Memory, Latches, & Registers

Size: px

Start display at page:

Download "Memory, Latches, & Registers"

Malcolm Moody
5 years ago
Views:

1 Memory, Latches, & Registers 1) Structured Logic Arrays 2) Memory Arrays 3) Transparent Latches 4) How to save a few bucks at toll booths 5) Edge-triggered Registers L13 Memory 1

2 General Table Lookup Synthesis A B AB Fn(A,B) MUX Logic Fn(A,B) Generalizing: Remember from a few lectures ago that, in theory, we can build any 1-output combinational logic block with multiplexers. For an N-input function we need a input multiplexer. BIG Multiplexers? How about 10-input function? 20-input? L13 Memory 2

3 General Table Lookup Synthesis A B AB Fn(A,B) MUX Logic Fn(A,B) Generalizing: Remember from a few lectures ago that, in theory, we can build any 1-output combinational logic block with multiplexers. 2 N For an N-input function we need a input multiplexer. BIG Multiplexers? How about 10-input function? 20-input? L13 Memory 3

4 A Mux s Guts A decoder generates all possible product terms for a set of inputs ecoder Selector Multiplexers A B A B A B A B I 00 I 01 I 10 I 11 Y can be partitioned into two sections. A ECOER that identifies the desired input,and a SELECTOR that enables that input onto the output. Hmmm, by sharing the decoder part of the logic MUXs could be adapted to make lookup tables with any number of outputs L13 Memory 4

5 A New Combinational evice k 1 2 N ECOER: k SELECT inputs, N = 2 k ATA OUTPUTs. Selected j HIGH; all others LOW. Have I mentioned that HIGH is a synonym for 1 and LOW means the same as 0 NOW, we are well on our way to building a general purpose table-lookup device. We can build a 2-dimensional ARRAY of decoders and selectors as follows... L13 Memory 5

6 Shared ecoding Logic A B C in ecoder S C out Configurable Selector We can build a general purpose table-lookup device called a Read-Only Memory (ROM), from which we can implement any truth table and, thus, any combinational device Made from PREWIRE connections, and CONFIGURABLE connections that can be either connected or not connected L13 Memory 6

7 Shared ecoding Logic A B C in ecoder These are just emorgan ized NOR gates S C out Configurable Selector We can build a general purpose table-lookup device called a Read-Only Memory (ROM), from which we can implement any truth table and, thus, any combinational device Made from PREWIRE connections, and CONFIGURABLE connections that can be either connected or not connected L13 Memory 7

8 Shared ecoding Logic There s an extra level of inversion that isn t necessary in the logic. However, it reduces the capacitive load on the module driving this one. A B C in ecoder These are just emorgan ized NOR gates S C out Configurable Selector We can build a general purpose table-lookup device called a Read-Only Memory (ROM), from which we can implement any truth table and, thus, any combinational device Made from PREWIRE connections, and CONFIGURABLE connections that can be either connected or not connected L13 Memory 8

9 Shared ecoding Logic There s an extra level of inversion that isn t necessary in the logic. However, it reduces the capacitive load on the module driving this one. A B C in ecoder These are just emorgan ized NOR gates S This ROM stores 16 bits in 8 words of 2 bits. C out Configurable Selector We can build a general purpose table-lookup device called a Read-Only Memory (ROM), from which we can implement any truth table and, thus, any combinational device Made from PREWIRE connections, and CONFIGURABLE connections that can be either connected or not connected L13 Memory 9

10 Logic According to ROMs ROMs ignore the structure of combinational functions... Size, layout, and design are independent of function Any Truth table can be programmed by minor reconfiguration: - Metal layer (masked ROMs) - Fuses (Field-programmable PROMs) - Charge on floating gates (EPROMs)... etc. Model: LOOK UP value of function in truth table... Inputs: ARESS of a T.T. entry ROM SIZE = # TT entries for an N-input boolean function, size = L13 Memory 10

11 Logic According to ROMs ROMs ignore the structure of combinational functions... Size, layout, and design are independent of function Any Truth table can be programmed by minor reconfiguration: - Metal layer (masked ROMs) - Fuses (Field-programmable PROMs) - Charge on floating gates (EPROMs)... etc. Model: LOOK UP value of function in truth table... Inputs: ARESS of a T.T. entry ROM SIZE = # TT entries for an N-input boolean function, size = 2 N x #outputs L13 Memory 11

12 Analog Storage: Using Capacitors We ve chosen to encode information using voltages and we know from physics that we can store a voltage as charge on a capacitor: bit line word line V REF N-channel FET serves as an access switch To write: rive bit line, turn on access fet, force storage cap to new voltage To read: precharge bit line, turn on access fet, detect (small) change in bit line voltage Pros: compact! Cons: it leaks! refresh complex interface reading a bit, destroys it (you have to rewrite the value after each read) it s NOT a digital circuit This storage circuit is the basis for commodity RAMs L13 Memory 12

13 RAM Organization L13 Memory 13

5 MeV (megaelectron volts) Sounds like a lot! Until you consider other sources.

14 RAM Errors Typical RAM cell stores about 75 fc (femtocoulombs) of charge. That s about ½ million electrons Or at 3 Volts about 1.5 MeV (megaelectron volts) Sounds like a lot! Until you consider other sources. Google reports that error rates are 100 s to 1000 s of times higher than thought. Over 3700 errors per IMM per year. Cosmic Ray Flux vs Particle Energy (link) L13 Memory 14

15 A igital Storage Element It s also easy to build a settable IGITAL storage element (called a latch) using a MUX and FEEBACK: A B 0 1 Y S L13 Memory 15

16 A igital Storage Element It s also easy to build a settable IGITAL storage element (called a latch) using a MUX and FEEBACK: A B 0 1 Y S L13 Memory 16

17 A igital Storage Element It s also easy to build a settable IGITAL storage element (called a latch) using a MUX and FEEBACK: Here s a feedback path, so it s no longer a combinational circuit. A B 0 1 Y S L13 Memory 17

18 A igital Storage Element It s also easy to build a settable IGITAL storage element (called a latch) using a MUX and FEEBACK: Here s a feedback path, so it s no longer a combinational circuit. A 0 G IN OUT B SG 1 Y L13 Memory 18

19 A igital Storage Element It s also easy to build a settable IGITAL storage element (called a latch) using a MUX and FEEBACK: Here s a feedback path, so it s no longer a combinational circuit. state signal appears as both input and output A 0 G IN OUT B SG 1 Y L13 Memory 19

20 A igital Storage Element It s also easy to build a settable IGITAL storage element (called a latch) using a MUX and FEEBACK: Here s a feedback path, so it s no longer a combinational circuit. state signal appears as both input and output A 0 G IN OUT B SG 1 Y stable follows L13 Memory 20

21 Looking Under the Covers Let s take a quick look at the equivalent circuit for our MUX when the gate is LOW (the feedback path is active) G=0 0 1 G=0 1 1 This storage circuit is the basis for commodity SRAMs Advantages: 1) Maintains remembered state for as long as power is applied. 2) State is IGITAL isadvantage: 1) Requires more transistors L13 Memory 21

22 Why oes Feedback = Storage? BIG IEA: use positive feedback to maintain storage indefinitely. Our logic gates are built to restore marginal signal levels, so noise shouldn t be a problem! V IN V OUT Result: a bistable storage element L13 Memory 22

23 Why oes Feedback = Storage? BIG IEA: use positive feedback to maintain storage indefinitely. Our logic gates are built to restore marginal signal levels, so noise shouldn t be a problem! V IN V OUT Result: a bistable storage element V OUT Waveform for inverter pair V IN L13 Memory 23

24 Why oes Feedback = Storage? BIG IEA: use positive feedback to maintain storage indefinitely. Our logic gates are built to restore marginal signal levels, so noise shouldn t be a problem! V IN V OUT Result: a bistable storage element V OUT Waveform for inverter pair Feedback constraint: V IN = V OUT V IN L13 Memory 24

25 Why oes Feedback = Storage? BIG IEA: use positive feedback to maintain storage indefinitely. Our logic gates are built to restore marginal signal levels, so noise shouldn t be a problem! V IN V OUT Result: a bistable storage element V OUT Waveform for inverter pair Feedback constraint: V IN = V OUT Not affected by noise Three solutions: two end-points are stable middle point is unstable V IN We ll get back to this! L13 Memory 25

26 Static Latch G G Positive latch follows Negative latch What is the difference? 1 G G 0 stable static means latch will hold data (i.e., value of ) while G is inactive, however long that may be. L13 Memory 26

27 A YNAMIC iscipline esign of sequential circuits MUST guarantee that inputs to sequential devices are valid and stable during periods when they may influence state changes. This is assured with additional timing specifications. G L13 Memory 27

28 A YNAMIC iscipline esign of sequential circuits MUST guarantee that inputs to sequential devices are valid and stable during periods when they may influence state changes. This is assured with additional timing specifications. G >t PULSE t PULSE : minimum pulse width guarantee G is active for long enough for latch to capture data L13 Memory 28

29 A YNAMIC iscipline esign of sequential circuits MUST guarantee that inputs to sequential devices are valid and stable during periods when they may influence state changes. This is assured with additional timing specifications. G >t PULSE >t SETUP t PULSE : minimum pulse width guarantee G is active for long enough for latch to capture data t SETUP : setup time guarantee that value has propagated through feedback path before latch closes L13 Memory 29

30 A YNAMIC iscipline esign of sequential circuits MUST guarantee that inputs to sequential devices are valid and stable during periods when they may influence state changes. This is assured with additional timing specifications. G >t PULSE >t SETUP >t HOL t PULSE : minimum pulse width guarantee G is active for long enough for latch to capture data t SETUP : setup time guarantee that value has propagated through feedback path before latch closes t HOL : hold time guarantee latch is closed and is stable before allowing to change L13 Memory 30

31 Flakey Control Systems Here s a strategy for saving 2 bucks the next time you find yourself at a toll booth! L13 Memory 31

32 Flakey Control Systems Here s a strategy for saving 2 bucks the next time you find yourself at a toll booth! L13 Memory 32

33 Flakey Control Systems Here s a strategy for saving 2 bucks the next time you find yourself at a toll booth! L13 Memory 33

34 Flakey Control Systems Here s a strategy for saving 2 bucks the next time you find yourself at a toll booth! WARNING: Professional rivers Used! ON T try this At home! L13 Memory 34

35 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 35

36 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 36

37 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 37

38 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 38

39 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 39

40 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 40

41 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 41

42 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 42

43 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 43

44 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 44

45 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 45

46 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 46

47 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 47

48 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 48

49 Escapement Strategy The Solution: Add two gates and only open one at a time. L13 Memory 49

50 Escapement Strategy The Solution: Add two gates and only open one at a time. KEY: At no time is there an open path through both gates L13 Memory 50

51 Edge-triggered Flip Flop logical escapement G master G slave CLK CLK Transitions mark instants, not intervals Observations: only one latch transparent at any time: master closed when slave is open (CLK is high) slave closed when master is open (CLK is low) no combinational path through flip flop only changes shortly after 0 1 transition of CLK, so flip flop appears to be triggered by rising edge of CLK L13 Memory 51

52 Flip Flop Waveforms CLK master slave G G CLK CLK master closed slave open slave closed master open L13 Memory 52

53 Two Issues G master slave G CLK Must allow time for the input s value to propagate to the Master s output while CLK is LOW. This is called SET-UP time Must keep the input stable, just after CLK transitions to HIGH. This is insurance in case the SLAVE s gate opens just before the MASTER s gate closes. This is called HOL-TIME Can be zero (or even negative!) Assuring set-up and hold times is what limits a computer s performance L13 Memory 53

54 Flip-Flop Timing Specs CLK CLK L13 Memory 54

55 Flip-Flop Timing Specs CLK CLK t P : maximum propagation delay, CLK L13 Memory 55

56 Flip-Flop Timing Specs CLK CLK <t P t P : maximum propagation delay, CLK L13 Memory 56

57 Flip-Flop Timing Specs CLK CLK <t P >t SETUP t P : maximum propagation delay, CLK t SETUP : setup time guarantee that has propagated through feedback path before master closes L13 Memory 57

58 Flip-Flop Timing Specs CLK CLK <t P t P : maximum propagation delay, CLK >t SETUP >t HOL t SETUP : setup time guarantee that has propagated through feedback path before master closes t HOL : hold time guarantee master is closed and data is stable before allowing to change L13 Memory 58

59 Summary Regular Arrays can be used to implement arbitrary logic functions ROMs decode every input combination (fixed-an array) and compute the output for it (customized-or array) PLAs decode an minimal set of input combinations (both AN and OR arrays customized) Memories ROMs are HARWIRE memories RAMs include storage elements at each WOR-line and BIT-line intersection dynamic memory: compact, only reliable short-term static memory: controlled use of positive feedback Level-sensitive -latches for static storage ynamic discipline (setup and hold times) L13 Memory 59

Combinational vs Sequential

Combinational vs Sequential inputs X Combinational Circuits outputs Z A combinational circuit: At any time, outputs depends only on inputs Changing inputs changes outputs No regard for previous inputs