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In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values. It is also a special case of a De Morgan algebra and a Kleene algebra.
Claude Elwood Shannon was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and as the "father of the Information Age". Shannon was the first to describe the Boolean gates that are essential to all digital electronic circuits, and was one of the founding fathers of artificial intelligence. Shannon is credited with laying the foundations of the Information Age.
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for instance, zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device.
George Boole Jnr was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought (1854), which contains Boolean algebra. Boolean logic, essential to computer programming, is credited with helping to lay the foundations for the Information Age.
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics which work primarily with analog signals. Despite the name, digital electronics designs includes important analog design considerations.
In automata theory, combinational logic is a type of digital logic that is implemented by Boolean circuits, where the output is a pure function of the present input only. This is in contrast to sequential logic, in which the output depends not only on the present input but also on the history of the input. In other words, sequential logic has memory while combinational logic does not.
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ. With multiple inputs, XOR is true if and only if the number of true inputs is odd.
A binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary string of eight bits can represent any of 256 possible values and can, therefore, represent a wide variety of different items.
Gilbert Sandford Vernam was a Worcester Polytechnic Institute 1914 graduate and AT&T Bell Labs engineer who, in 1917, invented an additive polyalphabetic stream cipher and later co-invented an automated one-time pad cipher. Vernam proposed a teleprinter cipher in which a previously prepared key, kept on paper tape, is combined character by character with the plaintext message to produce the ciphertext. To decipher the ciphertext, the same key would be again combined character by character, producing the plaintext. Vernam later worked for the Postal Telegraph Company, and became an employee of Western Union when that company acquired Postal in 1943. His later work was largely with automatic switching systems for telegraph networks.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set. Alternative names are switching function, used especially in older computer science literature, and truth function, used in logic. Boolean functions are the subject of Boolean algebra and switching theory.
The First Draft of a Report on the EDVAC is an incomplete 101-page document written by John von Neumann and distributed on June 30, 1945 by Herman Goldstine, security officer on the classified ENIAC project. It contains the first published description of the logical design of a computer using the stored-program concept, which has come to be known as the von Neumann architecture; the name has become controversial due to von Neumann's failure to name other contributors.
In computer engineering, logic synthesis is a process by which an abstract specification of desired circuit behavior, typically at register transfer level (RTL), is turned into a design implementation in terms of logic gates, typically by a computer program called a synthesis tool. Common examples of this process include synthesis of designs specified in hardware description languages, including VHDL and Verilog. Some synthesis tools generate bitstreams for programmable logic devices such as PALs or FPGAs, while others target the creation of ASICs. Logic synthesis is one step in circuit design in the electronic design automation, the others are place and route and verification and validation.
The history of computer science began long before the modern discipline of computer science, usually appearing in forms like mathematics or physics. Developments in previous centuries alluded to the discipline that we now know as computer science. This progression, from mechanical inventions and mathematical theories towards modern computer concepts and machines, led to the development of a major academic field, massive technological advancement across the Western world, and the basis of a massive worldwide trade and culture.
Logic optimization is a process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. This process is a part of a logic synthesis applied in digital electronics and integrated circuit design.
Victor Ivanovich Shestakov (1907–1987) was a Russian/Soviet logician and theoretician of electrical engineering. In 1935 he discovered the possible interpretation of Boolean algebra of logic in electro-mechanical relay circuits. He graduated from Moscow State University (1934) and worked there in the General Physics Department almost until his death.
Switching circuit theory is the mathematical study of the properties of networks of idealized switches. Such networks may be strictly combinational logic, in which their output state is only a function of the present state of their inputs; or may also contain sequential elements, where the present state depends on the present state and past states; in that sense, sequential circuits are said to include "memory" of past states. An important class of sequential circuits are state machines. Switching circuit theory is applicable to the design of telephone systems, computers, and similar systems. Switching circuit theory provided the mathematical foundations and tools for digital system design in almost all areas of modern technology.
In Boolean logic, a formula for a Boolean function f is in Blake canonical form (BCF), also called the complete sum of prime implicants, the complete sum, or the disjunctive prime form, when it is a disjunction of all the prime implicants of f.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and negation (not) denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations.
Boolean differential calculus (BDC) is a subject field of Boolean algebra discussing changes of Boolean variables and Boolean functions.
Akira Nakashima was a Japanese electrical engineer of the NEC.
References
- ↑ Agarwal, Ravi P; Sen, Syamal K (2014). Creators of Mathematical and Computational Sciences. Cham: Springer International Publishing. p. 425. doi:10.1007/978-3-319-10870-4. ISBN 978-3-319-10869-8.
- ↑ Fox, Charles (2024). Computer Architecture: From the Stone Age to the Quantum Age. San Francisco: No Starch Press. p. 114. ISBN 978-1-7185-0286-4.
- ↑ Caldwell, Samuel H. (1965) [1958]. Switching Circuits and Logical Design, Sixth Printing. New York: John Wiley & Sons. p. 34. ISBN 978-0471129691.
[Shannon] constructed a calculus based on a set of postulates which described basic switching ideas; e.g., an open circuit in series with an open circuit is an open circuit. Then he showed that his calculus was equivalent to certain elementary parts of the calculus of propositions, which in turn was derived from the algebra of logic developed by George Boole.
- ↑ Wheen, Andrew (2011). Dot-Dash to Dot.Com: How Modern Telecommunications Evolved from the Telegraph to the Internet. New York, NY: Springer New York. p. 77. doi:10.1007/978-1-4419-6760-2. ISBN 978-1-4419-6759-6.
- ↑ Wright, Alex (2023). Informatica: Mastering Information through the Ages. Cornell University Press. p. 188. doi:10.7591/j.ctv2rtgnvk. ISBN 978-1-5017-6867-5.
- 1 2 Kawanishi, Toma (2019). "Prehistory of Switching Theory in Japan: Akira Nakashima and His Relay-circuit Theory". Historia Scientiarum. Second Series. 29 (1): 136–162. doi:10.34336/historiascientiarum.29.1_136.
- ↑ Norman, Jeremy M. (2005). From Gutenberg to the Internet: A Sourcebook on the History of Information Technology. Novato, Calif: Historyofscience.com. p. 749. ISBN 978-0-930405-87-8. OCLC 57124414.
- ↑ Aleksander, Igor; Morton, Helen (2012). Aristotle's Laptop: The Discovery of our Informational Mind. Series on Machine Consciousness. Vol. 1. World Scientific Publishing. p. 22. doi:10.1142/8113. ISBN 978-981-4343-49-7.
- ↑ Matthews, Suzanne J.; Newhall, Tia; Webb, Kevin C. (2022). Dive Into Systems: A Gentle Introduction to Computer Systems. San Francisco: No Starch Press. p. 234. ISBN 978-1-7185-0136-2.
- ↑ Domingos, Pedro [@pmddomingos] (2023-12-20). "The most important master's thesis of all time" (Tweet). Retrieved 2024-11-05– via Twitter.
- ↑ Goldstine, Herman A. (1972). The Computer: From Pascal to von Neumann. p. 119-20.
- ↑ Smith, Nancy Duvergne (2011-08-15). "Claude Shannon: Digital Pioneer's Work Still Reverberates". alum.mit.edu. Retrieved 2024-01-11.
- ↑ Shannon, C. E. (1938). "A Symbolic Analysis of Relay and Switching Circuits" (PDF). Trans. AIEE. 57 (12): 713–723. doi:10.1109/T-AIEE.1938.5057767. hdl: 1721.1/11173 . S2CID 51638483.