# Digital Logic Design And Synthesis Of Combinational And Sequential Circuits Pdf

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*In automata theory , sequential logic is a type of logic circuit whose output depends not only on the present value of its input signals but on the sequence of past inputs, the input history as well. That is, sequential logic has state memory while combinational logic does not.*

- EECS 303 Advanced Digital Design
- Digital electronics
- Lecture Schedulesubject to change
- Edinburgh Napier University

*Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them.*

## EECS 303 Advanced Digital Design

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 and analog signals. Digital electronic circuits are usually made from large assemblies of logic gates , often packaged in integrated circuits. Complex devices may have simple electronic representations of Boolean logic functions. The binary number system was refined by Gottfried Wilhelm Leibniz published in and he also established that by using the binary system, the principles of arithmetic and logic could be joined.

Digital logic as we know it was the brain-child of George Boole in the mid 19th century. In an letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits. Ludwig Wittgenstein introduced a version of the row truth table as proposition 5.

Walther Bothe , inventor of the coincidence circuit , shared the Nobel Prize in physics, for the first modern electronic AND gate in Mechanical analog computers started appearing in the first century and were later used in the medieval era for astronomical calculations.

In World War II , mechanical analog computers were used for specialized military applications such as calculating torpedo aiming. During this time the first electronic digital computers were developed. Originally they were the size of a large room, consuming as much power as several hundred modern personal computers PCs.

The Z3 was an electromechanical computer designed by Konrad Zuse. Finished in , it was the world's first working programmable , fully automatic digital computer.

At the same time that digital calculation replaced analog, purely electronic circuit elements soon replaced their mechanical and electromechanical equivalents. John Bardeen and Walter Brattain invented the point-contact transistor at Bell Labs in , followed by William Shockley inventing the bipolar junction transistor at Bell Labs in At the University of Manchester , a team under the leadership of Tom Kilburn designed and built a machine using the newly developed transistors instead of vacuum tubes.

From onwards, transistors replaced vacuum tubes in computer designs, giving rise to the "second generation" of computers. Compared to vacuum tubes, transistors were smaller, more reliable, had indefinite lifespans, and required less power than vacuum tubes - thereby giving off less heat, and allowing much denser concentrations of circuits, up to tens of thousands in a relatively compact space. While working at Texas Instruments in July , Jack Kilby recorded his initial ideas concerning the integrated circuit IC , then successfully demonstrated the first working integrated on 12 September The following year, Robert Noyce at Fairchild Semiconductor invented the silicon integrated circuit.

The basis for Noyce's silicon IC was the planar process , developed in early by Jean Hoerni , who was in turn building on Mohamed Atalla 's silicon surface passivation method developed in In the early days of integrated circuits , each chip was limited to only a few transistors, and the low degree of integration meant the design process was relatively simple. Manufacturing yields were also quite low by today's standards.

The transistor count of both, individual devices and total production rose to unprecedented heights. The total amount of transistors produced until has been estimated to be 1. Discrete cosine transform DCT coding, a data compression technique first proposed by Nasir Ahmed in , [31] enabled practical digital media transmission, [32] [33] [34] with image compression formats such as JPEG , video coding formats such as H. An advantage of digital circuits when compared to analog circuits is that signals represented digitally can be transmitted without degradation caused by noise.

In a digital system, a more precise representation of a signal can be obtained by using more binary digits to represent it. While this requires more digital circuits to process the signals, each digit is handled by the same kind of hardware, resulting in an easily scalable system. In an analog system, additional resolution requires fundamental improvements in the linearity and noise characteristics of each step of the signal chain. With computer-controlled digital systems, new functions to be added through software revision and no hardware changes.

Often this can be done outside of the factory by updating the product's software. So, the product's design errors can be corrected after the product is in a customer's hands.

Information storage can be easier in digital systems than in analog ones. The noise immunity of digital systems permits data to be stored and retrieved without degradation. In an analog system, noise from aging and wear degrade the information stored. In a digital system, as long as the total noise is below a certain level, the information can be recovered perfectly.

Even when more significant noise is present, the use of redundancy permits the recovery of the original data provided too many errors do not occur. In some cases, digital circuits use more energy than analog circuits to accomplish the same tasks, thus producing more heat which increases the complexity of the circuits such as the inclusion of heat sinks. In portable or battery-powered systems this can limit use of digital systems. For example, battery-powered cellular telephones often use a low-power analog front-end to amplify and tune in the radio signals from the base station.

However, a base station has grid power and can use power-hungry, but very flexible software radios. Such base stations can be easily reprogrammed to process the signals used in new cellular standards. Many useful digital systems must translate from continuous analog signals to discrete digital signals.

This causes quantization errors. Quantization error can be reduced if the system stores enough digital data to represent the signal to the desired degree of fidelity. The Nyquist—Shannon sampling theorem provides an important guideline as to how much digital data is needed to accurately portray a given analog signal.

In some systems, if a single piece of digital data is lost or misinterpreted, the meaning of large blocks of related data can completely change. For example, a single-bit error in audio data stored directly as linear pulse-code modulation causes, at worst, a single click. Instead, many people use audio compression to save storage space and download time, even though a single bit error may cause a larger disruption. Because of the cliff effect , it can be difficult for users to tell if a particular system is right on the edge of failure, or if it can tolerate much more noise before failing.

Digital fragility can be reduced by designing a digital system for robustness. For example, a parity bit or other error management method can be inserted into the signal path. These schemes help the system detect errors, and then either correct the errors , or request retransmission of the data. A digital circuit is typically constructed from small electronic circuits called logic gates that can be used to create combinational logic.

Each logic gate is designed to perform a function of boolean logic when acting on logic signals. A logic gate is generally created from one or more electrically controlled switches, usually transistors but thermionic valves have seen historic use.

The output of a logic gate can, in turn, control or feed into more logic gates. Another form of digital circuit is constructed from lookup tables, many sold as " programmable logic devices ", though other kinds of PLDs exist. Lookup tables can perform the same functions as machines based on logic gates, but can be easily reprogrammed without changing the wiring. This means that a designer can often repair design errors without changing the arrangement of wires.

Therefore, in small volume products, programmable logic devices are often the preferred solution. They are usually designed by engineers using electronic design automation software.

Integrated circuits consist of multiple transistors on one silicon chip, and are the least expensive way to make large number of interconnected logic gates. Integrated circuits are usually interconnected on a printed circuit board which is a board which holds electrical components, and connects them together with copper traces. Engineers use many methods to minimize logic redundancy in order to reduce the circuit complexity. Reduced complexity reduces component count and potential errors and therefore typically reduces cost.

Logic redundancy can be removed by several well-known techniques, such as binary decision diagrams , Boolean algebra , Karnaugh maps , the Quine—McCluskey algorithm , and the heuristic computer method.

These operations are typically performed within a computer-aided design system. Embedded systems with microcontrollers and programmable logic controllers are often used to implement digital logic for complex systems that don't require optimal performance. These systems are usually programmed by software engineers or by electricians, using ladder logic.

Representations are crucial to an engineer's design of digital circuits. To choose representations, engineers consider types of digital systems. The classical way to represent a digital circuit is with an equivalent set of logic gates. Each logic symbol is represented by a different shape.

This can be represented as a truth table. Most digital systems divide into combinational and sequential systems. A combinational system always presents the same output when given the same inputs. A sequential system is a combinational system with some of the outputs fed back as inputs.

This makes the digital machine perform a sequence of operations. The simplest sequential system is probably a flip flop , a mechanism that represents a binary digit or " bit ". Sequential systems are often designed as state machines. In this way, engineers can design a system's gross behavior, and even test it in a simulation, without considering all the details of the logic functions.

Sequential systems divide into two further subcategories. Synchronous sequential systems are made of well-characterized asynchronous circuits such as flip-flops, that change only when the clock changes, and which have carefully designed timing margins.

For logic simulation , digital circuit representations have digital file formats that can be processed by computer programs. The usual way to implement a synchronous sequential state machine is to divide it into a piece of combinational logic and a set of flip flops called a state register. The state register represents the state as a binary number. The combinational logic produces the binary representation for the next state. On each clock cycle, the state register captures the feedback generated from the previous state of the combinational logic and feeds it back as an unchanging input to the combinational part of the state machine.

The clock rate is limited by the most time-consuming logic calculation in the combinational logic. Most digital logic is synchronous because it is easier to create and verify a synchronous design. However, asynchronous logic has the advantage of its speed not being constrained by an arbitrary clock; instead, it runs at the maximum speed of its logic gates. Nevertheless, most systems need to accept external unsynchronized signals into their synchronous logic circuits. This interface is inherently asynchronous and must be analyzed as such.

Examples of widely used asynchronous circuits include synchronizer flip-flops, switch debouncers and arbiters. Asynchronous logic components can be hard to design because all possible states, in all possible timings must be considered.

## Digital electronics

Prerequisite — Combinational circuits using Decoder , Introduction of Sequential Circuits Combinational circuits are defined as the time independent circuits which do not depends upon previous inputs to generate any output are termed as combinational circuits. Sequential circuits are those which are dependent on clock cycles and depends on present as well as past inputs to generate any output. Attention reader! Writing code in comment? Please use ide. Skip to content. Related Articles.

Introduction to Logic Circuits: Variables, functions, truth tables, gates and networks. Introduction to Logic Circuits: Boolean algebra. Introduction to Logic Circuits: Design Examples. Implementation Technology: Buffers, Tri-state gates, Transmission gates. Exam 1 Sample Questions.

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Symbolic Design of Combinational and Sequential Logic Circuits Implemented by Two-Level Logic Macros Abstract: This paper presents a method for the optimal synthesis of combinational and sequential circuits implemented by two-level logic macros, such as programmable logic arrays. Optimization consists of finding representations of switching functions corresponding to minimal-area implementations. The design of optimization is based on two steps: symbolic minimization and constrained encoding. Symbolic minimization yields an encoding-independent sum of products representation of a switching function which is minimal in the number of product terms.

PDF | The reversible logic will be having more importance in today's era due to This paper proposes the different reversible sequential circuits. presented in this paper can be used in regular circuits realizing Boolean functions. of works has been done on reversible combinational logic synthesis, only.

## Lecture Schedulesubject to change

Note: All reading assignments are in Wakerly. DLD Lab. Basic knowledge will be reviewed and exercise problems involving encoders and decoders solved. Solve problems related to lectures 16—19; answer question questions related to homework 5.

*Course Description.*

### Edinburgh Napier University

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Pragmatic Logic presents the analysis and design of digital logic systems.

Combinational logic circuits. – Sequential logic circuits. – How digital logic gates are built using transistors. – Design and build of digital logic systems.

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Teacher Samuele Salti.

PDF | Electronic circuits can be separated into two groups, digital and analog The basic logic design steps are generally identical for sequential and combinational The Logic synthesis step automatically converts a logic-level behavior.