in the reaction [12] (Schl¨
ogl model)
E+ 2 B+k4
−−→
←−−
k5
3B+,(4)
B+k6
−−→ D,(5)
where Eand Ddenote auxiliary molecules types and k4,k5
and k6are reaction rates. After the reaction is completed, the
second membrane, connecting the threshold compartment to
the next layer, opens and the B+molecules are transferred
to the inlet compartments of the next layer. It is important to
note that the reactions (4) and (5) take place in every threshold
2An amplification between inlet and outlet can be achieved, by making the
outlet smaller than the inlet. In this case, the same number of molecules will
yield a higher concentration.
3Please note, that only B+is assumed to be able to penetrate the membrane.
Hence, the membrane realizes a ReLU function [6].
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
CB+
th (t)
CB+
equ,2
CB+
equ,1
CB+
equ,2
CB+
equ,3
Fig. 4: Flow field of the Schl¨
ogl model.
compartment, but for the sake of readability, we only consider
one compartment for the following analysis. Assuming, that
molecules of type Eare available in large quantities (i.e., CE=
const.), we obtain a single differential equation describing the
reaction
dCB+
th (t)
dt=k4CECB+
th (t)2−k5CB+
th (t)3−k6CB
th
(t).(6)
This equation has three equilibrium points, which are obtained
by equating the left hand side of (6) with zero. The first
equilibrium point is CB+
equ,1= 0mol.
m3and the other two
equilibrium points are given by
CB+
equ,(2,3) =k4CE
2k5
±sk4CE
2k52
−k6
k5
.(7)
Assuming k6=2(k4CE)2
9k5and substituting it into (7), we obtain
CB+
equ,2=Chigh =2
3
k4CE
k5
,(8)
CB+
equ,3=CB+
equ,2
2=1
3
k4CE
k5
.(9)
The three equilibrium points are shown in Fig. 4(CB+
equ,1and
CB+
equ,2) and blue (CB+
equ,3). The arrows indicate the direction
of change of (6) in a given state. We notice, that the equi-
librium point CB+
equ,3is unstable and the system trajectory
tends towards CB+
equ,1for all initial state values smaller than
CB+
equ,3and towards CB+
equ,2for all initial state values larger than
CB+
equ,3. Hence, the proposed threshold compartment realizing
the reactions (4) and (5) implement a threshold decision with
a threshold concentration level CB+
equ,3. The concentration level
corresponding to a logical ’0’ and ’1’ corresponds to CB+
equ,1
and CB+
equ,2, respectively. The temporal evolution for different
initial states is depicted in Fig. 5, which shows, that the time
until the threshold detection is finished depends on the initial
state value. For values that are close to the threshold level
CB+
equ,3it takes longer to settle to CB+
equ,1(logic ’0’) or CB+
equ,2
(logic ’1’). It is important to note that the concentration level
needs to be settled, before the molecules can be transferred to
the next layer.
In summary, the behavior of the threshold decision layer
can be formulated as
CB+,fin
th =
0mol.
m3,if CB+,init
th < CB+
equ,3,
CB+
equ,2,else,
(10)
where CB+,init
th indicates the initial input concentration in the
threshold compartment and CB+,fin
th the output concentration
after the threshold operation. For a threshold decision layer
0 2 4 6 8 10 12 14 16 18 20 22 24
0
0.2
0.4
0.6
0.8
1
Time tin s
CB+
th (t)
CB+
equ,2
CB+
,init
th
CB+
equ,2
= 0.25
CB+
,init
th
CB+
equ,2
= 0.49
CB+
,init
th
CB+
equ,2
= 0.51
CB+
,init
th
CB+
equ,2
= 0.75
Fig. 5: Response of a chemical threshold unit with a symmetric
threshold (Schl¨
ogl model).
consisting of multiple threshold compartments this can be
written as
CB+,fin
th =h(CB+,init
th −CB+
equ,3U),(11)
with the elementwise Heaviside step function h(·)and Ua
vector of same size as input vector CB+,init filled with all
ones.
C. Stacking of Layers
The proposed MADC discussed in the next section con-
sists of stacking a matrix multiplication layer, a threshold
decision layer and another matrix multiplication layer. When
stacking multiple layers some additional aspects need to be
considered [6], which were only partly discussed in the
previous subsections. The first matrix multiplication layer
can operate in the way described in Sec. III-A. Each output
compartment of this layer is connected via a channel to
the exactly one compartment of the threshold decision layer.
This connection includes a membrane, that can be switched
externally and allows only B+to propagate unidirectional.
Then, the threshold operation discussed in Sec. III-B is applied
and after it has finished, the B+molecules in the threshold
compartment are transferred to the inlet compartments of the
second matrix multiplication layer. Thus, the second layer
receives B+molecules as input, but requires Amolecules.
Hence, the second layer requires additional chemicals, that
take the place of C+,C−,B+and B−molecules discussed in
Sec. III-A having a similar behavior.
IV. MOL EC UL AR ADC
In the following, we describe, how the flash ADC and M3N
concept are combined to obtain a molecular ADC. Similar to
the flash ADC discussed in Sec. II, two steps are required for
the conversion. In the first step, M−1comparator signals Ki
are generated through threshold decision and in the second
step, an encoder network compresses the comparator signals
to a N-bit number.
A. Step 1 – Comparator Signals
In the flash ADC, the input voltage Uin is compared to
M−1different threshold voltages to obtain the signals Ki.
In contrast, the MADC scales the input signal to M−1
different signals and compares it to the same threshold, which
is equivalent to the aforementioned approach. The reason
for this procedure can be seen from (9), which shows that
whenever the threshold concentration CB+
equ,3is changed, also
the concentration level for a logic ’1’, CB+
equ,2=Chigh,
changes. Thus, if the threshold decision layer introduced in
Sec. III-B is used to design M−1different comparators, each
comparator would have a different concentration level for the
logical ’1’. On the other hand, if we create M−1comparators
with the same threshold, they will also have the same level for
the logical ’1’. Hence, by scaling the input signal we obtain
M−1threshold decisions (comparator signals) with the same
levels for ’0’ and ’1, corresponding to the same behavior as
the electronic flash ADC.
Assuming, that concentration level of a logic ’1’ is Chigh, we
set the threshold concentration Cth of all threshold units to
Cth =Chigh
2.(12)
If we would implement the concept in a electronic way
(i.e., with M−1distinct thresholds) the output is ’1’, if
CA,init
store > Cref
iand ’0’ otherwise. Thereby, CA,init
store denotes
the concentration of A-molecules used to represent the input
to the ADC and Cref
ican be defined similar to (1)
Cref
i=i−0.5
MCmax, i ∈ {1, . . . , M −1},(13)
where Cmax denotes the highest possible input concentration
and has to be known in advance. Since for the MADC we
use the same threshold for all comparators, we demand that
CA,init
store Θi> Cth if CA,init
store > Cref
i, which holds if the scaling
factor Θiis given by
Θi=Cth
Cref
i
.(14)
Hence, the scaled input signal can be determined using a
molecular matrix multiplication, which can be expressed as
H=ΘCA,init
store ,(15)
with the scaling vector Θ= [Θ1,...,ΘM−1]T. Finally,
applying an elementwise threshold decision to the scaled input
signal Hresults in (cf. (11))
K=h(H−CthU),(16)
with the comparator signal vector K= [K1, . . . , KM−1]T.
B. Step 2 – Encoder Network
In the following, we discuss a molecular implementation of
the encoder network. It is important to note that the proposed
approach is specially designed for the compatibility with the
M3N concept and, thus, is different to common approaches
for the electronic flash ADC.
For the following discussion, we revisit the implementation
of a electronic flash ADC (cf. Sec. II). In particular, we
consider a 3-bit ADC and start with the most significant bit
B1and work our way towards the least significant bit B3.
Considering Fig. 6, the most significant bit is represented by
the comparator output K4(indicated in red). If the output of
this comparator is ’1’, the input voltage Uin is larger than
half the reference voltage U0and the encoder output must be
B1=K4. To decide on bit B2, we need three comparator
values, i.e., K2,K4and K6. The comparator signal K4has
already been used for B1, but is again needed for B2. There are
K1
K3
K4
K5
K7
K6
K2
B1 B2 B3
Analogue
Fig. 6: Conversion of an analog input signal Uin by a 3-bit flash
ADC. The decision for each bit Bndepends on the comparator
signals Ki.
four potential constellations of the three comparator signals,
i.e.,
B2=
0,for [K2, K4, K6] = [0,0,0],
1,for [K2, K4, K6] = [1,0,0],
0,for [K2, K4, K6] = [1,1,0],
1,for [K2, K4, K6] = [1,1,1].
(17)
We notice, that if the number of comparator signals that are
’0’ is even, B2must be ’1’ and if it is odd, B2must be ’0’.
This can be written as
B2=
3
X
i=1
(−1)(i+1)K2i.(18)
From the discussion above, we already notice a pattern that can
be used to determine the n-th bit. To determine Bn, we need
2n−1comparator signals. These signals alternate between
signals, that have never been used for the former bits and
signals, that have been used to determine previous bits. Let
ibe the largest index, for which the respective comparator
signal Kiis ’1’. If Kiwas already used for former bits, the
current bit Bnis ’0’, otherwise (i.e., Kiwas not used for
former bits), the current bit Bnis ’1’. Hence, the n-th bit can
be calculated as follows
Bn=
M−1
X
i=1
(−1)(i+1)KiM 2−n.(19)
Applying this relation to the least significant bit B3of the
3-bit flash ADC shown Fig. 6 results in
B3=
3
X
i=1
(−1)(i+1)Ki.(20)
It can be observed that if only K1is ’1’, we obtain B3= 1.
However, if also K2is ’1’ results in B3= 0, since the signals
K1and K2cancel each other out. Furthermore, if K3is ’1’,
we again obtain B3= 1. In summary, (19) ensures that always
one active (i.e., logic ’1’) used and unused comparator signal
cancel each other out. The relation in (19) can be written in
matrix-vector form as follows
B=TK (21)
Layer 1 Layer 2
Threshold
Fig. 7: Overall neural network structure for a 3-bit MADC.
with B= [B1, . . . , BN]Tand the N×M−1matrix Twith
the elements
Tn,i =
(−1) i
M2−n+1,if i%M2−n= 0,
0,else,
(22)
where %indicates the modulo operator. Hence, we have
shown that the encoder network can be realized by a matrix
multiplication of the matrix Twith comparator signal vector
K(see (16)).
Finally, we conclude that the electronic flash ADC can be im-
plemented using the M3N concept. First, the matrix multipli-
cation in (15) is applied, followed by a threshold decision (16)
and a final matrix multiplication (21). The overall relationship
between input concentration CA,init
store and bit vector Bcan be
expressed as
B=Th(ΘCA,init
store −CthI).(23)
A graphical representation of the overall neural network is
depicted in Fig. 7.
V. SIMULATION RESU LTS
In this section, we apply the proposed concept to design a
3-bit MADC. The simulation follows the procedure described
in [6] and [11]: The system of ordinary differential equations
(referred to as dynamical model) of each layer is simulated
until a steady state is reached. Then, the molecules in the
outlet/threshold compartment are instantaneously transferred
to the next layer and serve as initial condition for the sim-
ulation of the next system of differential equations. For the
design of the matrix multiplication unit, the naive algorithm
from [11] was used. This algorithm starts at the outlet volume
of the last layer and works its way towards the inlet com-
partment of the first layer. The reaction rates and diffusion
coefficient were taken from [6] and are D= 10−8m2s−1,
k1= 1 s−1,k2= 2.5×10−17 m3
s molecules ,k3= 1000 1
s,
k4CE= 1.5×10−21 m3
s molecules ,k5= 10−42 m6
smolecules2, and
k6= 0.51
s. Length and cross section area of the channels
are L= 0.1µmand S= 0.01 µm2, respectively. The scaling
vector Θcan be calculated using (14) and is given by
Θ= [8.0 2.667 1.6 1.143 0.889 0.727 0.615]TChigh
Cmax ,(24)
TABLE I: Compartment volumes for 3-bit MADC; superscript
in rectangular brackets denote the layer.
Parameter Value Parameter Value
V[1]
in,121.321 µm3V[2]
in,1/3/5/71µm3
V[1]
1,18µm3V[2]
in,2/62µm3
V[1]
1,25.333 µm3V[2]
in,43µm3
V[1]
1,31.6µm3V[2]
1...7,11µm3
V[1]
1,43.429 µm3V[2]
2/4/6,22µm3
V[1]
1,50.889 µm3V[2]
4,31µm3
V[1]
1,61.455 µm3V[2]
out,11µm3
V[1]
1,70.615 µm3Vtu,1/3/5/71µm3
V[1]
out,1/3/5/71µm3Vtu,2/62µm3
V[1]
out,2/62µm3Vtu,43µm3
V[1]
out,43µm3
where we chose Cmax =Chigh = 1021 mol.
m3. The matrix T
can be derived using (22) and reads as
T=
0001000
010−1 0 1 0
1−1 1 −1 1 −1 1
.(25)
The volumes of the inlet/intermediate/outlet compartments of
the two matrix multiplications layers are obtained using the
naive algorithm presented in [11] and are summarized in
Tab. I. Volumes belonging to matrix multiplication layers
are superscripted with the number of the respective layer in
square brakets. Threshold compartment volumes are indicated
by the index ”tu”. For the sake of compactness, if multiple
compartments have the same volume, we list them separated
by slashes (e.g., V[1]
out,1/3/5/7is the volume of the first, third,
fifth and seventh outlet compartment of the first layer).
The quantization curve of the 3-bit MADC is depicted in
Fig. 8. Each red circle corresponds to one simulation. The
value on the x-axis is the normalized input concentration and
the value on the y-axis is the digital to analog converted bit
vector B, which can be calculated as follows
ˆydec =Cmax
Chigh
3
X
n=1
23−n
23Bn.(26)
As a reference, the expected output of an ideal 3-bit ADC is
depicted as red line in Fig. 8 . The simulation matches the
expected characteristics almost perfectly, which validates the
proposed MADC concept. The small discrepancies (i.e., areas
where the quantization line does not go through the center of
the circles for the dynamic model) can be explained by the
finite simulation duration, since the required steady state is
only reached approximately. Although, the proposed MADC
can be straightforwardly extended to higher bit widths, the 3-
bit MADC is probably the most important application, since
it offers a good trade off between precision and structure size.
If higher precision is required, it is recommended to combine
multiple 1, 2 and 3-bit MADCs using a pipeline approach [10].
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
CA,init
store
Cmax
ˆydec
Cmax
Ideal quantization
Dynamic model
Fig. 8: Input-Output relation of the 3-bit MADC.
VI. CONCLUSIONS
We presented a molecular ADC (MADC) based on molec-
ular nano neural networks (M3N) using a neural network
representation of the electronic flash ADC. The proposed
MADC consists of two matrix multiplication layers linked by
a ReLU and threshold layer. It allows the precise conversion of
analog molecular signals to an N-bit parallel encoded digital
number, which was successfully validated for a 3-bit MADC.
Future works will include the realization of the pipeline ADC
concept to obtain a more fine-grained quantization.
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