数学代考| Application of Symbolic Logic to Digital Computing 离散数学代写代写

Claude Shannon (Fig. 14.7) was an American mathematician and engineer who made fundamental contributions to computing. He was the first person $^{4}$ to see the applicability of Boolean algebra to simplify the design of circuits and telephone routing switches. He showed that Boole’s symbolic logic developed in the nineteenth century provided the perfect mathematical model for switching theory and for the subsequent design of digital circuits and computers.

His influential Master’s Thesis is a key milestone in computing, and it shows how to layout circuits according to Boolean principles. It provides the theoretical foundation of switching circuits, and his insight of using the properties of electrical switches to do Boolean logic is the basic concept that underlies all electronic digital computers.

Shannon realized that you could combine switches in circuits in such a manner as to carry out symbolic logic operations. This allowed binary arithmetic and more complex mathematical operations to be performed by relay circuits. He designed a circuit, which could add binary numbers, and he later designed circuits that could make comparisons, and thus is capable of performing a conditional statement. This was the birth of digital logic and the digital computing age.

Vannevar Bush [5] was Shannon’s supervisor at MIT, and Shannon’s initial work was to improve Bush’s mechanical computing device known as the Differential Analyser. This machine had a complicated control circuit that was composed of one hundred switches that could be automatically opened and closed by an
$\overline{{ }^{4} \text { Victor Shestakov at Moscow State University also proposed a theory of electric switches based on }}$ Boolean algebra around the same time as Shannon. However, his results were published in Russian in 1941 whereas Shannon’s were published in $1937 .$

electromagnet. Shannon’s insight was his realization that an electronic circuit is similar to Boole’s symbolic algebra, and he showed how Boolean algebra could be employed to optimize the design of systems of electromechanical relays used in the analog computer. He also realized that circuits with relays could solve Boolean algebra problems.

He showed in his Master’s thesis “A Symbolic Analysis of Relay and Switching Circuits” $[6]$ that the binary digits (i.e. 0 and 1) can be represented by electrical switches. The implications of true and false being denoted by the binary digits one and zero were enormous since it allowed binary arithmetic and more complex mathematical operations to be performed by relay circuits. This provided electronics engineers with the mathematical tool they needed to design digital electronic circuits and provided the foundation of digital electronic design.

The design of circuits and telephone routing switches could be simplified with Boolean algebra. Shannon showed how to layout circuitry according to Boolean principles, and his Master’s thesis became the foundation for the practical design of digital circuits. These circuits are fundamental to the operation of modern computers and telecommunication systems, and his insight of using the properties of electrical switches to do Boolean logic is the basic concept that underlies all electronic digital computers.

Cryptosystem
A system that describes how to encrypt or decrypt messages
Plaintext
Message in its original form
Ciphertext
Message in its encrypted form
Cryptographer
Invents encryption algorithms
Cryptanalyst
Breaks encryption algorithms or implementations

编码理论代写

编码理论（英语：Coding theory）是研究编码的性质以及它们在具体应用中的性能的理论。编码用于数据压缩、加密、纠错，最近也用于网络编码中。不同学科（如信息论、电机工程学、数学、语言学以及计算机科学）都研究编码是为了设计出高效、可靠的数据传输方法。这通常需要去除冗余并校正（或检测）数据传输中的错误。

编码共分四类：^[1]