* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Digital Switching Overview - Lyle School of Engineering
Survey
Document related concepts
Transcript
Introduction to Digital Logic in Telecom EETS8320 SMU Lecture 8 (print slides only, no notes pages) Page 1 ©1997-2005 R.Levine Digital Hardware • Typically uses non-linear properties of electronic devices – Electro-mechanical relays, vacuum tubes were used in the past – Electronic, Dielectric and Magnetic devices were also used historically – Semiconductor electronic devices are used primarily today due to high component density, rapid operation, and low cost of integrated circuits Page 2 ©1997-2005 R.Levine Semiconductor Devices – Diodes – Transistors • Junction • Field Effect (and Metal Oxide Silicon--MOS) – Advantages: • Small size – small, high-functionality in integrated circuit package • High reliability – failure mechanisms studied, understood, and avoided • Fast switching operation – but faster switching requires higher power! • Low power consumption vis-à-vis prior art – No heated filament, as in vacuum tubes • Low cost of major raw materials – Silicon is readily available everywhere, some dopant elements are scarce but are used in very small quantities Page 3 ©1997-2005 R.Levine Linear Electric Circuit vout = (R2•R3) •v1 + (R1•R3) •v2 R1•R2 + R2•R3 + R1•R3 R1 v1 R2 v2 R3 vout vout = (2) •v1 + (2) •v2 4 + 2 +2 Page 4 ©1997-2005 R.Levine Non-linear Electric Circuit Analysis using piece-wise linear model of diode, illustrated on voltage-current graph vout Ideal voltmeter reading: 0 volts vout v1 Ideal, vout=v1 10 V 9.37 V 10 V Actual reading: -10µA•10k= -0.1 V, due to non-zero reverse current in diode. Page 5 ©1997-2005 R.Levine v1 One Stage Electronic Amplifiers • Various different graphic symbols are used to represent the amplifier “ground return circuit” for +5 V power supply is customarily omitted on drawings. vout 6 Cutoff state 4 approximately linear amplification state of operation. Note negative slope. vout 2 vin -2 Page 6 ©1997-2005 R.Levine -1 0 Vin =0.2 V is -2 “edge” of cutoff -4 1 2 vin Saturation state Vin =0.9 V is “edge” of saturation Amplifier Distinctions I • Applications which use the approximately linear state: – Hi-fidelity audio amplifiers – Radio frequency amplifiers (some types) – Analog amplifiers in telephone transmission • First used in early 20th century with vacuum tubes • Linear state is not quite as linear as is needed for a chain of numerous amplifier stages – Cumulative distortion (“flattening” of the peaks of the waveform) occurred in long distance analog telephone conversations • Negative feedback (invented by H.S. Black of Bell Laboratories, ca. 1927) improves linearity, reduces internal noise generation Page 7 ©1997-2005 R.Levine Amplifier Distinctions II • Non-linear applications intentionally use primarily the cutoff and saturation states – Minimal power dissipated in these regions • power (watts) is product of voltage with current Power P= v•i • In these operating regions, either v or I is low – therefore low power dissipated in transistor – design objective is typically to switch through the linear region as rapidly as possible to minimize power consumption – Certain types of amplifiers (so-called Class C and D, etc.) use non-linear properties for special applications (not described in this course) Page 8 ©1997-2005 R.Levine Digital Logic is the Main Non-Linear Application • Technology and design knowledge to make digital logic equipment is highly developed • Fabrication in integrated circuit form is well known, widely available • Small devices switch between cutoff and saturation states quickly – thus minimizing power consumption Page 9 ©1997-2005 R.Levine Digital “Logic” • Performs “logical” operations on binary voltage variables – Value of binary voltage can be interpreted as Yes vs. No;True vs. False, etc. – Perform logical operations such as AND, inclusive OR, exclusive OR (XOR), NOT, etc. – Numeric variables can be represented in binary form (base 2, in contrast to base 10 decimal) – Ultimately numerical algebra operations (add, subtract, multiply, divide, etc.) can be performed using binary logic devices Page 10 ©1997-2005 R.Levine Digital Components • Any logical operation that can be described by a list, table or Boolean* formula can easily be designed using simple digital “building blocks” • We use OR, AND, NOT as the 3 basic building blocks (other choices are also possible) *Boolean logic was invented circa 1860 by George Boole; “reinvented” ca. 1940 with technical improvements applicable to electronic devices and electro-mechanical relays by Claude Shannon. Page 11 ©1997-2005 R.Levine Basic Building Blocks • In this course, we will use 3 basic building block devices: AND OR NOT (single input inverter) • In some system designs, the basic electronic building block modules may be NOR or NAND (that is: NotOR, NotAND) – Corresponds to one-stage output physical devices – Less hardware and less signal delay in some cases – Many abstract algebra structures have multiple choices for their basic building blocks. Further exploration of alternative building blocks is not done in this course. Page 12 ©1997-2005 R.Levine Boolean Algebra* Description •Boolean Algebra is the symbolic “language” of digital logic system design – Computers and digital switching systems almost all use hardware with 2 voltage levels – Multi-level (e.g. 4 level) hardware devices announced by Intel Corp. in 1998, but binary symbolism still used •Theoretical invention by George Boole (British mathematician ca. 1860) – “Re-discovered” by Claude E. Shannon and applied to relay logic circuit design in 1939 (master’s thesis). •Two-valued variables – Usually represented by the symbols 0 and 1 – Closely related to binary numbering system as well. *from the name of the first Arabic book known in Europe on classic algebra, Al'jabr, by Abu Ja’far Muhammed ibn Musa Al-Khwarizmi. Born approx. 780, he is credited with the introduction of the symbol for zero into Europe, and his name led to the word “algorithm.” Historically, Al’jabr means “repair of broken bones.” Today, in general, algebra means “rules for manipulation of symbols”; not limited to high school algebra using decimal numbers. Page 13 ©1997-2005 R.Levine Logic Operations Analogous to Ordinary Arithmetic • “Sum” (OR) analogous to addition, usually represented by +, or or + sign • “Product” (AND) analogous to multiplication, usually represented by • (or * on typewriter) • “NOT” has no direct arithmetic analogy. Represented in writing via overbar (macron) or apostrophe or negative sign ( x; x’; -x) • Confusion is possible when binary arithmetic is under discussion vs. binary Boolean logical operations – Read with care! Page 14 ©1997-2005 R.Levine Binary Variables • Two voltage levels are most widely used – Called TTL (Transistor-transistor logic) levels – Older equipment (and some recent Intel memory chips) use more than two levels in some cases • Typically zero (actually about 0.2) and 5 volts – Lately, 3 or 1.5 volts is also used for the “high” level, for faster switching and compatibility with battery voltage (~1.5 V per cell) • High level is symbolized by 1, low by 0 – Other symbols are occasionally used: T,F; H,L; ON, OFF, etc. – In some special cases, 0 is used for high and 1 for low. This is sometimes called “negative” or “active low” logic. We will not use this method here to avoid confusion. Page 15 ©1997-2005 R.Levine One-stage Amplifier forms an Inverter (graphic symbols) y x JEDEC (Joint Electronic Defense Department Experts Commission) Symbol y x The little circle is the true graphic indicator of inversion. International Electro-technical Commission (IEC) symbol x y 0 1 1 0 • Signal flow is graphically normally left-to-right • “Ground” wires are conventionally not drawn • The small circle represents the negation (logical negation changes 1 to 0; changes 0 to 1) • The triangle symbol is also used to represent a linear amplifier in other contexts. – Read with care! Page 16 ©1997-2005 R.Levine Two Chained Stages form a non-inverting device IEC Symbol y y x x y x x y 0 0 1 1 JEDEC Symbol • Logically, this does “nothing,” but in practical circuits it allows greater “fan-out” and delay • It produces greater delay – However, in modern devices, the delay per stage is typically 20 to 50 nanoseconds – Simple analysis in this course ignores delay – Intentional delay is desired in some cases to synchronize two signal paths Page 17 ©1997-2005 R.Levine Boolean Symbolic Operations • Finite number of combinations, well represented by a table • Only 2-input forms shown here, but multiple inputs are used in general Logical sum Logical product (inclusive OR) (AND) x y z=x+y x0 y0 z0 w =x • y 0 0 0 1 1 Note, in this context, that 1+1 is 1, not 2. Page 18 1 0 1 1 1 1 ©1997-2005 R.Levine 0 1 1 1 0 1 w 0 0 0 1 Logical OR Devices • Multiple input non-inverting device with any one input sufficient to raise the output – Examples here use only 2 inputs, but multiple input OR devices are widely used • Several implementations: – – – – Transistor with two controlling electrodes “side by side” Junction transistor with two emitters FET with two gates single control electrode (emitter or gate), with multiple inputs connected via resistors (used in past with discrete components) • Either controlling electrode alone can turn the anode current ON, thus lowering Vout. – Then a second chained inverting stage used to produce binary 1 output. Page 19 ©1997-2005 R.Levine Logical AND Device • Non-inverting device constructed so that all inputs must go ON to switch the output ON – Examples here use only 2 inputs, but 3, 4 or more input AND devices are widely used • FET Transistor constructed with multiple controlling electrodes “in series” – Any one electrode, if OFF, turns the device anode current OFF – Followed by chained inverting stage to get binary 1 output Page 20 ©1997-2005 R.Levine Other Implementations and Graphic Symbols & x JEDEC “shaped” symbol. Bullet nose, straight back y AND gate symbols • • • Hollow “box” graphic symbol represents amplifier on page 6. Via suitable resistor size choices, the circuit above could act either as an AND or an OR device (see pp. 30ff for details) A multi-input device with special input transistors can be an AND or an OR device Page 21 ©1997-2005 R.Levine JEDEC “shaped” symbol. Bullet or curved and pointed nose, concave back OR gate symbols Combinatorial Logical Design • No “ingenuity” is required to make a basic working system – of course, further optimization is possible • Desired logical functionality must first be stated in equation or table form, relating all logical inputs to desired output(s) • SUM OF PRODUCTS: Each row in the table which produces binary 1 output can be related to a multi-input AND device, and the outputs of all such devices can be used as input to a multi-input OR device. • PRODUCT OF SUMS: Alternatively, each row in the table which produces a binary 0 can be related to a multi-input OR device, and all these outputs can be used as input to a multi-input AND device. • Choice between these two methods based on smallest component count or other criterion (fastest switching time, minimization of the number of interconnections, etc.) • Many other synthesis or design methods are also known, but not described here Page 22 ©1997-2005 R.Levine Example Logic Table and Formula _ Negation of x denoted x in most documents. We write x’ due to typographic limitations. row 0 1 2 3 4 5 6 7 x 0 0 0 0 1 1 1 1 y 0 0 1 1 0 0 1 1 Page 23 z 0 1 0 1 0 1 0 1 u 1 0 1 0 1 0 1 0 u = (x’ •y’ •z’) + (x’• y • z’) + (x • y’ • z’) + (x • y • z’) This is a “sum of products” formula. An equally valid “product of sums” formula can also be stated. Since this example has 4 zero and 4 one values for u, either method is equally “efficient” using AND and OR building blocks. ©1997-2005 R.Levine Simple Logic Synthesis Note that • or T intersection in wiring graphics represents a connection. & x Small hollow circles represent negation at the input of a multi-input device. Multi-input AND (&) output is 1 when all inputs are 1. Multi-input OR is 1 when one (or more) input(s) is/are 1. & y u & z & Page 24 ©1997-2005 R.Levine Example corresponds to previous page sum of products This design can be simplified and redesigned to operate faster (less gates in the signal path) in different ways depending on the optimization criteria. Many Standard Logic Devices • Many logical functions are required in large quantities, and are typically mass produced in special purpose integrated circuit form. – Hardware logic “works” fast, uses less chip area, has other desirable properties (vis-à-vis software). – Desirable way to implement a function if the quantity needed is large and economically attractive. • Often Called Application Specific Integrated Circuits (ASICs). Examples: – Error protection coding and decoding – Encryption/decryption devices – Devices which scan for a special binary bit pattern (e.g., for synchronization bit string within a bit stream) Page 25 ©1997-2005 R.Levine “Wired” vs. Programmable Logic • Logical operations performed by a programmable computer usually require more time and power, since operations are performed sequentially • Because hardware design (and test) is a large “up-front” cost, special hardware is usually made only for a large quantity (mass produced) product • ASICs often combine special hardware with a CPU for both the flexibility of software and the speed of wired logic • Field “Programmable” Logic Arrays (FPLAs) have numerous multi-input gates on a chip, with interconnect “wiring” (a surface metallic pattern of connections) applied by the designer for a particular application. This allows the economy of mass production with the flexibility of small production quantities. Page 26 ©1997-2005 R.Levine Useful Example Digital Devices • Multiple Output Devices – Decoder example (used with memory) – Full Adder (used in CPU) – Path switch (and tri-state) • Digital Devices with Feedback – Output depends on past signal values – Produces memory devices • Multi-function Devices – Arithmetic-Logic Unit (ALU) Page 27 ©1997-2005 R.Levine Binary Numbering • • • Base 10 numbers and arithmetic are customary, but base 2 numbers are appropriate for two-state hardware. Binary logic symbols do not inherently represent numbers, but can be arranged to do so (another reason to use binary symbols) Decimal Value 0 1 2 21 column 0 0 1 20 column 0 1 0 3 1 1 Extending this table beyond decimal 3 value requires another digit column. Page 28 ©1997-2005 R.Levine Binary, Octal, Hexadecimal Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Page 29 Binary Octal Hexadecimal 0000 0 0 0001 1 1 0010 2 2 0011 3 3 0100 4 4 0101 5 5 0110 6 6 0111 7 7 1000 10 8 1001 11 9 1010 12 A 1011 13 B 1100 14 C 1101 15 D 1110 16 E 1111 17 F ©1997-2005 R.Levine • Alternate display/ documentation forms use integral powers of 2 as base for convenience (physical internal form is still binary) Binary joke: technical people confuse Halloween with Christmas, because Oct 31equals Dec 25. (In the early Roman Calendar: September, October, November And December were the 7th through 10th Months respectively.) Multiple Outputs • Graphic Symbols Decoder example for 3-bit binary number least significant bit & 20 & 21 Connections n=0 n=1 No Connection & most significant bit 22 & Page 30 n=2 ©1997-2005 R.Levine n=3 Note: this figure illustrates only 4 of the 8 distinct decoder outputs which are possible with a 3-bit input. Decoder Uses • Addressing Memory • Choosing one of several operations in a Central Processing Unit (CPU) • Sending signals to one selected device on a line or data bus – Example: IEEE-488 (HP-IB Lab) data bus – Internal data bus in a computer between CPU, memory and peripheral devices – Using a decoder, all the printed wiring cards on a shelf can be connected to the same “back-plane” bus, but only one card receives the electrical bus signals when a selection code for that particular card is sent. Page 31 ©1997-2005 R.Levine 1-Line “Switch” or Router • Steers or directs “high” signal to desired output • Unselected output is always 0 (low) • Multiple AND devices used for parallel signal lines (bus) binary data signal & A steering or control signal: & 0 for output A, B 1 for output B. When one of the two outputs has been selected, it mimics the data input, while the other output is continuously zero. Page 32 ©1997-2005 R.Levine Three-state Line Drivers • We cannot connect multiple ordinary device outputs to the same line – Contradictory high vs. low voltage outputs on the same line are logically “illegal” • Output value of +5 V from one device and 0 V from another device cannot exist on the same wire in our abstract model – In practice, one or both devices will overheat from excessive output current • Instead, a special device type is used, called a 3-state or Tri-state driver – Has a transistor “current switch” in the output Page 33 ©1997-2005 R.Levine Multiple DriversSimplified output common output line ordinary device with constant output impedance signal 1 control 1 current switch. FET channel is pinched off by “low” control, producing “high output impedance” signal signal 2 control 2 control Conceptual Simplified Internal Diagram Symbol may differ: may be in rectangular outline, may have circles to indicate negation on34control line.©1997-2005 R.Levine Page 3-state Uses • Allows shared use of a single output wire when different devices do not produce useful output at the same time – “pin count” (quantity of external connection “wires”) is a major cost and complexity factor with many integrated circuits – “connections” often cost more than silicon components in integrated circuits! • Allows use of same wire(s) for opposite direction signal flow at different times – Example: Memory input/output (I/O Bus) Page 35 ©1997-2005 R.Levine Binary Arithmetic • 2-input forms shown here: Arithmetic sum Arithmetic Carry (exclusive OR) (AND) s=x XOR y x y s c =x • y x y c Also called “ring sum” or “modulo-2 sum.” The 0 0 1 1 0 1 0 1 0 1 1 0 symbol is sometimes used. Page 36 ©1997-2005 R.Levine 0 0 1 1 0 1 0 1 0 0 0 1 2-input (“half”)adder x & y s sum out & & Page 37 c carry out ©1997-2005 R.Levine 3-input, 2-output “full” adder • Table definitions (3 inputs, 2 outputs) carry input 0 0 0 x y c out s out 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 Page 38 ©1997-2005 R.Levine Full Arithmetic Sum & x & y s & cin & Page 39 ©1997-2005 R.Levine Full Arithmetic Carry & x & y cout & cin Note that bottom AND gate is common on both pages. & Page 40 ©1997-2005 R.Levine Combined Symbol • Two previous structures in one box • Common elements such as lower AND gate need not be repeated – This minimizes the component count • This is available as a medium-scaleintegrated circuit (MSI) • Also available as a “standard cell” which can be placed in a large-scale-integrated (LSI) circuit overall design layout, as needed. Page 41 ©1997-2005 R.Levine Graphic Symbols x y ADD cin Diagram showing data flow from top input to bottom output is convenient here to show separate bits of binary number, with least significant bit at viewer’s right. In 3-bit full adder below. cin0 is set to 0. x2 cout s y2 cin2 ADD cout s2 Page 42 ©1997-2005 R.Levine x1 y1 ADD cout s1 cin1 x0 y0 ADD cout s0 Page 17 cin0 ADDer is a Simple Arithmetic-Logic Unit (ALU) Example • “Real” ALU has at least 4 parallel bits. – Also 8, 12*, 16, 18*, 32, 60* and 64 bit units have been made • Real ALU has multiple functions aside from ADDing. Here is an example – Arithmetic subtraction performed by means of ADDing 2’s complement negative values – Complementation is another operation • 1’s complement: comp1(0001) is 1110 • 2’s complement: comp2(0001) is 1111. Sum of 1111 with 0001 produces 0000, and carry out. * these values are rarely used today, only for special-purpose computers Page 43 ©1997-2005 R.Levine Negative Numbers via 2’s Complement • 2’s complement of binary number formed in 2 steps: – Form 1’s complement (01; 10) – Add ...000001 – example: 3 in binary is 0011. 1’s comp value is 1100. Add 1, giving 1101, which is the 2’s comp representation of -3. Check by adding 1101 with 0011. Result is 0000 (with carry out). – Most modern computers (PCs, Macintosh, etc.) use 2’s complement for negative numbers • Some older computers, for example Cray or CDC (or modern emulation,via e.g. Sun Sparc, for backward software compatibility) used 1’s complement – telecom PCM* binary values do not use 2’s complement for negative values. (First bit is sign, remaining bits are magnitude of encoded value. Conversion is required before doing 2’s complement arithmetic with PCM samples.) *PCM=pulse code modulation. Examples are µ-law and A-law. Page 44 ©1997-2005 R.Levine Logic Functions • ALU could perform logical AND on its inputs by using only the lowest device in previous diagrams (pp. 14,15). • Requires additional AND gates in the 4 lines entering the final box. • Other input to the the new AND gate is a function control • This control line can be an output of a decoder. Page 45 ©1997-2005 R.Levine Graphic ALU Symbol x y Thick lines represent parallel wires (4, 8, etc.) For hand drawn pictures, an alternative graphic symbol uses a diagonal mark and sometimes a number ALU operation control code (op-code) ALU typically contains a decoder, not shown explicitly But represented by the red box 8 cout Page 46 output ©1997-2005 R.Levine Early Electronic Computers • Prior to 1950s • Many single function logic processor units were available (Add, Multiply, etc) – few were multiple function ALUs • Computer was “programmed” by wiring output from one processor into input of next step – Output of a multiplier was wired into input of an adder, etc. • “Program” was saved on a removable plug-board with wire jumpers Page 47 ©1997-2005 R.Levine “Von Neumann” Structure • In late 1940s, Johann “Johnny” Von Neumann, a noted American mathematician and refugee from Nazi Germany, proposed – Use a multiple function ALU – Store the program steps as binary operation codes in random access memory (RAM) – Also store the data to be processed and (temporarily) output data in RAM. – Known as “Von Neumann” computer architecture • Magnetic devices were most popular for memory in that era – Magnetic memory is still used today in disks, tape, etc., but not described in this course Page 48 ©1997-2005 R.Levine Early Software • Computers designed since about 1948 thus use stored programs • A sequence of – operation step binary codes, and – RAM address values indicating • where to get input data • where to store results temporarily (ultimately the results are typically sent out to a “peripheral” device: a printer, display screen, or other device at a later step in the program) • Historically, the program was stored on punched cards or magnetic media (typically tape) when not in use. Page 49 ©1997-2005 R.Levine “Memory” is Needed • RAM or main memory – Stores data – Stores programs (physically separate RAM or ROM used for data vs. program in some computers, particularly high reliability units) – Access to a particular part of memory is organized according to a numbering scheme (addresses) • Many bit-storage devices in the central processor unit (CPU) also hold data, control codes, etc. – Registers hold a “byte” or other “chunk” of bits – Single bits indicating overflow, etc. • “Mass” memory: usually disk, tape, etc. for more storage “space” at lower cost. Non-volatile data, not lost if power off. – Mass memory has slower access to a designated address than RAM • For example, one must wait for disk to rotate to proper angular sector location, etc. Page 50 ©1997-2005 R.Levine Digital Memory Devices • Many digital memory devices today use internal feedback to produce a bi-stable electronic device (so-called “static” RAM). • Some digital memory also is based on a tiny capacitor which retains electric charge • Called “dynamic” RAM memory • It requires auxiliary electronic devices to scan the electronic capacitors to “refresh” any charge that leaks away due to imperfect insulation • Its cycle time is faster, but it requires more standby power to operate. – Magnetic memory devices are little used today in internal computer circuits: • Still extensively used for mass memory and backup. Page 51 ©1997-2005 R.Levine Digital Memory Devices • Feedback of a digital output to an input can produce different effects: 1. Bi-stable conditions (two consistent stable values of the voltage) – Actual physical value then depends on history of electric signals -thus: “memory” 2. Mono-stable conditions (like a non-feedback structure) 3. Inconsistent conditions (no logically consistent voltage, neither high nor low) - In physical implementations, inconsistent logical conditions typically cause oscillation - In the humorous American folk song “The Arkansas Traveler” a donkey is described in the second verse with two limitations on its movement: “He couldn’t go ahead and he couldn’t stand still.” The conclusion was that the donkey’s position oscillated since he couldn’t remain in either stable condition: “So he went up and down like an old saw mill.” Page 52 ©1997-2005 R.Levine “Inconsistent” Device • NOT inverter device with output connected to input is “inconsistent” – Diagram implies x=y. Table implies xy. y x x y 0 1 1 0 – Actual voltage oscillates with frequency equal to reciprocal of device delay time (typically 20 ns delay time corresponds to 50 MHz frequency) – Delay time was never previously specified as a significant parameter in this course! – A doorbell buzzer is an electromechanical oscillator device of this general type. Page 53 ©1997-2005 R.Levine Consistent Bi-stable Device • Two consistent stable states: x=0,y=1; or x=1,y=0 1 0 0 y 1 z x • Only one state exists at a given time • Actual state depends on history (previous time values of x, y) • In fact, there are 3 consistent states, but only two of them are stable. Page 54 ©1997-2005 R.Levine Page 29 Physical Description Right graph is composite or chain result of “two stage amplifier” vz c,d b a vz c f vy a e 45° line (vx=vz) d a vx b vy b c d vx This lower left graph is same as upper left, but was rotated clockwise 90° for convenience to make two vy axes align. • Trace points a,b,c,d to find composite relationship between vx, vz • Connecting x with z on previous page makes vx=vz. Three consistent values: points a, e, f… but e is unstable in region of linear amplification. Any small disturbance will drive voltage to either of points a or f (reasons not shown here). Page 55 ©1997-2005 R.Levine NOR (NOT OR) Gate • One stage inverting amplifier with two ORed inputs • First internal part of practical noninverting OR gate x z y Page 56 ©1997-2005 R.Levine x 0 0 1 1 y 0 1 0 1 z 1 0 0 0 “Flip Flop” from NOR Gates • Value of two input signals controls state of this binary “flip flop” s q’ r q s 0 0 1 1 ©1997-2005 R.Levine q 1/0 0 1 0 Middle node often designated by q’ since it has opposite value from q in all consistent states except bottom row. 1/0 in table indicates that either 1 or 0 is a consistent value. We check each row of chart by assuming a value for q and tracing around the circuit to verify assumption of consistency. Page 57 r 0 1 0 1 Flip Flop Analysis 1 • Check consistency of row 2 (row 3 test not shown but similar) 0 q’ 1 0 1 s 01!! q 0 s 0 0 1 1 r 0 1 0 1 q 1/0 0 1 0 row 2 starting point r Method: Begin by assuming q=0 and inputs s=0, r=1. Then q and s are inputs to left NOR, and output (q’) is 1 according to chart on earlier page. With 1 and 1 as inputs to right NOR, output is 0) which is consistent with original assumptions. Assuming q=1 is inconsistent (gives q=0 result) Page 58 ©1997-2005 R.Levine Flip Flop Analysis 2 • Check consistency of row 1 0 0 1 q’ 0 s q 1 0 s 0 0 1 1 r 0 1 0 1 q 1/0 0 1 0 row 1 starting point r Method: Begin by assuming q=0 (or 1) and inputs s=0, r=0. Then compute q’ from left NOR using NOR chart. Result of r and q’ inputs to right NOR is consistent with both original assumptions. In a physical device, the actual state will also be dependent on previous time value of q. This is the bi-stable state of the flip flop. Page 59 ©1997-2005 R.Levine Flip Flop Analysis 3 • Check consistency of row 4 0 q’ 0 1 1 s 01!! q 0 s 0 0 1 1 r 0 1 0 1 q 1/0 0 1 0 row 4 starting point r Method: Begin by assuming q=0 (or 1) and inputs s=1, r=1. Then compute q’ output from left NOR using NOR chart (0 for both initial assumptions!). Result of r and q’ inputs to right NOR is 0 in both cases, which is inconsistent with original assumption of 1 for q value, but consistent with q=0. This is not a good state to use at a time just before the s=0, r=0 state because it presents a history which does not properly set up the bistable state of the flip flop. Page 60 ©1997-2005 R.Levine Conclusions • NOR flip flop has “memory” when s=0,r=0. It “remembers” previous state of q corresponding to opposite values of s vs. r. • The state s=1, r=1 is consistent, but causes both q and q’ to be zero. It is to be avoided just before setting s=0, r=0. – In a real device, if we pulse both s and r, and then turn them both off (0 value), the actual flip flop will always take a specific state (like q=1, q’=0) which depends on small differences in the component values (resistance, etc.) of the two NOR devices, rather than on the history. This is not helpful, since we then can’t use the device as a memory element. Page 61 ©1997-2005 R.Levine Physical Memory • The flip flop “remembers” because electric charge stored in each transistor (in depletion layers, etc.), like an electric capacitor, prevents the voltage from changing in a discontinuous jump • A large current pulse is required to make the voltage change suddenly in a capacitor, and such a pulse does not occur here. • Therefore, the voltage across various semiconductor junctions does not suddenly change, but “remembers” its immediately previous value Page 62 ©1997-2005 R.Levine Partial Model Gives Partial Solution to the Problem • Because our abstract model of the electronic components does not include delay or storage of electric charge, we cannot calculate the time needed to switch from (symbolic) 0 to 1. – We also cannot accurately determine which of the three consistent states is stable vs. unstable. – If we included some capacitors in the correct places in our circuit diagram, to represent the storage of electric charge in the depletion layers inside the transistors, we could get at least an approximate answer to these questions. • However, even with a simplified model, we can still determine which output states are consistent, and we can infer which previous inputs will produce those consistent outputs. Page 63 ©1997-2005 R.Levine Memory Device Applications • Digital memory devices (memory registers) can be used in the central processor unit (CPU) of a computer to hold data used as input or output of the ALU. Organized into “registers” • Digital memory devices can be used in large arrays as random access memory (RAM) to store data and program code in a computer. • A “shift register” can be used to convert data presentation between serial and parallel formats. Page 64 ©1997-2005 R.Levine Memory Cell Devices • NOR flip-flop used with added modules can make several useful devices: – Gated or clocked memory cell – D-type memory cell (sampling gate) • Arrays of D units make up static RAM memory – Sequential pulse counters – Serial-parallel converter (shift register) Page 65 ©1997-2005 R.Levine Gated Flip Flop • Gated devices only respond to inputs when the gate/clock signal is high. Device “remembers” status at instant the gate/clock signal goes low. • Jargon note: a whole module is also called a “gate” in some cases. This module is called an S-R (set-reset) ff. Reset or clear & q Gate or clock pulse & Set Page 66 ©1997-2005 R.Levine q’ G 0 0 0 0 S 0 0 1 1 R 0 1 0 1 q 1/0 1/0 1/0 1/0 1 1 1 1 0 0 1 1 0 1 0 1 1/0 0 1 0 1/0 in table describes last value of s input at time before the state of the row indicated. D (latch) Flip Flop • “Samples” the data line and saves the value in g place when gate signal drops 0 data & q gate or clock pulse d q d(t-) d(t-) 0 1 q g & q’ Page 67 0 1 1 d 0 1 0 1 ©1997-2005 R.Levine One type of graphic symbol Memory Cell • A 64 Kbit (8 Kbyte) memory uses 65536 of these cells* • Address decoder (not shown here) produces the enable signal for each cell. Eight such cells store a byte/octet. Note that both data input and output use the same line, due to 3-state output, and they are never simultaneous. cycle (a short pulse to cause a read or write) cycle data I/O line D & enable Q 3-state driver G write & cell enable signal write1(vs. read 0) [write stores data in the D latch] *Capital K represents 1024 while small k represents 1000. Page 68 ©1997-2005 R.Levine When a cycle pulse occurs with the write input high, the D latch captures the data on the I/O line. When the write is low (indicating read) the 3-state driver pulses the I/O line with the output from the D latch. Static RAM Structure • Static RAM is an array of D cells. Write/read and cycle pulse signals are connected to each cell but not shown. data I/O line bit7 cell data I/O line bit6 cell decoder 5 columns of cells omitted from this diagram for simplicity data I/O line bit0 cell 8191 (decimal) cell enable line 8190 rows of cells omitted from this diagram. cell cell 0 (decimal) cell enable line Address presented on 13 parallel lines for 8Kbyte memory. Page 69 ©1997-2005 R.Levine cell Dynamic RAM • Dynamic RAM uses an insulated gate MOS transistor and other components as a capacitor data storage cell to store electric charge (logical high voltage) or store no charge (logical low voltage) on the gate electrode, rather than using a D storage cell – Switches faster, and most designs use less power than static RAM when storage is short term anyway • Because the charged electrode is not perfectly insulated from its surroundings, charge can gradually flow away if not “refreshed.” To refresh the binary data: – An internal address sequence generator rapidly scans each data storage cell, and performs a read operation – If detected analog voltage is near the high voltage level, the gate is is then recharged to full voltage (a write operation) – Special circuits prevent undesired interaction of the refresh operation with a “genuine” read or write. Page 70 ©1997-2005 R.Levine “Flash” ROM/RAM • So-called FLASH memory uses isolated electrodes to store electric charge in a capacitor structure. • It retains stored binary data for months or more without power. • It is “slow” compared to traditional dynamic or static RAM with regard to the cycle time to read or write data, and requires considerable power to “write.” • Useful for semi-permanent data such as a list of frequently used telephone numbers in a cell ‘phone. Page 71 ©1997-2005 R.Levine Chain of RS Flip Flops • Also called a shift register – Note right-to-left signal flow in diagram. Some shift registers are constructed with AND gates and additional cross-wiring to permit flow in either chosen direction serial output serial input q p s q’ c r q p s q’ c r q p s q’ c r q p s q’ c r q p s q’ c r Notes: Gate/clock not shown but connected to all cells. Additional signals: p is parallel preset, sets q=1 regardless of gate/clock. c is parallel clear, “clears” (makes q=0) regardless of clock. Details of p and c not shown here. When the gate/clock is pulsed, the q value at the left side of a cell is “copied” into the cell to its immediate left. The internal signal delays in each cell allow the cell to assume its new value shortly after its old value is sensed by the next cell. Page 72 ©1997-2005 R.Levine Shift Register Uses • Serial-parallel inter-conversion – When gate/clock pulses are synchronized with a serial input bit stream, • one bit is “captured” at input for each clock pulse • bit values shift (to left in our figure) with each clock pulse • the q outputs show a historical sequence of the past input pulses, “oldest” on the left – When each cell is first parallel preset (or cleared) from a simultaneous parallel signal source, and then the gate/clock signal begins repetitive pulsing • serial output shows each bit in sequence, starting with the left one first • output bit rate is controlled by the gate/clock pulse rate Page 73 ©1997-2005 R.Levine “Elastic” Buffer • A structure (not shown) using two shift registers can be designed to take in a serial bit string at one end and deliver it later as output at the other end, although the instantaneous bit rates at the two ends do not always match. – One register holds the data, the second register indicates which bits are active storage. – The bits not yet output are stored in serial order inside one of the shift registers (or some designs use a parallel byte access memory) – The long term average bit rates must agree, or the amount of stored data would grow without bound (if input rate > output rate), a condition called “overflow.” Alternatively, the stored data would be totally emptied, and there would be a “gap” in the output bit stream (if input rate < output rate), called “underflow.” • First In First Out (FIFO) elastic buffers are used extensively in conjunction with serial multiplexers that make use of bit or byte stuffing (examples: DS-3, SONET/SDH, etc.) to produce a uniform output bit rate even though internal bit rate has short-term “jitter” for various reasons. Page 74 ©1997-2005 R.Levine “Register” Uses • Bit storage devices used in the CPU are historically called “registers.” This jargon term dates from days of mechanical “cash registers” to store/display numbers. • To store output from 4-bit arithmetic, 5-bit registers are needed to include possible carry-out (“overflow”) value • In previous diagram, right bit is conventionally considered 20 bit, left bit (of 5) is 24 bit (called carry or overflow) – left shift by 1 bit is symbolic equivalent of: “multiply by 2” – general “long” multiplication can be done by repeated shifting, AND, and adding – multiplying two n-bit numbers requires storage of a product which may be as long as 2n+1 bits • Input and output of parallel signals can be controlled by use of AND gates on p,c input and 3-state drivers on q outputs (but not shown in our figures) Page 75 ©1997-2005 R.Levine Parallel vs. Serial • Almost all computers and telecom signal processors, switches, etc. are internally parallel – Parallel connections are used within one room, one cabinet or shorter distances • Intermediate distances (shelf-to-shelf or peripheral-- printer or disk -- in same room) may be serial or parallel • Longer distance digital transmission (across the building floor to across the world) are almost all serial connections. • Parallel structure allows “parallel processing”* -- usually faster • Example: small computers have evolved from 8-bit parallel internal connections to 16 and 32 and now 64 bits *In recent years, the term “parallel processing” has been used to describe algorithmic processes utilizing separate CPUs operating simultaneously on different parts of the data. On this page, the term only implies separate bits processed by separate hardware modules simultaneously. Page 76 ©1997-2005 R.Levine Parallel vs. Serial • Parallel structure requires more components, – but this is less economically significant today due to low cost, very large scale integrated (VLSI) circuits • Serial transmission is used over long distances because: – Very difficult to maintain parallel bit synchronization on separate lines over long distance, due to jitter and related factors – Failure of one line of a parallel group renders data from the entire parallel group useless • Bad economic result to the owner or renter/leaser of transmission facilities – Practical parallel transmission systems (such as distinct wavelengths in wavelength division multiplexing -WDM- via fiber optics) usually transmit unrelated serial signal waveforms on each parallel link Page 77 ©1997-2005 R.Levine Computer Structure • A general purpose computer, and a special purpose computer for control of a telephone switch have similar major elements: – Central Processor Unit (CPU), comprising: • Arithmetic Logic Unit (ALU) – Choice of operations, controlled by a parallel op-code input used in conjunction with a decoder to activate the desired signal paths for each operation. A sequence controller is also used when a sequence of operations is needed – For this purpose, a special op-code (instruction) register is used, to hold the op-code value for the duration of the operation, – in our simple example, we will use a 4-bit op-code (16 code choices) • Register(s) to temporarily hold the inputs and the output of the ALU – in our simple example we use only one dedicated input or output holding register – in modern integrated circuit CPUs, often 16 or 32 (or more) registers are provided (or even multiple sets of registers), and they may be used flexibly for various ALU-related input or output purposes – Random Access Memory (RAM) – Direct Memory Access (DMA) input/output module(s) Page 78 ©1997-2005 R.Levine Computer Block Diagram Central Processor Unit (CPU) Int DMA Control Signals Direct Memory Access Unit (DMA) Address Bus Data Bus Key: •Int=interrupt “I'm finished”signal from DMA to CPU •R/W (read/write) control signals from CPU or DMA to RAM •clock and some other signals not shown R/W control Random Access Memory (RAM) Page 79 ©1997-2005 R.Levine Data Input/ Output (I/O) Simplified CPU Diagram • Clock, power, other wires not shown op-code decoder holding register Ain Bin ALU output C control signals to everything op-code numeric part part Read/write control (to RAM) Although almost all parts are connected, signals only pass from one part to another when control signals from the op-code decoder cause specific signal transfers. Page 80 two RAM address registers, incrementing circuits, etc. ©1997-2005 R.Levine instruction register main data bus, to/from RAM address bus to RAM Typical ALU Operations • ALU has 2 inputs and 1 output*. Typical operations: – ADD two inputs • One input is the holding register • Other input is usually a designated data byte in RAM • Output goes back into holding register. – Internal time delay prevents premature erasure of the input! – SUBtract, by first 2’s complementing one input and then adding – AND, OR, XOR the corresponding bits from the inputs – Other arithmetic operations, such as multiply, by repeated shift and add. (Requires special long output holding register – not shown here.) *Inputs and output are each a parallel bus. We use 4-bit bus in our examples. Page 81 ©1997-2005 R.Levine Modern Computers • Modern computers typically have multiple holding registers, while our example shows only one. – Each operation also includes a code value specifying which of the holding registers is used, e.g. for the 1 or 2 inputs, and which one holds the output (we don’t show this) – Some registers can be automatically incremented or decremented by 1 without using the main ALU (we don’t show this) • These registers have a separate dedicated mini-add/subtract circuit with wired input to add or subtract 1 upon command • Later we will discuss “interrupt processing”-- responding to an external electrical signal by running a special program – this occurs when a subscriber lifts a handset or dials a digit in a small telephone switch – a multiple-register computer can save all the intermediate results of prior computations so it can return to the “background” program after the program required by the interrupt is completed. Depending on the specific design, the register contents may be saved in a pre-determined part of the RAM memory, in a separate set of “backup” registers in the CPU, or elsewhere. Page 82 ©1997-2005 R.Levine More CPU Stuff • CPU also contains: – “Steering” circuits, which cause signal or bit flow to/from the RAM, to/from particular registers by means of 3-state drivers and gate/clock signals on the bit-storage registers involved. – Two “address” registers: • Instruction Address:holds the address value used to extract a program step instruction from RAM. – Usually this register is “incremented” by adding 1 after each program step, using special dedicated add-only hardware. (Not all computer designs add 1 -- this depends on the number of bytes in an instruction “word.”) – When a program “go to” occurs, a new program address is loaded into this register rather than adding 1 to the previous value • Data Address: holds the address used to extract or store data from/to RAM – Clock signals from an oscillator (clock), which cause a predetermined sequence of events, such as reading a new instruction from RAM Page 83 ©1997-2005 R.Levine Further CPU Stuff • The CPU includes a module to decode the op-codes and produce output signals which cause the correct actions in response to each op-code • This control module may itself be “microprogrammed” to perform a sequence of operations. For example: “multiply” operation requires a sequence of several left-shifts and ADDs. This requires more clock cycles than a simple one-step operation. Page 84 ©1997-2005 R.Levine Control Module • Certain operations are controlled by the control decoder: – LOAD a data value from a designated byte in RAM to the holding register (this name only used for putting data into a register) – STORE the data from the holding register to a designated byte in memory (this name only used for putting data into RAM) – JUMP (change the next instruction step address in the address register) instead of incrementing that register • corresponds to GO TO in certain programming languages – Conditional JUMP, with specified test bit: • corresponds to IF(… test condition…) THEN GOTO… in program • bit tested (in holding register) could be – test the most significant bit (sign bit) of a 2’s complement number for “jump if result of last calculation is negative.” – test overflow (carry-out) bit – test if all bits are zero – etc., etc. Page 85 ©1997-2005 R.Levine Random Access Memory (RAM) • RAM in general contains both stored program steps (object code) and data – Program steps include an op-code and relevant address • In our simple example computer, the 8-bit storage byte/octet contains a 4-bit op-code and a 4-bit address • In many telecom computers, the program steps are in a physically separate memory module from the data – This program memory can be altered only when loading a new version of the program code (requiring certain mechanical switches to be used). This protects against inadvertent alteration of the program code while operating. Page 86 ©1997-2005 R.Levine DMA I/O • • Direct Memory Access (DMA) I/O modules are widely used in computers for “fast” data transfer to/from disks, screen display or printer (also low bit rate devices like keyboards, etc.) since the 1960s. DMA module can transfer data to/from a section of RAM independent of what the CPU is then doing – During part of an op-code execution cycle, the CPU accesses RAM, during another part it does internal operations. The DMA module acts during this second part of the cycle. • Comment: A special type of DMA module is used with a separate buffer memory to perform time switching or timespace switching on PCM samples in a multiplexed transmission bit stream for telecommunications switching. – Serial-parallel conversion via shift registers is used as an interface between such a switch and serial wire links like T-1 or E-1 or SONET/SDH optical fiber. – Very similar to computer memory hardware… more on this in a future session. Page 87 ©1997-2005 R.Levine A Few Example Op-codes Mnemonic L ST HLT ADD Binary 0110 0111 0001 1001 Hex 6 7 1 9 • In a simple example we will use these op-codes*: – Load from designated RAM address to holding register – STore data from the holding register to the designated address in RAM – HaLT: stop the clock and the incrementation of the instruction address register • In some multi-user computers, this operation is “privileged” so one ordinary user can’t stop the computer. – Add the contents of the holding register to the contents of the designated byte in RAM. Result is in holding register *op-code values here are patterned after Motorola 68000 family CPU. L and ST operations are both “copy data” operations, but have distinct jargon names. Page 88 ©1997-2005 R.Levine A Simple Program • Assume that we can put data into memory and start the instruction address register at an address we choose (choose address 5) • Consider a “starting value” pre-setting for instruction register (here we don’t explain how this is done) • Consider that a separate DMA device loads the RAM, to give one method of getting program into memory • Next page shows contents of memory before and after program runs. How we get the result out of RAM is not described here. Page 89 ©1997-2005 R.Levine What is in RAM? address (decimal) contents before symbolizing contents after (binary) 0 1 2 3 4 5 6 7 8 00000111 00001001 00000000 00000000 00000000 01100001 10010000 01110010 00010000 (hex) 07 09 00 00 00 61 90 72 10 Page 90 ©1997-2005 R.Levine (decimal) (binary) 7 9 0 0 0 97 144 114 16 00000111 00001001 00010000 00000000 00000000 01100001 10010000 01110010 00010000 Interpretation • This example program starts at address 5. The “input” data is at addresses 0 and 1, and the result will be stored at address 2 (which is the only byte in memory which has a different stored value after the program run ends). • Address and meaning of each step: 5 6 7 8 • Load holding reg. with contents of address 1 Add contents of address 0 Store the result from the holding reg. to address 2 Halt the computer. If you identify addresses 0,1,2 with symbolic names x,y,z respectively, this corresponds to a programming statement: z:= y+x in a language like Pascal, C language, Fortran, etc. • In “assembly language” this program is written: L ADD ST HLT y x z Page 91 ©1997-2005 R.Levine Operating Systems • In our previous example, we did not show how to put/get programs or data into, or out of, RAM • This is usually done by means of operating system (called OS, or just “system”) software. Examples: Windows, Unix or Linux, MS-DOS, SOS, DMERT, etc. – Uses prepared programs (“drivers”) to operate specific displays and printers, or accept input from keyboards and disks • The internal binary numbers must be converted to a decimal representation, and then each decimal digit must be represented as an ASCII code character, to operate a printer • System input/output programs are generally written in the form of subroutines (to be discussed) which are called by the application programmer by means of statements like PRINT x,y,z • System software also manages and organizes data and programs stored on disks, and schedules programs to run in a predetermined sequence Page 92 ©1997-2005 R.Levine Software to Make Software • Writing programs in binary code (or even in Hexadecimal code) is difficult, tedious, and prone to error • Several “translator” programs exist to make writing the program easier. For historical reasons none of them are called “translators”: • Assembly language “assembler” • One-to-one correspondence between internal computer operation codes and program steps • Mnemonic alphabetic names may be used for opcodes and for addresses Page 93 ©1997-2005 R.Levine Assembler Program Properties • Object code runs only on the CPU for which it was written (uses specific CPU op-codes) – Programmer needs detailed knowledge of that one CPU • Can exploit special capabilities to make a very compact and fast running program – Example: Higher level programming languages sometimes un-necessarily store intermediate results in RAM. Intermediate results need not be stored in RAM if programmer knows they have no permanent significance. They can be stored temporarily in CPU register(s) only. – When run-time “speed” and small program size are essential, assembly language is still used extensively – Some higher level languages have special extensions to allow writing in-line assembly steps, or to designate specific registers to hold data, etc. Page 94 ©1997-2005 R.Levine Higher Level Languages • Also called application programming languages – Examples: Algol, Basic, C, C++, Fortran, Pascal, Protel, Java, PERL, etc. • Translation from “source” coding to “object” (opcodes and addresses). One source statement typically corresponds to many object operations. Conversion performed by “compiler” software • Complicated algebra-like expressions are “parsed” (analyzed) into an equivalent sequence of machine steps. • Mostly target-CPU independent – Many compilers exist for a given “source” language to produce object code for various CPUs • Far less tedious and intricate for programmers Page 95 ©1997-2005 R.Levine Interpreter vs. Compiler • Many languages are also supported by interpreter system software (as well as compilers) – A compiler translates source code into object code once, and object code can then be put into RAM and run/executed as many times as desired – An interpreter translates source code into object code each time the program is run • Interpreter implementations are good for programs which must frequently be modified in small ways for particular applications – But much more computer resources (memory and CPU operations) are needed to “run” an interpreter • Some languages (e.g. Basic, JAVA, PERL) are traditionally implemented only as an interpreter – Some are available either way • Use the interpreter for test and debug, the compiler for the “final” version Page 96 ©1997-2005 R.Levine Datafill vs. Programming • In many cases program code cannot be modified, but it makes extensive use of tables for different purposes to control a variety of actions • Example: the choice of a particular outgoing link (trunk) to use from a telephone switch is a result of the area code (or telephone central office code) dialed. This is expressed in a table with the area code as an index and the trunk/link number as the “output” data • The entry or writing/modification of these tables is often loosely described as “programming,” but more accurately as “data fill” – The use of different values in the data fill tables do not qualitatively change what the software can do, but make a choice from among a finite number of distinct choices Page 97 ©1997-2005 R.Levine