CS Spring Introduction - 6. Concept of state in digital systems y Analogous to variables and program counters in software systems

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1 CS 5 - Spring 2 - Introduction - Welcome to CS 5: Components and Design Techniques for Digital Sstems Wh are we here? Course staff Rand Kat (Instructor), Po Yan (Head T) Teaching ssistants: Steve Fang, Mark Feng, Neha Kumar, Mike Lowe, Samm S, Laura Todd, Jeff Tsai Readers: Wen Hui Guan, inh Ho Course web This week What is logic design? What is digital hardware? What will we be doing in this class? Obvious reasons Course is required (L&S/CS), prerequisite for CS 52 Implementation basis for all modern computing devices uilding large things from small components Provide another view of what a computer is More important reasons Inherent parallelism in hardware; first eposure to parallel computation Offers interesting counterpoint to software design; useful in generall furthering our understanding of computation Class administration, overview of course web, and logistics CS 5 - Spring 2 - Introduction - 2 What will we learn in CS 5? pplications of logic design Language of logic design oolean algebra, logic minimiation, state, timing, CD tools Concept of state in digital sstems nalogous to variables and program counters in software sstems How to specif/simulate/compile our designs Hardware description languages Tools to simulate the workings of our designs Logic compilers to snthesie the hardware blocks of our designs Mapping onto programmable hardware (code generation) Contrast with software design oth map well-posed problems to phsical devices oth must be flawless the price we pa for using discrete math Conventional computer design CPUs, busses, peripherals Networking and communications Phones, modems, routers Embedded products Cars, tos, appliances, entertainment devices Scientific equipment Testing, sensing, reporting World of computing much bigger than just PCs! CS 5 - Spring 2 - Introduction - 3 CS 5 - Spring 2 - Introduction - 4 quick histor lesson What is logic design? 85: George oole invents oolean algebra Maps logical propositions to smbols Permits manipulation of logic statements using mathematics 938: Claude Shannon links oolean algebra to switches His Masters thesis What is design? Given a specification of a problem, come up with a wa of solving it choosing appropriatel from a collection of available components While meeting some criteria for sie, cost, power, beaut, elegance, etc. 945: John von Neumann develops first stored program computer Its switching elements are vacuum tubes (a big advance from relas) 946: ENIC--world s first all electronic computer 8, vacuum tubes Several hundred multiplications per minute 947: Shockle, rittain, and ardeen invent the transistor replaces vacuum tubes enable integration of multiple devices into one package gatewa to modern electronics What is logic design? Determining the collection of digital logic components to perform a specified and/or data manipulation and/or communication function and the interconnections between them Which logic components to choose? there are man implementation technologies (e.g., off-the-shelf fied-function components, programmable devices, transistors on a chip, etc.) The design ma need to be optimied and/or transformed to meet design constraints CS 5 - Spring 2 - Introduction - 5 CS 5 - Spring 2 - Introduction - 6

2 CS 5 - Spring 2 - Introduction - 7 What is digital hardware? What is happening now in digital design? Collection of devices that sense and/or wires carring a digital value (i.e., a phsical quantit interpreted as a or ) e.g., digital logic where voltage <.8v is a and > 2.v is a e.g., pair of transmission wires where a or is distinguished b which wire has a higher voltage (differential) e.g., orientation of magnetiation signifies a or a Primitive digital hardware devices Logic computation devices (sense and drive) two wires both - make another be (ND) at least one of two wires - make another be (OR) a wire - then make another be (NOT) Memor devices (store) sense store a value ND recall a value previousl stored sense drive Source: Microsoft Encarta ig change in how industr does hardware design Larger and larger designs Shorter and shorter time to market Cheaper and cheaper products Scale Pervasive use of computer-aided design tools over hand methods Multiple levels of design representation Time Emphasis on abstract design representations Programmable rather than fied function components utomatic snthesis techniques Importance of sound design methodologies Cost Higher levels of integration Use of simulation to debug designs CS 5 - Spring 2 - Introduction - 8 CS 5: concepts/skills/abilities Understanding the basics of logic design (concepts) Understanding sound design methodologies (concepts) Modern specification methods (concepts) Familiarit with a full set of CD tools (skills) ppreciation for the differences and similarities (abilities) in hardware and software design New abilit: to accomplish the logic design task with the aid of computer-aided design tools and map a problem description into an implementation with programmable logic devices after validation via simulation and understanding of the advantages/disadvantages as compared to a software implementation CS 5 - Spring 2 - Introduction - 9 Computation: abstract vs. implementation Computation as a mental eercise (paper, programs) vs. implementing computation with phsical devices using voltages to represent logical values asic units of computation: representation: "", "" on a wire set of wires (e.g., for binar integers) assignment: = data operations: + 5 : sequential statements: ; ; C conditionals: if == then loops: for (i=;i==,i++) procedures: ; proc(...); ; Stud how these are implemented in hardware and composed into computational structures CS 5 - Spring 2 - Introduction - Switches: basic element of phsical implementations Switches (cont d) Implementing a simple circuit (arrow shows action if wire changes to ): Compose switches into more comple ones (oolean functions): close switch (if is or asserted) and turn on light bulb () ND and open switch (if is or unasserted) and turn off light bulb () OR or CS 5 - Spring 2 - Introduction - CS 5 - Spring 2 - Introduction - 2

3 CS 5 - Spring 2 - Introduction - 3 Switching networks Rela networks Switch settings Determine whether or not a conducting path eists to light the light bulb To build larger computations Use a light bulb (output of the network) to set other switches (inputs to another network). Connect together switching networks Construct larger switching networks, i.e., there is a wa to connect outputs of one network to the inputs of the net. simple wa to convert between conducting paths and switch settings is to use (electro-mechanical) relas. What is a rela? conducting path composed of switches closes circuit current flowing through coil magneties core and causes normall (nc) contact to be pulled open when no current flows, the spring of the contact returns it to its normal position CS 5 - Spring 2 - Introduction - 4 Transistor networks MOS transistors Relas aren't used much anmore Some traffic light lers are still electro-mechanical Modern digital sstems are designed in CMOS technolog MOS stands for Metal-Oide on Semiconductor C is for complementar because there are both normall-open and normall- switches MOS transistors act as voltage-led switches Similar, though easier to work with than relas. MOS transistors have three terminals: drain, gate, and source the act as switches as follows: if voltage on gate terminal is (some amount) higher/lower than source terminal then a conducting path is established between drain and source terminals G G S n-channel D S p-channel D open when voltage at G is low when voltage at G is low closes when: opens when: voltage(g) > voltage (S) + voltage(g) < voltage (S) CS 5 - Spring 2 - Introduction - 5 CS 5 - Spring 2 - Introduction - 6 MOS networks Two input networks X Y 3v v X Y what is the relationship between and? volts 3 volts 3v v 3v X Y what is the relationship between, and? volts volts volts 3 volts 3 volts volts 3 volts 3 volts v CS 5 - Spring 2 - Introduction - 7 CS 5 - Spring 2 - Introduction - 8

4 CS 5 - Spring 2 - Introduction - 9 Speed of MOS networks Representation of digital designs What influences the speed of CMOS networks? charging and discharging of voltages on wires and gates of transistors Phsical devices (transistors, relas) Switches Truth tables oolean algebra Gates Waveforms Finite state behavior Register-transfer behavior Concurrent abstract specifications scope of CS 5 CS 5 - Spring 2 - Introduction - 2 Digital vs. analog Mapping from phsical world to binar world It is convenient to think of digital sstems as having onl discrete, digital, input/output values In realit, real electronic components ehibit continuous, analog, behavior Wh do we make this abstraction? Wh does it work? Technolog State State Rela logic Circuit Open Circuit Closed CMOS logic.-. volts volts Transistor transistor logic (TTL).-.8 volts volts Fiber Optics Light off Light on Dnamic RM Discharged capacitorcharged capacitor Nonvolatile memor (erasable) Trapped electrons No trapped electrons Programmable ROM Fuse blown Fuse intact ubble memor No magnetic bubble ubble present Magnetic disk No flu reversal Flu reversal Compact disc No pit Pit CS 5 - Spring 2 - Introduction - 2 CS 5 - Spring 2 - Introduction - 22 Combinational vs. sequential digital circuits Combinational logic smbols simple model of a digital sstem is a unit with inputs and outputs: Common combinational logic sstems have standard smbols called logic gates uffer, NOT inputs sstem outputs ND, NND Combinational means "memor-less" a digital circuit is combinational if its output values onl depend on its input values OR, NOR eas to implement with CMOS transistors (the switches we have available and use most) CS 5 - Spring 2 - Introduction - 23 CS 5 - Spring 2 - Introduction - 24

5 CS 5 - Spring 2 - Introduction - 25 Sequential logic Snchronous sequential digital sstems Sequential sstems Ehibit behaviors (output values) that depend not onl on the current input values, but also on previous input values In realit, all real circuits are sequential The outputs do not change instantaneousl after an input change Wh not, and wh is it then sequential? fundamental abstraction of digital design is to reason (mostl) about stead-state behaviors Look at outputs onl after sufficient time has elapsed for the sstem to make its required changes and settle down Outputs of a combinational circuit depend onl on current inputs fter sufficient time has elapsed Sequential circuits have memor Even after waiting for the transient activit to finish The stead-state abstraction is so useful that most designers use a form of it when constructing sequential circuits: Memor of a sstem is represented as its state Changes in sstem state are onl allowed to occur at specific times led b an eternal periodic clock Clock period is the time that elapses between state changes it must be sufficientl long so that the sstem reaches a stead-state before the net state change at the end of the period CS 5 - Spring 2 - Introduction - 26 Eample of combinational and sequential logic bstractions Combinational: input, wait for clock edge observe C wait for another clock edge observe C again: will sta the same Sequential: input, wait for clock edge observe C wait for another clock edge observe C again: ma be different Clock C Some we've seen alread digital interpretation of analog values transistors as switches switches as logic gates use of a clock to realie a snchronous sequential circuit Some others we will see truth tables and oolean algebra to represent combinational logic encoding of signals with more than two logical values into binar form state diagrams to represent sequential logic hardware description languages to represent digital logic waveforms to represent temporal behavior CS 5 - Spring 2 - Introduction - 27 CS 5 - Spring 2 - Introduction - 28 n eample Implementation in software Calendar subsstem: number of das in a month (to watch displa) used in ling the displa of a wrist-watch LCD screen inputs: month, leap ear flag outputs: number of das integer number_of_das ( month, leap_ear_flag) { switch (month) { case : return (3); case 2: if (leap_ear_flag == ) then return (29) else return (28); case 3: return (3);... case 2: return (3); default: return (); } } CS 5 - Spring 2 - Introduction - 29 CS 5 - Spring 2 - Introduction - 3

6 CS 5 - Spring 2 - Introduction - 3 Implementation as a combinational digital sstem Combinational eample (cont d) Encoding: how man bits for each input/output? binar number for month four wires for 28, 29, 3, and 3 ehavior: combinational truth table specification month leap d28 d29 d3 d3 month leap d28 d29 d3 d3 Truth-table to logic to switches to gates d28 = when month= and leap= d28 = m8' m4' m2 m' leap' smbol for or smbol for and d3 = when month= or month= or... month= d3 = (m8' m4' m2' m) + (m8' m4' m2 m) +... (m8 m4 m2' m') d3 = can we simplif more? month leap d28 d29 d3 d3... smbol for not CS 5 - Spring 2 - Introduction - 32 Combinational eample (cont d) Combinational eample (cont d) d28 = m8' m4' m2 m' leap d29 = m8' m4' m2 m' leap d3 = (m8' m4 m2' m') + (m8' m4 m2 m') + (m8 m4' m2' m) + (m8 m4' m2 m) d3 = (m8' m4' m2' m) + (m8' m4' m2 m) + (m8' m4 m2' m) + (m8' m4 m2 m) + (m8 m4' m2' m4') + (m8 m4' m2 m') + (m8 m4 m2' m') d28 = m8' m4' m2 m' leap d29 = m8' m4' m2 m' leap d3 = (m8' m4 m2' m') + (m8' m4 m2 m') + (m8 m4' m2' m) + (m8 m4' m2 m) d3 = (m8' m4' m2' m) + (m8' m4' m2 m) + (m8' m4 m2' m) + (m8' m4 m2 m) + (m8 m4' m2' m4') + (m8 m4' m2 m') + (m8 m4 m2' m') CS 5 - Spring 2 - Introduction - 33 CS 5 - Spring 2 - Introduction - 34 nother eample Implementation in software Door combination lock: punch in 3 values in sequence and the door opens; if there is an error the lock must be ; once the door opens the lock must be inputs: sequence of input values, outputs: door open/close memor: must remember combination or alwas have it available as an input integer combination_lock ( ) { integer v, v2, v3; integer error = ; static integer c[3] = 3, 4, 2; while (!new_value( )); v = read_value( ); if (v!= c[]) then error = ; while (!new_value( )); v2 = read_value( ); if (v2!= c[2]) then error = ; while (!new_value( )); v3 = read_value( ); if (v2!= c[3]) then error = ; CS 5 - Spring 2 - Introduction - 35 } if (error == ) then return(); else return (); CS 5 - Spring 2 - Introduction - 36

7 CS 5 - Spring 2 - Introduction - 37 Implementation as a sequential digital sstem abstract Encoding: how man bits per input value? how man values in sequence? how do we know a new input value is entered? how do we represent the states of the sstem? ehavior: clock wire tells us when it s ok to look at inputs (i.e., the have settled after change) sequential: sequence of values must be entered sequential: remember if an error occurred finite-state specification clock new value state Finite-state diagram States: 5 states represent point in eecution of machine each state has outputs Transitions: 6 from state to state, 5 self transitions, global changes of state occur when clock sas it s ok ERR based on value of inputs Inputs:, new, results of comparisons Output: open/ C!=value C2!=value C3!=value S S2 S3 OPEN open C=value C2=value C3=value open/ not new not new not new CS 5 - Spring 2 - Introduction - 38 data-path vs. finite-state machine Internal structure data-path storage for combination comparators finite-state machine ler for data-path state changes led b clock value comparator C C2 C3 multipleer mu new ler clock Finite-state machine refine state diagram to include internal structure ERR S S2 S3 OPEN open mu=c mu=c2 mu=c3 not new not new not new open/ CS 5 - Spring 2 - Introduction - 39 CS 5 - Spring 2 - Introduction - 4 finite-state machine encoding Finite-state machine generate state table (much like a truth-table) ERR Encode state table state can be: S, S2, S3, OPEN, or ERR S S2 S3 OPEN needs at least 3 bits to encode:,,,, and as man as 5:,,,, open mu=c mu=c2 mu=c3 not new not new not new net new state state mu open/ S C choose 4 bits:,,,, output mu can be: C, C2, or C3 needs 2 to 3 bits to encode choose 3 bits:,, output open/ can be: open or S S C S ERR S S2 C2 needs or 2 bits to encode choose bits:, S2 S2 C2 S2 ERR S2 S3 C3 S3 S3 C3 S3 ERR S3 OPEN open OPEN OPEN open ERR ERR CS 5 - Spring 2 - Introduction - 4 CS 5 - Spring 2 - Introduction - 42

8 CS 5 - Spring 2 - Introduction - 43 encoding ler implementation Encode state table state can be: S, S2, S3, OPEN, or ERR choose 4 bits:,,,, output mu can be: C, C2, or C3 choose 3 bits:,, output open/ can be: open or choose bits:, net new state state mu open/ good choice of encoding! mu is identical to last 3 bits of state open/ is identical to first bit of state Implementation of the ler special circuit element, new called a register, for remembering inputs when told to b clock mu ler clock new open/ mu comb. logic state clock open/ CS 5 - Spring 2 - Introduction - 44 Design hierarch Summar sstem That was what the entire course is about Converting solutions to problems into combinational and sequential networks effectivel organiing the design hierarchicall data-path Doing so with a modern set of design tools that lets us handle large designs effectivel Taking advantage of optimiation opportunities code registers multipleer comparator state registers combinational logic Now lets do it again this time we'll take the rest of the semester! register logic switching networks CS 5 - Spring 2 - Introduction - 45 CS 5 - Spring 2 - Introduction - 46