1. 11/12/2004EE 42 fall 2004 lecture 311 Lecture #31 Flip-Flops, Clocks, Timing Last lecture: –Finite State Machines This lecture: –Digital circuits with feedback –Clocks –Flip-Flops

2. 11/12/2004EE 42 fall 2004 lecture 312 Clocked Logic In the last few lectures, we have been discussing the implementation of circuits which can break a problem down into a sequence of events, as contrasted with evaluation of a single Boolean expression (Combinatorial Logic)

3. 11/12/2004EE 42 fall 2004 lecture 313 Definition: Combinatorial logic Combinatorial logic is a set of digital gates which produces an output based solely on its current inputs. A combinatorial logic circuit can be described using a truth table

4. 11/12/2004EE 42 fall 2004 lecture 314 Definition: Truth table A Truth table is a description of a digital circuit which is a tabulation of all possible inputs, and the outputs which will result from those inputs. Two combinatorial logic circuits are considered logically equivalent if they have the same truth table

5. 11/12/2004EE 42 fall 2004 lecture 315 Sequential Logic In order to solve more complex problems using a sequence of steps, we looked at the concept of feedback of the output of intermediate results back into the circuit for additional processing. In solving the problems caused by this, we arrived at the finite state machine with latched and clocked feedback.

6. 11/12/2004EE 42 fall 2004 lecture 316 In the next two lectures, we will discuss the implementation of sequential logic, latches, clocks, and the various problems which can occur in dynamic digital logic circuits.

7. 11/12/2004EE 42 fall 2004 lecture 317 R S Q Q' R S Q R' S' Q Q Q' S' R' Memory with Cross-coupled Gates Cross-coupled NOR gates –Similar to inverter pair, with capability to force output to 0 (reset=1) or 1 (set=1) Cross-coupled NAND gates –Similar to inverter pair, with capability to force output to 0 (reset=0) or 1 (set=0)

8. 11/12/2004EE 42 fall 2004 lecture 318 Reset Hold Set Reset Race R S Q \Q 100 Timing Behavior R S Q Q'

9. 11/12/2004EE 42 fall 2004 lecture 319 Race condition on falling edge of S/R If both set and reset are high, then the value latched will be whichever falling edge happens last. If this is controlled by delays in the logic, then the outcome of which is first might be random, erratic, or dependent on other parameters.

10. 11/12/2004EE 42 fall 2004 lecture 3110 Definition: Race, or Race condition A Race condition is when a device's output depends on two [or more] nearly simultaneous events to occur, and where which signal arrives first will change the output of the circuit. If the race condition is so close in time, the output may be unpredictable. When the circuit is manufactured, slight differences can cause a change in the operation of the circuit. A race condition can be a logic hazard, or can result in a random value being held in a latch.

11. 11/12/2004EE 42 fall 2004 lecture 3111 Definition: Glitch, Hazard A Glitch is a momentary output of a digital circuit of an incorrect value A Static Hazard is when a single variable change at the input causes a momentary change in the output. A Dynamic Hazard occurs when a change in the input causes multiple changes in the output. Latches can remove glitches by allowing the output to progress only after the logic has had adequate time to stabilize on the correct output. It is desirable to design out hazard in the logic, because the extra transitions consume power and produce excess noise. If Static Hazards are removed from the design, Dynamic Hazards will not occur. If not removed by latches or Flip-Flops, timing hazards will develop as random or intermittent circuit failures.

12. 11/12/2004EE 42 fall 2004 lecture 3112 Definition: Latch A latch is a digital circuit which will hold a value when the level of a latching signal is at a certain level. For example, while the reset signal is low, the SR latch will hold the value of Q, (and set it if Set goes high). The alternative is to set the output only at an rising or falling edge, which is referred to as being edge triggered.

13. 11/12/2004EE 42 fall 2004 lecture 3113 Level Trigger A level trigger refers to the capture of a value while a signal (clock, for example, is high (or low). The data must be held valid and stable during the entire time it is being sampled Data Clock

14. 11/12/2004EE 42 fall 2004 lecture 3114 enable' S' Q' Q R' R S Gated R-S Latch Control when R and S inputs matter –Otherwise, the slightest glitch on R or S while enable is low could cause change in value stored Set Reset S' R' enable' Q Q' 100

15. 11/12/2004EE 42 fall 2004 lecture 3115 clock R' and S' changingstablechangingstable R-S latch controlled with clock Controlling an R-S latch with a clock –Can't let R and S change while clock is active (allowing R and S to pass) –Only have half of clock period for signal changes to propagate –Signals must be stable for the other half of clock period clock' S' Q' Q R' R S active low

16. 11/12/2004EE 42 fall 2004 lecture 3116 Edge Trigger Edge Trigger refers to the capture of a value at a rising or falling edge of a signal. For example, the data from a memory might be held valid and sampled at a rising edge of a clock Data Clock

17. 11/12/2004EE 42 fall 2004 lecture 3117 Definition: Flip-Flop A flip flop is a digital circuit which will capture a value at a rising (or falling) edge, and will hold that value. It will only change the value held at an edge, and will not pass on transitions from the inputs while the clock or latch signal is either high or low.

18. 11/12/2004EE 42 fall 2004 lecture 3118 clock R SQ Q'R SQ R S Cascading Latches Connect output of one latch to input of another How to stop changes from racing through chain? –Need to control flow of data from one latch to the next –Advance from one latch per clock period –Must worry about logic between latches (arrows) that is too fast

19. 11/12/2004EE 42 fall 2004 lecture 3119 Master-Slave Structure Break flow by alternating clocks (like an air-lock) –Use positive clock to latch inputs into one R-S latch –Use negative clock to change outputs with another R-S latch View pair as one basic unit –master-slave flip-flop –twice as much logic –output changes a few gate delays after the falling edge of clock but does not affect any cascaded flip-flops master stage slave stage P P' CLK R SQ Q'R SQ R S

20. 11/12/2004EE 42 fall 2004 lecture 3120 Set 1s catch S R CLK P P' Q Q' Reset Master Outputs Slave Outputs The 1s Catching Problem In first R-S stage of master-slave FF –0-1-0 glitch on R or S while clock is high "caught" by master stage –Leads to constraints on logic to be hazard-free master stage slave stage P P' CLK R SQ Q'R SQ R S

21. 11/12/2004EE 42 fall 2004 lecture 3121 10 gates D Flip-Flop Make S and R complements of each other –Eliminates 1s catching problem –Can't just hold previous value (must have new value ready every clock period) –Value of D just before clock goes low is what is stored in flip-flop –Can make R-S flip-flop by adding logic to make D = S + R' Q –The value at the output (Q, Q’) only changes based on the value of the falling edge of the clock of the master stage D Q Q' master stage slave stage P P' CLK R SQ Q'R SQ

22. 11/12/2004EE 42 fall 2004 lecture 3122 Edge triggering The proceeding slide showed how a flip flop could be designed by using two latches which are cascaded in a master- slave relationship. Another way of creating an edge triggered flip flop is to use logic with feedback, as in the following slide.

23. 11/12/2004EE 42 fall 2004 lecture 3123 Q D Clk=1 R S Q’ negative edge-triggered D flip-flop (D-FF) 4-5 gate delays must respect setup and hold time constraints to successfully capture input characteristic equation Q(t+1) = D holds D' when clock goes low holds D when clock goes low Edge-Triggered Flip-Flops More efficient solution: only 6 gates –sensitive to inputs only near edge of clock signal (not while high)

24. 11/12/2004EE 42 fall 2004 lecture 3124 Q D Clk=0 R S D D’ D when clock goes high-to-low data is latched when clock is low data is held Edge-Triggered Flip-Flops (cont’d) Step-by-step analysis Q new D Clk=0 R S D D’ D new D  old D

25. 11/12/2004EE 42 fall 2004 lecture 3125 positive edge-triggered FF negative edge-triggered FF D CLK Qpos Qpos' Qneg Qneg' 100 Edge-Triggered Flip-Flops (cont’d) Positive edge-triggered –Inputs sampled on rising edge; outputs change after rising edge Negative edge-triggered flip-flops –Inputs sampled on falling edge; outputs change after falling edge

26. 11/12/2004EE 42 fall 2004 lecture 3126 Timing Methodologies Rules for interconnecting components and clocks –Guarantee proper operation of system when strictly followed Approach depends on building blocks used for memory elements –Focus on systems with edge-triggered flip-flops Found in programmable logic devices –Many custom integrated circuits focus on level-sensitive latches Basic rules for correct timing: –(1) Correct inputs, with respect to time, are provided to the flip-flops –(2) No flip-flop changes state more than once per clocking event

27. 11/12/2004EE 42 fall 2004 lecture 3127 there is a timing "window" around the clocking event during which the input must remain stable and unchanged in order to be recognized clock data changingstable input clock T su ThTh clock data DQDQ Timing Methodologies (cont’d) Definition of terms –clock: periodic event, causes state of memory element to change; can be rising or falling edge, or high or low level –setup time: minimum time before the clocking event by which the input must be stable (Tsu) –hold time: minimum time after the clocking event until which the input must remain stable (Th)

28. 11/12/2004EE 42 fall 2004 lecture 3128 behavior is the same unless input changes while the clock is high DQDQ CLK positive edge-triggered flip-flop DQDQ G CLK transparent (level-sensitive) latch D CLK Qedge Qlatch Comparison of Latches and Flip-Flops

29. 11/12/2004EE 42 fall 2004 lecture 3129 TypeWhen inputs are sampledWhen output is valid unclockedalwayspropagation delay from input change latch level-sensitiveclock highpropagation delay from input change latch(Tsu/Th around fallingor clock edge (whichever is later) edge of clock) master-slaveclock highpropagation delay from falling edge flip-flop(Tsu/Th around fallingof clock edge of clock) negativeclock hi-to-lo transitionpropagation delay from falling edge edge-triggered(Tsu/Th around fallingof clock flip-flopedge of clock) Comparison of Latches and Flip-Flops (cont’d)

30. 11/12/2004EE 42 fall 2004 lecture 3130 all measurements are made from the clocking event that is, the rising edge of the clock Typical Timing Specifications Positive edge-triggered D flip-flop –Setup and hold times –Minimum clock width –Propagation delays (low to high, high to low, max and typical) Th 5ns Tw 25ns Tplh 25ns 13ns Tphl 40ns 25ns Tsu 20ns D CLK Q Tsu 20ns Th 5ns

31. 11/12/2004EE 42 fall 2004 lecture 3131 Definition: Metastability Metastability is a condition in which a latch or a Flip-Flop is exactly balanced between the logic high and logic low states. This can be caused by an asynchronous data signal input to a clocked Flip Flop. The resulting output may stay undefined for some time.

32. 11/12/2004EE 42 fall 2004 lecture 3132 IN Q0 Q1 CLK 100 Cascading Edge-triggered Flip-Flops Shift register –New value goes into first stage –While previous value of first stage goes into second stage –Consider setup/hold/propagation delays (prop must be > hold) CLK IN Q0Q1 DQDQOUT

33. 11/12/2004EE 42 fall 2004 lecture 3133 timing constraints guarantee proper operation of cascaded components assumes infinitely fast distribution of the clock Cascading Edge-triggered Flip- Flops (cont’d) Why this works –Propagation delays exceed hold times –Clock width constraint exceeds setup time –This guarantees following stage will latch current value before it changes to new value T su 4ns T p 3ns T h 2ns In Q0 Q1 CLK T su 4ns T p 3ns T h 2ns

34. 11/12/2004EE 42 fall 2004 lecture 3134 original state: IN = 0, Q0 = 1, Q1 = 1 due to skew, next state becomes: Q0 = 0, Q1 = 0, and not Q0 = 0, Q1 = 1 CLK1 is a delayed version of CLK0 In Q0 Q1 CLK0 CLK1 100 Clock Skew The problem –Correct behavior assumes next state of all storage elements determined by all storage elements at the same time –tThis is difficult in high-performance systems because time for clock to arrive at flip-flop is comparable to delays through logic –Effect of skew on cascaded flip-flops:

35. 11/12/2004EE 42 fall 2004 lecture 3135 Summary of Latches and Flip- Flops Development of D-Flip-Flop –Level-sensitive used in custom integrated circuits can be made with 4 switches –Edge-triggered used in programmable logic devices –Good choice for data storage register Historically J-K Flip Flop was popular but now never used –Similar to R-S but with 1-1 being used to toggle output (complement state) –Can always be implemented using D-FF Preset and clear inputs are highly desirable on flip-flops –Used at start-up or to reset system to a known state