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omputer 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 1958 jack kilby recorded his initial ideas concerning the integrated circuit ic then successfully demonstrated the first working integrated circuit on 12 september 1958 8 kilby s chip was made of germanium 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 1959 by jean hoerni who was in turn building on mohamed atalla s silicon surface passivation method developed in 1957 9 this new technique the integrated circuit allowed for quick low cost fabrication of complex circuits by having a set of electronic circuits on one small plate chip of semiconductor material normally silicon the metal oxide semiconductor field effect transistor mosfet also known as the mos transistor was invented by mohamed atalla and dawon kahng at bell labs in 1959 10 11 12 the mosfet s advantages include high scalability 13 affordability 14 low power consumption and high transistor density 15 its rapid on off electronic switching speed also makes it ideal for generating pulse trains 16 the basis for electronic digital signals 17 18 in contrast to bjts which more slowly generate analog signals resembling sine waves 16 along with mos large scale integration lsi these factors make the mosfet an important switching device for digital circuits 19 the mosfet revolutionized the electronics industry 20 21 and is the most common semiconductor device 11 22 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 wide adoption of the mosfet transistor by the early 1970s led to the first large scale integration lsi chips with more than 10 000 transistors on a single chip 23 following the wide adoption of cmos a type of mosfet logic by the 1980s millions and then billions of mosfets could be placed on one chip as the technology progressed 24 and good designs required thorough planning giving rise to new design methods the transistor count of devices and total production rose to unprecedented heights the total amount of transistors produced until 2018 has been estimated to be 1 3 10 22 13 sextillion 25 the wireless revolution the introduction and proliferation of wireless networks began in the 1990s and was enabled by the wide adoption of mosfet based rf power amplifiers power mosfet and ldmos and rf circuits rf cmos 26 27 28 wireless networks allowed for public digital transmission without the need for cables leading to digital television gps satellite radio wireless internet and mobile phones through the 1990s 2000s properties edit an advantage of digital circuits when compared to analog circuits is that signals represented digitally can be transmitted without degradation caused by noise 29 for example a continuous audio signal transmitted as a sequence of 1s and 0s can be reconstructed without error provided the noise picked up in transmission is not enough to prevent identification of the 1s and 0s 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 can be added through software revision and no hardware changes are needed often this can be done outside of the factory by updating the product s software this way the product s design errors can be corrected even 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 the use of digital systems for example battery powered cellular phones often use a low power analog front end to amplify and tune 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 easily be 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 nevertheless many people use audio compression to save storage space and download time even though a single bit error may cause a large 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 construction edit a binary clock hand wired on breadboards 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 design edit 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 representation edit representations are crucial to an engineer s design of digital circuits to choose representations engineers consider different 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 the actual set of shapes was introduced in 1984 under ieee ansi standard 91 1984 and is now in common use by integrated circuit manufacturers 30 another way is to construct an equivalent system of electronic switches usually transistors 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 change state all at once when a clock signal changes state asynchronous sequential systems propagate changes whenever inputs change 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 synchronous systems edit a 4 bit ring counter using d type flip flops is an example of synchronous logic each device is connected to the clock signal and update together main article synchronous logic 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 asynchronous systems edit 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 a building an asynchronous system using faster parts makes the circuit faster 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 the usual method is to construct a table of the minimum and maximum time that each such state can exist and then adjust the circuit to minimize the number of such states the designer must force the circuit to periodically wait for all of its parts to enter a compatible state this is called self resynchronization without careful design it is easy to accidentally produce asynchronous logic that is unstable that is real electronics will have unpredictable results because of the cumulative delays caused by small variations in the values of the electronic components register transfer systems edit example of a simple circuit with a toggling output the inverter forms the combinational logic in this circuit and the register holds the state many digital systems are data flow machines these are usually designed using synchronous register transfer logic and written with hardware description languages such as vhdl or verilog in register transfer logic binary numbers are stored in groups of flip flops called registers a sequential state machine controls when each register accepts new data from its input the outputs of each register are a bundle of wires called a bus that carries that number to other calculations a calculation is simply a piece of combinational logic each calculation also has an output bus and these may be connected to the inputs of several registers sometimes a register will have a multiplexer on its input so that it can store a number from any one of several buses b asynchronous register transfer systems such as computers have a general solution in the 1980s some researchers discovered that almost all synchronous register transfer machines could be converted to asynchronous designs by using first in first out synchronization logic in this scheme the digital machine is characterized as a set of data flows in each step of the flow a synchronization circuit determines when the outputs of that step are valid and instructs the next stage when to use these outputs citation needed computer design edit intel 80486dx2 microprocessor the most general purpose register transfer logic machine is a computer this is basically an automatic binary abacus the control unit of a computer is usually designed as a microprogram run by a microsequencer a microprogram is much like a player piano roll each table entry of the microprogram commands the state of every bit that controls the computer the sequencer then counts and the count addresses the memory or combinational logic machine that contains the microprogram the bits from the microprogram control the arithmetic logic unit memory and other parts of the computer including the microsequencer itself in this way the complex task of designing the controls of a computer is reduced to a simpler task of programming a collection of much simpler logic machines almost all comput...