Multiple-Valued Computing in Quantum Molecular Biology: Arithmetic and Combinational Circuits, Volume 1

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Author
Preface
Acknowledgments
Acronyms
Introduction
I. Multiple-Valued Quantum and DNA Computing
Overview
1. Multiple-Valued Quantum Computing
1.1. Introduction
1.2. Quantum Physics and Quantum Computing
1.2.1. Applications of Quantum Physics
1.3. What is Quantum Computing?
1.3.1. Quantum Computing Properties
1.3.2. How Does Quantum Computer Work?
1.4. Multiple-Valued Logic
1.4.1. History of Multiple-Valued Logic
1.4.2. Advantages of Multiple-Valued Quantum Computing over Binary Logic
1.5. Ternary Logic in Quantum Computing
1.5.1. Quantum Ternary Fundamental Logic Operations
1.6. Applications of Multiple-Valued Quantum Computing
1.7. Demerits of Multiple-Valued Quantum Computing
1.7.1. Challenges in Multiple-Valued Quantum Computing
1.8. Summary
Bibliography
2. Multiple-Valued DNA Computing
2.1. Introduction
2.2. What is DNA Computing?
2.2.1. History of DNA Computing
2.3. Some Related Terminologies
2.3.1. Molecular Biology
2.3.2. DNase Enzyme
2.3.3. Fluorescence Detection
2.4. How Does a DNA Computing Work?
2.4.1. DNA Computing for Binary Logic System
2.5. Multiple-Valued DNA Computing
2.5.1. How Can Multiple-Valued Operations Be Performed in DNA Computing?
2.6. Advantages of Multiple-Valued DNA Computing
2.7. Limitations of Multiple-Valued DNA Computing
2.8. Applications of Multiple-Valued DNA Computing
2.9. Challenges in Multiple-Valued DNA Computing
2.10. Motivations toward Multiple-Valued DNA Computing
2.11. Summary
Bibliography
3. Multiple-Valued Quantum-DNA Computing
3.1. Introduction
3.2. Quantum Mechanics and Quantum Molecular Biology
3.2.1. Why Quantum Molecular Biology Is an Important Field?
3.3. Relationship between Multi-Valued and Two-Valued Quantum and DNA Computing
3.3.1. Multiple-Valued Quantum-DNA Computing: A New Computing Approach
3.3.2. Data Conversion Circuits to Convert Qutrits to DNA Base Sequences
3.3.3. Intermediatory System to Control Quantum-DNA Data Flow
3.3.4. Heat Transfer Circuit
3.4. Advantages of Multiple-Valued Quantum-DNA Computing
3.5. Disadvantages of Multiple-Valued Quantum-DNA Computing
3.6. Summary
Bibliography
4. Multiple-Valued DNA-Quantum Computing
4.1. Introduction
4.2. Relationship between Multi-Valued DNA Computing and Multi-Valued Quantum Computing with Two-Valued DNA Computing and Quantum Computing
4.3. Multiple-Valued DNA-Quantum Computing
4.3.1. General Organization of Multiple-Valued DNA-Quantum Computing
4.4. Difference between Multiple-Valued Quantum-DNA and DNA-Quantum Computing
4.5. Advantages of Multiple-Valued DNA-Quantum Computing
4.6. Summary
Bibliography
II. Heat Measurement, Heat Transfer, Speed Calculation, Data Conversion, and Data Management in Multiple-Valued Quantum and DNA Computing
Overview
5. Heat Calculation
5.1. Introduction
5.2. Basic Definitions for Heat Calculation in Quantum Circuit
5.3. Heat Calculation in Multiple-Valued Quantum Circuit
5.3.1. Quantum Multi-Valued Half Adder
5.3.2. Quantum Multi-Valued Half Subtractor
5.3.3. Quantum Multi-Valued 3-to-1 Multiplexer
5.4. Basic Definitions for Heat Calculation in DNA Circuit
5.5. Heat Calculation in Multi-Valued DNA Circuit
5.5.1. DNA Multi-Valued Decoder
5.5.2. DNA Multi-Valued 3-to-1 Multiplexer
5.6. Heat Calculation in Multi-Valued Quantum-DNA Circuit
5.6.1. Multi-Valued Quantum-DNA Half Adder
5.7. Heat Calculation in Multi-Valued DNA-Quantum Circuit
5.7.1. Multi-Valued DNA-Quantum Half Subtractor
5.8. Summary
Bibliography
6. Speed Calculation
6.1. Introduction
6.2. Speed Calculation for a Quantum Operation
6.3. Speed Calculation in Multi-Valued Quantum Circuit
6.3.1. Quantum Multi-Valued 3-to-1 Multiplexer
6.3.2. Quantum Multi-Valued Half Adder
6.3.3. Quantum Multi-Valued Half Subtractor
6.4. Speed Calculation for DNA Operation
6.5. Speed Calculation in Multi-Valued DNA Circuit
6.5.1. DNA Multi-Valued Decoder
6.5.2. DNA Multi-Valued 3-to-1 Multiplexer
6.6. Speed Calculation in Multi-Valued Quantum-DNA Circuit
6.6.1. Multi-Valued Half Adder at 0-Kelvin
6.6.2. Multi-Valued Half Subtractor at 0-Kelvin
6.6.3. Multi-Valued Multiplexer at 0-Kelvin
6.7. Speed Calculation in Multi-Valued DNA-Quantum Circuit
6.7.1. Multi-Valued Half Subtractor at room temperature
6.8. Summary
Bibliography
7. Heat Transfer
7.1. Introduction
7.2. Heat Transfer in Multiple-Valued Quantum-DNA Circuits
7.2.1. Heat Transfer in Multi-Valued Quantum-DNA Full Subtractor (Difference)
7.2.2. Heat Transfer in Multi-Valued Quantum-DNA Half Adder
7.3. Summary
Bibliography
8. Data Conversion
8.1. Introduction
8.2. Data Conversion in Multiple-Valued Quantum-DNA Circuits
8.2.1. NMR Relaxation at Room Temperature
8.3. Data Conversion in Multiple-Valued DNA-Quantum Circuits
8.3.1. Quadrupole Ion Trap
8.4. Summary
Bibliography
9. Data Management
9.1. Introduction
9.2. Data Management in Quantum-DNA Circuits
9.2.1. Construction of an Intermediary System to Control Quantum-DNA Data Flow
9.2.2. Multiple-Valued Quantum-DNA Half Adder
9.3. Data Management in DNA-Quantum Circuits
9.3.1. Construction of an Intermediary System to Control DNA-Quantum Data Flow
9.4. Summary
Bibliography
III. Multiple-Valued Arithmetic Circuits in Quantum Molecular Biology
Overview
10. Multiple-Valued Logic Operations in Quantum Computing
10.1. Introduction
10.2. Quantum Ternary Logic
10.2.1. Why Ternary Logic in Quantum Computing?
10.3. Quantum Fundamental Gates in Multi-Valued Logic
10.3.1. Quantum Ternary Shift Gates
10.3.2. Quantum Ternary C2 NOT Gate
10.4. Quantum Multi-Valued Basic Logic Operations
10.4.1. Ternary Quantum-AND Operation
10.4.2. Ternary Quantum-NAND Operation
10.4.3. Ternary Quantum-OR Operation
10.4.4. Ternary Quantum-NOR Operation
10.4.5. Ternary Quantum XOR Operation
10.4.6. Ternary Quantum XNOR Operation
10.5. Summary
Bibliography
11. Multiple-Valued Quantum Arithmetic Operations
11.1. Introduction
11.2. Multiple-Valued Quantum Half-Adder
11.2.1. The Architecture of Quantum Ternary Half-Adder Operation
11.2.2. Working Principles of Quantum Ternary Half-Adder Operation
11.3. Multiple-Valued Quantum Full-Adder
11.3.1. The Circuit Architecture of Quantum Ternary Full-Adder Operation
11.3.2. Working Principles of Quantum Ternary Full-Adder Operation
11.4. Multiple-Valued Quantum Half-Subtractor
11.4.1. The Circuit Architecture of Quantum Ternary Half-Subtractor Operation
11.4.2. Working Principles of Quantum Ternary Half-Subtractor Operation
11.5. Multiple-Valued Quantum Full-Subtractor Operation
11.5.1. The Circuit Architecture of Quantum Ternary Full-Subtractor Operation
11.5.2. Working Principles of Quantum Ternary Full-Subtractor Operation
11.6. Multiple-Valued Quantum Parallel Adder
11.6.1. General Organizations of Multiple-Valued Quantum Parallel Adder
11.6.2. Circuit Architecture of Quantum Multiple-Valued Parallel Adder
11.6.3. The Working Principles of Quantum Multiple-Valued Parallel Adder
11.7. Multiple-Valued Quantum Carry-Lookahead Adder
11.7.1. General Organizations of Quantum Ternary Carry-Lookahead Adder
11.7.2. The Architecture of Quantum Ternary Carry-Lookahead Adder
11.7.3. The Working Principles of Quantum Ternary Carry-Lookahead Adder
11.8. Multiple-Valued Quantum Carry-Skip Adder
11.8.1. How Does Quantum Ternary Carry-Skip Adder Work?
11.8.2. The General Architecture of Quantum Ternary Carry-Skip Adder
11.8.3. The Working Principles of Quantum Ternary Carry-Skip Adder
11.9. Multiple-Valued Quantum Multiplier
11.9.1. How Does the Quantum Ternary Multiplier Work?
11.9.2. The Architecture of the Quantum Ternary 2 x 2 Multiplier
11.9.3. The Working Procedure of the Quantum Ternary 2 x 2 Multiplier
11.10. Multiple-Valued Quantum Divider
11.10.1. How Does the Quantum Ternary Divider Work?
11.10.2. Circuit Architecture of the Quantum Ternary Divider
11.10.3. The Working Procedures of the Quantum Ternary Divider
11.11. Multiple-Valued Quantum Comparator
11.11.1. Circuit Architecture of Multiple-Valued Quantum Comparator
11.11.2. Working Principle Multiple-Valued Quantum Comparator
11.12. Summary
Bibliography
12. Multiple-Valued Logic Operations in DNA Computing
12.1. Introduction
12.2. How Can Multiple-Valued Operations be Performed in DNA Computing?
12.3. Performing Fundamental Operations in Ternary Logic in DNA Computing
12.3.1. Ternary DNA-NOT Operation
12.3.2. Ternary DNA-AND Operation
12.3.3. Ternary DNA NAND Operation
12.3.4. Ternary DNA-OR Operation
12.3.5. Ternary DNA-NOR Operation
12.3.6. Ternary DNA-XOR Operation
12.3.7. Ternary DNA XNOR Operation
12.4. Summary
Bibliography
13. Multiple-Valued Arithmetic Operations in DNA Computing
13.1. Introduction
13.2. Multi-Valued DNA Half-Adder
13.2.1. The Circuit Architecture of DNA Ternary Half-Adder Operation
13.2.2. Working Principles of Quantum Ternary Half-Adder Operation
13.3. Multi-Valued DNA Full-Adder
13.3.1. The Architecture of DNA Ternary Full-Adder Operation
13.3.2. Working Principles of Quantum Ternary Full-Adder Operation
13.4. Ternary DNA Half-Subtractor Operation
13.4.1. Circuit Architecture of DNA Ternary Half-Subtractor Operation
13.4.2. Working Principles of DNA Ternary Half-Subtractor Operation
13.5. Multiple-Valued DNA Full Subtractor
13.5.1. Circuit Architecture of Multiple-Valued DNA Full Subtractor
13.5.2. Working Principle of Multiple-Valued DNA Full Subtractor
13.6. Multiple-Valued DNA Parallel Adder
13.6.1. General Organizations of DNA Multiple-Valued Parallel Adder
13.6.2. The Architecture of DNA Multiple-valued Parallel Adder
13.6.3. The Working Principles of DNA Multiple-Valued Parallel Adder
13.7. Multiple-Valued DNA Carry-Lookahead Adder
13.7.1. General Organizations of DNA Ternary Carry-Lookahead Adder
13.7.2. The Circuit Architecture of DNA Ternary Carry-Lookahead Adder
13.7.3. The Working Principles of Quantum Ternary Carry-Lookahead Adder
13.8. Multi-Valued DNA Carry-Skip Adder
13.8.1. The General Architecture of DNA Ternary Carry-Skip Adder
13.8.2. The Working Principles of DNA Ternary Carry-Skip Adder
13.9. Multi-Valued DNA Ternary Multiplier
13.9.1. How Does The DNA Ternary Multiplier Work?
13.9.2. The Architecture of the DNA Ternary 2 x 2 Multiplier
13.9.3. The Working Procedure of the Quantum Ternary 2 x 2 Multiplier
13.10. Multi-Valued DNA Divider
13.10.1. The Construction of the DNA Ternary Divider
13.11. Multiple-Valued DNA Comparator
13.11.1. Circuit Architecture Multiple-Valued DNA Comparator
13.11.2. Working Principle Multiple-Valued DNA Comparator
13.12. Summary
Bibliography
14. Multiple-Valued Arithmetic Operations in Quantum-DNA Computing
14.1. Introduction
14.2. Establishing Quantum-DNA Cross-Platform for the Ternary Logic System
14.3. Multiple-Valued Quantum-DNA Half Adder
14.3.1. Multiple-Valued Quantum-DNA Half Adder
14.3.2. Working Principle of Multiple-Valued Quantum-DNA Half Adder
14.4. Multiple-Valued Quantum-DNA Full Adder
14.4.1. Circuit Architecture of Multiple-Valued Quantum-DNA Full Adder
14.4.2. Working Principle of Multiple-Valued Quantum-DNA Full Adder
14.5. Multiple-Valued Quantum-DNA Half Subtractor
14.5.1. Circuit Architecture Multiple-Valued Quantum-DNA Half Subtractor
14.5.2. Working Principle of Multiple-Valued Quantum-DNA Half Subtractor
14.6. Multiple-Valued Quantum-DNA Full Subtractor
14.6.1. Circuit Architecture of Multiple-Valued Quantum-DNA Full Subtractor
14.6.2. Working Principle of Multiple-Valued Quantum-DNA Full Subtractor
14.7. Quantum-DNA Ternary Parallel Adder
14.7.1. The Circuit Design of the Quantum-DNA Ternary Parallel Adder
14.7.2. The Working Principles of Quantum-DNA Ternary Parallel Adder
14.8. Quantum-DNA Ternary Carry-Lookahead Adder
14.8.1. The Circuit Architecture of Quantum-DNA Ternary Carry-Lookahead Adder
14.8.2. The Working Principles of Quantum-DNA Ternary Carry-Lookahead Adder
14.9. Quantum-DNA Ternary Carry-Skip Adder
14.9.1. The General Organizations of Quantum-DNA Ternary Carry-Skip Adder
14.9.2. The Circuit Architecture of Quantum-DNA Ternary Carry-Skip Adder
14.9.3. The Working Principles of Quantum-DNA Ternary Carry-Skip Adder
14.10. Quantum-DNA Ternary Multiplier
14.10.1. The Circuit Architecture of the Quantum-DNA Ternary 2 x 2 Multiplier
14.10.2. The Working Procedure of the Quantum-DNA Ternary 2 x 2 Multiplier
14.11. Quantum-DNA Ternary Divider
14.11.1. The Construction of the Quantum-DNA Ternary Divider
14.12. Multiple-Valued Quantum-DNA Comparator
14.12.1. Circuit Architecture of Multiple-Valued Quantum-DNA Comparator
14.12.2. Working Principle of Multiple-Valued Quantum-DNA Comparator
14.13. Summary
Bibliography
15. Multiple-Valued Arithmetic Operations in DNA-Quantum Computing
15.1. Introduction
15.2. Establishing DNA-Quantum Cross-Platform for the Multi-Valued Logic System
15.3. Multiple-Valued DNA-Quantum Half Adder
15.3.1. Circuit Architecture of Multiple-Valued DNA-Quantum Half Adder
15.3.2. Working Principle of Multiple-Valued DNA-Quantum Half Adder
15.4. Multiple-Valued DNA-Quantum Full Adder
15.4.1. Circuit Architecture of Multiple-Valued DNA-Quantum Full Adder
15.4.2. Working Principle of Multiple-Valued DNA-Quantum Full Adder
15.5. Multiple-Valued DNA-Quantum Half Subtractor
15.5.1. Circuit Architecture of Multiple-Valued DNA-Quantum Half Subtractor
15.5.2. Working Principle of Multiple-Valued DNA-Quantum Half Subtractor
15.6. Multiple-Valued DNA-Quantum Full Subtractor
15.6.1. Architecture of Multiple-Valued DNA-Quantum Full Subtractor
15.6.2. Working Principle of Multiple-Valued DNA-Quantum Full Subtractor
15.7. DNA-Quantum Ternary Parallel Adder
15.7.1. The Architecture of Quantum-DNA Ternary Parallel Adder
15.7.2. The General Organizations of the DNA-Quantum Ternary Parallel Adder
15.7.3. The Circuit Design of the DNA-Quantum Ternary Parallel Adder
15.7.4. The Working Principles of DNA-Quantum Ternary Parallel Adder
15.8. DNA-Quantum Ternary Carry-Lookahead Adder
15.8.1. The General Organizations of DNA-Quantum Ternary Carry-Lookahead Adder
15.8.2. The Circuit Architecture of Quantum-DNA Ternary Carry-Lookahead Adder
15.8.3. The Working Principles of DNA-Quantum Ternary Carry-Lookahead Adder
15.9. DNA-Quantum Ternary Carry-Skip Adder
15.9.1. The General Organizations of DNA-Quantum Ternary Carry-Skip Adder
15.9.2. The Circuit Architecture of the DNA-Quantum Ternary Carry-Skip Adder
15.9.3. The Working Principles of DNA-Quantum Ternary Carry-Skip Adder
15.10. DNA-Quantum Ternary Multiplier
15.10.1. The Circuit Architecture of the DNA-Quantum Ternary 2 x 2 Multiplier
15.10.2. The Working Procedure of the DNA-Quantum Ternary 2 x 2 Multiplier
15.11. DNA-Quantum Ternary Divider
15.11.1. The Construction of the DNA-Quantum Ternary 2 x 2 Multiplier
15.12. Multiple-Valued DNA-Quantum Comparator
15.12.1. Circuit Architecture of Multiple-Valued DNA-Quantum Comparator
15.12.2. Working Principle of Multiple-Valued DNA-Quantum Comparator
15.13. Summary
Bibliography
IV. Multiple-Valued Combinational Circuits in Quantum Molecular Biology
Overview
16. Multiple-Valued Quantum Combinational Circuits
16.1. Introduction
16.2. Multiple-Valued Quantum Multiplexer
16.2.1. Circuit Architecture of Multiple-Valued Quantum Multiplexer
16.2.2. Working Principle of Multiple-Valued Quantum Multiplexer
16.3. Multiple-Valued Quantum Demultiplexer
16.4. Circuit Architecture of Multiple-Valued Quantum Demultiplexer
16.4.1. Working Principle of Multiple-Valued Quantum Demultiplexer
16.5. Multiple-Valued Quantum Encoder
16.5.1. Circuit Architecture of Multiple-Valued Quantum Encoder
16.5.2. Working Principle of Multiple-Valued Quantum Encoder
16.6. Multiple-Valued Quantum Decoder
16.6.1. Circuit Architecture of Multiple-Valued Quantum Decoder
16.6.2. Working Principle of Multiple-Valued Quantum Decoder
16.7. Summary
Bibliography
17. Multiple-Valued DNA Combinational Circuits
17.1. Introduction
17.2. Multiple-Valued DNA Multiplexer
17.2.1. Circuit Architecture of Multiple-Valued DNA Multiplexer
17.2.2. Working Principle of Multiple-Valued DNA Multiplexer
17.3. Multiple-Valued DNA Demultiplexer
17.3.1. Circuit Architecture of Multiple-Valued DNA Demultiplexer
17.3.2. Working Principle of Multiple-Valued DNA Demultiplexer
17.4. Multiple-Valued DNA Encoder
17.4.1. Circuit Architecture of Multiple-Valued DNA Encoder
17.4.2. Working Principle of Multiple-Valued DNA Encoder
17.5. Multiple-Valued DNA Decoder
17.5.1. Circuit Architecture of Multiple-Valued DNA Decoder
17.5.2. Working Principle of Multiple-Valued DNA Decoder
17.6. Summary
Bibliography
18. Multiple-Valued Quantum-DNA Combinational Circuits
18.1. Introduction
18.2. Multiple-Valued Quantum-DNA Multiplexer
18.2.1. Circuit Architecture of Multiple-Valued Quantum-DNA Multiplexer
18.2.2. Working Principle of Multiple-Valued Quantum-DNA Multiplexer
18.3. Multiple-Valued Quantum-DNA Demultiplexer
18.3.1. Circuit Architecture of Multiple-Valued Quantum-DNA Demultiplexer
18.3.2. Working Principle of Multiple-Valued Quantum-DNA Demultiplexer
18.4. Multiple-Valued Quantum-DNA Encoder
18.4.1. Circuit Architecture of Multiple-Valued Quantum-DNA Encoder
18.4.2. Working Principle of Multiple-Valued Quantum-DNA Encoder
18.5. Multiple-Valued Quantum-DNA Decoder
18.5.1. Circuit Architecture of Multiple-Valued Quantum-DNA Decoder
18.5.2. Working Principle of Multiple-Valued Quantum-DNA Decoder
18.6. Summary
Bibliography
19. Multiple-Valued DNA-Quantum Combinational Circuits
19.1. Introduction
19.2. Multiple-Valued DNA-Quantum Multiplexer
19.2.1. Circuit Architecture of Multiple-Valued DNA-Quantum Multiplexer
19.2.2. Working Principle of Multiple-Valued DNA-Quantum Multiplexer
19.3. Multiple-Valued DNA-Quantum Demultiplexer
19.3.1. Circuit Architecture of Multiple-Valued DNA-Quantum Demultiplexer
19.3.2. Working Principle of Multiple-Valued DNA-Quantum Demultiplexer
19.3.3. Multiple-Valued DNA-Quantum Encoder
19.3.4. Circuit Architecture of Multiple-Valued DNA-Quantum Encoder
19.3.5. Working Principle of Multiple-Valued DNA-Quantum Encoder
19.4. Multiple-Valued DNA-Quantum Decoder
19.4.1. Circuit Architecture of Multiple-Valued DNA-Quantum Decoder
19.4.2. Working Principle of Multiple-Valued DNA-Quantum Decoder
19.5. Summary
Bibliography
Final Remarks
Index