Fuzzy Reversible Logic using Toffoli-like gates

Slides:

Advertisements

Similar presentations

ADDER, HALF ADDER & FULL ADDER

Advertisements

Synthesis of Reversible Synchronous Counters Mozammel H A Khan Department of Computer Science and Engineering, East West University, 43 Mohakhali, Dhaka.

Documentation Standards

Chapter 2 Logic Circuits.

Diagram 1 shows a four wires (w1, w2, w3 & w4) logic circuit.

Fuzzy Reversible Logic using Toffoli-like gates. Building reversible fuzzy Toffoli gate We have to design such gate that knowing P,Q,R we will be able.

Designing Oracles for Grover Algorithm

A Transformation Based Algorithm for Reversible Logic Synthesis D. Michael Miller Dmitri Maslov Gerhard W. Dueck Design Automation Conference, 2003.

Binary Decision Diagrams1 BINARY DECISION DIAGRAMS.

Marek Perkowski Reversible Logic Synthesis with Garbage Bits Lecture 6.

Relationship Between Basic Operation of Boolean and Basic Logic Gate The basic construction of a logical circuit is gates Gate is an electronic circuit.

Derivatives of Perkowski’s Gate k f2 g h t t De Vos gates  f1f1  A B P Q Feynman gates A B P f 2f 2  C Q R Toffoli gates Q P f 2 A C R B S D 0.

A Transformation Based Algorithm for Ternary Reversible Logic Synthesis using Universally Controlled Ternary Gates Erik Curtis, Marek Perkowski.

Regular Structures. Levelized Structures Standard Lattice Diagrams for continuous, multiple-valued and binary logic.

 2001 CiesielskiBDD Tutorial1 Decision Diagrams Maciej Ciesielski Electrical & Computer Engineering University of Massachusetts, Amherst, USA

 2000 M. CiesielskiPTL Synthesis1 Synthesis for Pass Transistor Logic Maciej Ciesielski Dept. of Electrical & Computer Engineering University of Massachusetts,

Grover’s Algorithm in Machine Learning and Optimization Applications

Research Potential We should develop a set of unified standardized CAD tools for synthesizing, verifying, testing and simulating of quantum computers.

Part 2: DESIGN CIRCUIT. LOGIC CIRCUIT DESIGN x y z F F = x + y’z x y z F Truth Table Boolean Function.

Circuit, State Diagram, State Table

TODAY YOU ARE LEARNING to explain why data is represented in computer systems in binary form 2. to understand and produce simple logic diagrams.

ADDERS Half Adders Recall that the basic rules of binary addition are as indicated below in Table 2-9. A circuit known as the half-adder carries out these.

Computer Organization 1 Logic Gates and Adders. Propositions –Venn Diagrams.

Basic Logic Operations and Standard Logic Gates (Lecture #1) ECE 331 – Digital System Design.

Logic Gates. Outline  Logic Gates  The Inverter  The AND Gate  The OR Gate  The NAND Gate  The NOR Gate  The XOR Gate  The XNOR Gate  Drawing.

Sneha.  Gates Gates  Characteristics of gates Characteristics of gates  Basic Gates Basic Gates  AND Gate AND Gate  OR gate OR gate  NOT gate NOT.

1 Lecture 6 BOOLEAN ALGEBRA and GATES Building a 32 bit processor PH 3: B.1-B.5.

Logic Gates. The Inverter The inverter (NOT circuit) performs the operation called inversion or complementation. Standard logic symbols: 1 1 input output.

1 EG 32 Digital Electronics Thought for the day You learn from your mistakes..... So make as many as you can and you will eventually know everything.

CEC 220 Digital Circuit Design Timing Diagrams, MUXs, and Buffers Mon, Oct 5 CEC 220 Digital Circuit Design Slide 1 of 20.

Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.

Generating Toffoli Networks from ESOP Expressions Yasaman Sanaee Winter 2009 University of New Brunswick.

Logic Gates. AND gate Produces an output only if both inputs are on Input AInput BOutput (Q) Q=

Designing Combinational Logic Circuits

Functional Modeling.

COMBINATIONAL LOGIC.

CLASSICAL LOGIC SRFPGA layout With I/O pins.

How does a Computer Add ? Logic Gates within chips: AND Gate A B Output OR Gate A B Output A B A B

Controlled- Controlled NOTControlled- Controlled NOT = Toffoli Gate.

Logic Gates and Boolean Algebra Introduction to Logic II.

Programmable Logic Controller

BDD-based Synthesis of Reversible Logic for Large Functions Robert Wille Rolf Drechsler DAC’09 Presenter: Meng-yen Li.

Very good news for People who know Reed-Muller Logic 1.Quantum XOR 1.Quantum XOR is the most important gate in Quantum Logic 2.Synthesis of Quantum Circuits.

Hoda Roodaki Boolean Algebra Hoda Roodaki

FIGURE 3.1 Two-variable K-map

Eng. Mai Z. Alyazji October, 2016

Boolean Algebra.

Lecture 6 Topics Combinational Logic Circuits

ECE 331 – Digital System Design

Figure 12-13: Synchronous Binary Counter

Digital Logic Design 1st Exam Solution

Computer Architecture CST 250

Instructor: Alexander Stoytchev

Kerntopf Gate and Regular Structures for Symmetric Functions

ECE 667 Synthesis and Verification of Digital Systems

Instructor: Alexander Stoytchev

Boolean Algebra & Logic Circuits

Agenda – 2/12/18 Questions? Readings: CSI 4, P

Lecture 4 Topics Boolean Algebra Huntington’s Postulates Truth Tables

Reading: Hambley Ch. 7 through 7.5

ECE 171 Digital Circuits Chapter 6 Logic Circuits

Homework 2 This homework is the first use of quantum gates. In lectures we learned about the following gates: inverter, Feynman (controlled NOT), Toffoli.

Chapter 4 Gates and Circuits.

LOGIC Circuits.

Design of new quantum primitives

Circuit Simplification and

Presentation transcript:

Fuzzy Reversible Logic using Toffoli-like gates

Building reversible fuzzy Toffoli gate We have to design such gate that knowing P,Q,R we will be able to find unique values of A,B and C. If we know values of P and Q we can find uniquely the value of X. We need now to find a fuzzy operator that can find in an uniqe way C from X and R and that will make the whole gate reversible. Observe that this must be continuous operator, but similar in operation to modulo, XOR or Latin Square. * OP A B C P Q R X Assume arithmetic addition What should be the OP?

Solution to OP Several solutions to OP are discussed in R. Rovatti, G. Baccarani, “Fuzzy Reversible Logic”, Proc. 1998 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE'98) - + * 1 X1 N X2 N(X) Operations * , - and + are arithmetic X 1-X Generalized inverter N needs discontinuity

a a * + a 1 1 Now we can generate all fuzzy functions of a single variable

The same circuit for fuzzy reversible functions of two variables (c0 b+c1)a +(c2 b+c3) = c0 ba +c1 a +c2 b +c3 c0 b+c1 c0 a * + c2 b+c3 c2 a b * + * + b c0 c1 c2 c3 Realization of Positive Polarity Reed-Muller for functions of two variables The same circuit for fuzzy reversible functions of two variables

fuzzy reversible lattice for three variables * + c2 b+c3 c2 a b * + * + b c c0 c+c1 * + * + * + c c0 c1 c2 c3 c4 c5 Explanation of fuzzy reversible lattice for three variables * + c

Graphical method to calculate decision diagram from Toffoli gates * + A B f g X Y= C 1 C  C 00 01 11 10 0 1 AB C 0 1 1 0 1 1 f A’ X=f A’ f A f B’ f B’  f B Graphical method to calculate decision diagram from Toffoli gates

C 1 + C * + A B f g X Y= C 1 C  C  C f + B * + X Y= C A * + A

Realizations of binary logic with Toffoli and reversible logic with Toffoli-like circuits Kronecker functional Diagram Kronecker function-driven Diagram ESOP Kronecker Lattice Diagram PPRM-like forms other canonical Reversible Fuzzy Diagrams