Logic Design
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Logic Design
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. History The roots of logic synthesis can be traced to the treatment of logic by George Boole (1815 to 1864), in what is now termed Boolean algebra. In 1938, Claude Shannon showed that the two-valued Boolean algebra can describe the operation of switching circuits. In the early days ...
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Computer Engineering
Computer engineering (CE, CoE, or CpE) is a branch of engineering specialized in developing computer hardware and software. It integrates several fields of electrical engineering, electronics engineering and computer science. Computer engineering is referred to as ''electrical and computer engineering'' or '' computer science and engineering'' at some universities. Computer engineers require training in hardware-software integration, software design, and software engineering. It can encompass areas such as electromagnetism, artificial intelligence (AI), robotics, computer networks, computer architecture and operating systems. Computer engineers are involved in many hardware and software aspects of computing, from the design of individual microcontrollers, microprocessors, personal computers, and supercomputers, to circuit design. This field of engineering not only focuses on how computer systems themselves work, but also on how to integrate them into the larger pictur ...
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Boolean Algebra
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 variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as Logical conjunction, 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 algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to ...
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University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher George Berkeley, it is the state's first land-grant university and is the founding campus of the University of California system. Berkeley has an enrollment of more than 45,000 students. The university is organized around fifteen schools of study on the same campus, including the UC Berkeley College of Chemistry, College of Chemistry, the UC Berkeley College of Engineering, College of Engineering, UC Berkeley College of Letters and Science, College of Letters and Science, and the Haas School of Business. It is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". Lawrence Berkeley National Laboratory was originally founded as par ...
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Programmable Logic Array
A programmable logic array (PLA) is a kind of programmable logic device used to implement combinational logic circuits. The PLA has a set of programmable AND gate planes, which link to a set of programmable OR gate planes, which can then be conditionally complemented to produce an output. It has 2N AND gates for N input variables, and for M outputs from the PLA, there should be M OR gates, each with programmable inputs from all of the AND gates. This layout allows for many logic functions to be synthesized in the sum of products canonical forms. PLAs differ from programmable array logic devices ( PALs and GALs) in that both the AND and OR gate planes are programmable. PAL has programmable AND gates but fixed OR gates History In 1970, Texas Instruments developed a mask-programmable IC based on the IBM read-only associative memory or ROAM. This device, the TMS2000, was programmed by altering the metal layer during the production of the IC. The TMS2000 had up to 17 inputs ...
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Discrete Logic
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 (see ideal and real op-amps for comparison). The primary way of building logic gates uses diodes or transistors acting as electronic switches. Today, most logic gates are made from MOSFETs (metal–oxide–semiconductor field-effect transistors). ''From Integrated circuit'' They can also be constructed using vacuum tubes, electromagnetic relays with relay logic, fluidic logic, pneumatic logic, optics, molecules, acoustics, or even mechanical or thermal elements. Logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the alg ...
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Bell Labs
Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the company operates several laboratories in the United States and around the world. As a former subsidiary of the American Telephone and Telegraph Company (AT&T), Bell Labs and its researchers have been credited with the development of radio astronomy, the transistor, the laser, the photovoltaic cell, the charge-coupled device (CCD), information theory, the Unix operating system, and the programming languages B (programming language), B, C (programming language), C, C++, S (programming language), S, SNOBOL, AWK, AMPL, and others, throughout the 20th century. Eleven Nobel Prizes and five Turing Awards have been awarded for work completed at Bell Laboratories. Bell Labs had its origin in the complex corporate organization of the Bell System telepho ...
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Finite-state Machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of ''State (computer science), states'' at any given time. The FSM can change from one state to another in response to some Input (computer science), inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types—Deterministic finite automaton, deterministic finite-state machines and Nondeterministic finite automaton, non-deterministic finite-state machines. For any non-deterministic finite-state machine, an equivalent deterministic one can be constructed. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions d ...
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Espresso Heuristic Logic Minimizer
The ESPRESSO logic minimizer is a computer program using heuristic and specific algorithms for efficiently reducing the complexity of digital logic gate circuits. ESPRESSO-I was originally developed at IBM by Robert K. Brayton et al. in 1982. and improved as ESPRESSO-II in 1984. Richard L. Rudell later published the variant ESPRESSO-MV in 1986 and ESPRESSO-EXACT in 1987. Espresso has inspired many derivatives. Introduction Electronic devices are composed of numerous blocks of digital circuits, the combination of which performs some required task. The efficient implementation of logic functions in the form of logic gate circuits (such that no more logic gates are used than are necessary) is necessary to minimize production costs, and/or maximize a device's performance. Designing digital logic circuits All digital systems are composed of two elementary functions: memory elements for storing information, and combinational circuits that transform that information. State machines ...
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Two-level Minimization
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. Generally, the circuit is constrained to a minimum chip area meeting a predefined response delay. The goal of logic optimization of a given circuit is to obtain the smallest logic circuit that evaluates to the same values as the original one. Usually, the smaller circuit with the same function is cheaper, takes less space, consumes less power, has shorter latency, and minimizes risks of unexpected cross-talk, hazard of delayed signal processing, and other issues present at the nano-scale level of metallic structures on an integrated circuit. In terms of Boolean algebra, the optimization of a complex Boolean expression is a process of finding a simpler one, which would upon evaluation ultimately produce the same results as the or ...
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Quine–McCluskey Algorithm
The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward J. McCluskey in 1956. As a general principle this approach had already been demonstrated by the logician Hugh McColl in 1878, was proved by Archie Blake in 1937, and was rediscovered by Edward W. Samson and Burton E. Mills in 1954 and by Raymond J. Nelson in 1955. Also in 1955, Paul W. Abrahams and John G. Nordahl as well as Albert A. Mullin and Wayne G. Kellner proposed a decimal variant of the method. The Quine–McCluskey algorithm is functionally identical to Karnaugh mapping, but the tabular form makes it more efficient for use in computer algorithms, and it also gives a deterministic way to check that the minimal form of a Boolean F has been reached. It is sometimes referred to as the tabulation method. The Quine-McCluskey algorithm works as follows: # Finding ...
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Logic Minimization
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. Generally, the circuit is constrained to a minimum chip area meeting a predefined response delay. The goal of logic optimization of a given circuit is to obtain the smallest logic circuit that evaluates to the same values as the original one. Usually, the smaller circuit with the same function is cheaper, takes less space, consumes less power, has shorter latency, and minimizes risks of unexpected cross-talk, hazard of delayed signal processing, and other issues present at the nano-scale level of metallic structures on an integrated circuit. In terms of Boolean algebra, the optimization of a complex Boolean expression is a process of finding a simpler one, which would upon evaluation ultimately produce the same results as the or ...
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