# Digital Logic and Signal

### Presentations text content in Digital Logic and Signal

Digital Logic and Signal Processing Computations with Molecular Reactions

Hua

Jiang

PhD Candidate, Electrical Engineering

University

of Minnesota Advisors Professor Keshab Parhi and Professor Marc Riedel

Slide2Synthetic Biology

“design and construction of new biological functions and systems not found in nature”

Slide3Chemically, molecular quantities, or concentrations, represent the digital signal.

Sequential Computation

A digital signal is a sequence of numbers.

Electronically, numbers are represented by binary strings (zeros and ones are voltages).

A sequential system takes an input sequence and produces an output sequence.

10, 2, 12, 8, 4, 8, 10, 2, …

5, 6, 7, 10, 6, 6, 9, 6, …

1010

0101

0010

1100

0110

0111

input

output

Computation

Electronics

Molecular

Reactions

Slide4Analysis: From Chemical Reactions to Differential Equations

Slide5Synthesis: From Input/Output Specification to Chemical Reactions?

input

output

Low Pass Filtering?

Chemical

Reactions?

Rates?

Slide6Motivation

Performing

sequential computations

Digital signal

processing

Sequential digital logic

Robustness

Rate-independent

Physically implementable

DNA strand displacement

Slide7Overview

Self-timed

implementation of digital signal processing systems

Synchronous

implementation of digital signal processing systems

Implementing sequential digital logic based on a

bi-stable

bit

representation

Discussion and future

w

ork

Slide8Overview

Self-timed

implementation of digital signal processing systems

Synchronous implementation of digital signal processing systems

Implementing sequential digital logic based on a bi-stable bit representation

Discussion and future work

Slide9…

…

DSP with Reactions

Reactions

Time-varying changes in concentrations of an input molecular type.

Time-varying changes in concentrations of output molecular type.

10, 2, 12, 8, 4, 8, 10, 2, …

5, 6, 7, 10, 6, 6, 9, 6, …

Input

Output

Slide10Molecular

Reactions

time

time

But how do we

achieve the synchronization?

Moving Average Filter:

Molecular

Slide11Constant Multiplier

Fanout

Delay Element

DSP Building

Blocks

Adder

Most DSP systems can be specified in terms of

4 major components:

constant

multipliers,

fanouts

, adders

and

delay elements

.

Slide12Constant Multiplier

Computational Modules

X

Y

Slide13Computational Modules

Adder

Slide14Fanout

Computational Modules

X

B

A

Slide15Delay Element

Molecular quantities are preserved over “computational cycles.” Contents of different delay elements are transferred synchronously.

Slide163-Phase Scheme

We use a three compartment configuration for delay elements: we categorize the types into three groups: red, green and blue.

Every delay element D

i is assigned Ri, Gi, and Bi

Slide17R

r

Absence Indicators

But how do we know that agroup of molecules is absent?

Slide18Moving Average Filter

absence

indicators

Slide19RGB Scheme

R

,

G, and B converge!

Slide20RGB Scheme

Oscillating!

Slide21Moving Average Filter

Signal transfer

Computation

Absence indicator

Slide22Simulation

Molecular

Reactions

DSD

Mapper

DSD

R

eactions

System

ODE

ODE

Solver

Transient

Response

Slide23Simulation Results:

Moving Average

Slide24General DSP System

Slide25Biquad Filter

Slide26Biquad Filter

Absence indicator

Signal transfer

Computation

Slide27Simulation Results:

Biquad

Slide28Overview

Self-timed implementation of digital signal processing systems

Synchronous

implementation of digital signal processing systems

Implementing sequential digital logic based on a bi-stable bit representation

Discussion and future work

Slide29Synchronous Sequential Computation

Slide30Implementing Clock

Slide31Implementing Memory

Blue phase:

Red phase:

D

1

’

D1

D2’

D2

Slide32Examples

FIR filter

Slide33Examples

IIR filter

Slide34Examples

4-point FFT

Slide35Examples

Slide36Examples

4-point FFT

Slide37Overview

Self-timed implementation of digital signal processing systems

Synchronous implementation of digital signal processing systems

Implementing sequential digital logic based on a

bi-stable

bit representation

Discussion and future work

Slide38Bit Representation

Slide39AND Gate

Outputting 0

Outputting 1

Slide40OR Gate

Outputting1

Outputting 0

Slide41XOR Gate

Outputting 1

Outputting 0

Slide42Logic Gates

Slide43Implementing D Latch

Traditional method

Slide44Implementing D Latch

Recall the bit representation…

It’s a latch!

Slide45Implementing D Latch

Adding control reactions

Slide46Implementing D Flip Flop

Master-slave configuration

Slide47Example: 3-Bit Counter

Slide48Example: Linear Feedback Shift Register

Slide49Overview

Self-timed implementation of digital signal processing systems

Synchronous implementation of digital signal processing systems

Implementing sequential digital logic based on a bi-stable bit representation

Discussion and future work

Slide50Discussion

Synthesize a design for a precise, robust, programmable computation – with abstract types and reactions.

Computational Chemical Design

vis-a-vis

Technology-Independent

Logic Synthesis

Implement design by selecting specific types and reactions – say from “toolkit”.

Experimental Design

vis-a-vis

Technology Mapping

in Circuit Design

Slide51DNA Strand Displacement

X

1

X

2

X

3

+

D.

Soloveichik

et al

:

“

DNA as a Universal Substrate for Chemical Kinetics

.” PNAS, Mar 2010

Slide52DNA Strand Displacement

X

1

X

3

X2

+

D.

Soloveichik

et al

:

“

DNA as a Universal Substrate for Chemical Kinetics

.” PNAS, Mar 2010

Slide53Moving Average Filter: DNA Level Reactions

Slide54Future Work

System

optimization

Impact of specific DSP constructs

DSD level design

Computer-aided design

Molecular level

DSD level

System

Implementation

With DSD

Slide55Intel® Xeon® Processor, 2010

1.9 billion transistors3 GHz

Intel® 4004 Processor, 19712300 transistors740 kHz

DSP with chemical

reactions, 2012

?

Slide56Thank you!

(Advisors,

Committee, Fellow

Students, Funders, Audience…)

Slide57Slide58

Slide59

Slide60

Slide61

Slide62

Slide63

Slide64

Slide65

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Slide67

## Digital Logic and Signal

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