# EEC 116 Lecture #6: Sequential Logic. Rajeevan Amirtharajah University of California, Davis Jeff Parkhurst Intel Corporation

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1 EEC 116 Lecture #6: Sequential Logic Rajeevan Amirtharajah University of California, Davis Jeff Parkhurst Intel Corporation

2 Announcements Lab 3 extended, same due date as Lab 4 HW4 issued today Amirtharajah/Parkhurst, EEC 116 Fall

3 Outline Review: Arithmetic Finish Transmission Gate Circuits and Multipliers Sequential MOS Logic Circuits: Rabaey, (Kang & Leblebici, ) Next Topic: Latchup and Layout Guidelines Amirtharajah/Parkhurst, EEC 116 Fall

4 Sequential Logic Basic Definition Combinational circuits output is a function of the circuit inputs and a delay time Examples: NAND, NOR, XOR, adder, multiplier Sequential circuits output is a function of the circuit inputs, previous circuit state, and a delay time Examples: Latches, flip-flops, FSMs, pipelined adders and multipliers, microprocessors Sequential elements are critical to implementing techniques such as feedback or blocks such as memory Amirtharajah/Parkhurst, EEC 116 Fall

5 Sequential Logic Example: Mealy FSM In LOGIC t p,comb Out Φ Two information storage mechanisms Positive feedback-based (static) circuits Charge storage-based (dynamic) circuits Clock signal Φ controls timing of state (memory) updates Amirtharajah/Parkhurst, EEC 116 Fall

6 Positive Feedback: Bistability V i1 V = V 2 o1 i2 V o A V = V i1 o2 V = V C (metastable) i2 o1 V = V i1 o2 Amirtharajah/Parkhurst, EEC 116 Fall B

7 Metastability A A V o1 =V i2 C V o1 =V i2 C B B δ V i1 =V o2 δ V i1 =V o2 Gain should be larger than 1 in the transition region Amirtharajah/Parkhurst, EEC 116 Fall

8 Bistable Elements Bistable elements have two stable states or operation modes Cross-coupled inverters are the most basic bistable element Circuit forms the basis of latches and SRAM memory Stable points on the VTC are those with the lowest energy Points with high energy are unstable, perturbations are amplified Amirtharajah/Parkhurst, EEC 116 Fall

9 Set-Reset (SR) Latch Change inverters to NAND or NOR gates, with second inputs = S(set) and R(reset) S S R R Allows control of the state of the bistable element One input state is not allowed Gating S and R with the clock prevents the latch from responding except during one phase of the clock cycle Amirtharajah/Parkhurst, EEC 116 Fall

10 SR Latch Sequential circuits: circuits which store state : circuits with memory elements Latches: store previous output value for certain input combinations SR latch (NAND-based): S R not allowed memory S R next next Amirtharajah/Parkhurst, EEC 116 Fall

11 Clocked SR latch Other Latches Adds clock input. Latch output can only be set/reset when clk=1 (or clk=0) Other latch types: JK latch: Removes not allowed state e.g., toggles when inputs are both 1 T latch: Toggles when T input = 1 D latch: Output = D input Amirtharajah/Parkhurst, EEC 116 Fall

12 Latch Circuits Many methods for implementing latches Standard CMOS gates (cross-coupled NAND, etc) Transmission gates Tri-state inverters en A en tri-state inverter F When en=0, F is floating, i.e. high impedance Amirtharajah/Parkhurst, EEC 116 Fall

13 Positive Dynamic Transmission Gate Latch D I0 C 0 No feedback devices Data stored on input capacitance of inverter I0 Dynamic logic issues apply: leakage, capacitive coupling, charge sharing Amirtharajah/Parkhurst, EEC 116 Fall

14 Transmission Gate Positive Static Latch D Amirtharajah/Parkhurst, EEC 116 Fall

15 Positive Static Latch Timing Diagram D Amirtharajah/Parkhurst, EEC 116 Fall

16 NMOS Pass Gate Positive Static Latch D VDD V Tn Fewer devices, less area, lower clock load Threshold drop on internal nodes implies more static power, less noise margin Amirtharajah/Parkhurst, EEC 116 Fall

17 Master-Slave Flip-Flop By cascading two level-sensitive latches, one type of edge triggered flip-flop is created JK latch can be used for first stage so that no input combinations are invalid SR latch is then used for the second stage because inputs cannot be invalid Rather than using logic gate-based latches, can cascade latches such as above (e.g., transmission gate dynamic or static latches) Amirtharajah/Parkhurst, EEC 116 Fall

18 Edge-Triggered Flip-Flops Types of latches/flip-flops: Level-sensitive: output is set when clock is a certain level (0 or 1) Edge-triggered: output can only be set on a clock edge (rising or falling) Advantages of edge-triggered flip-flops: Data only needs to be stable at clock edge Reduces race conditions: potential errors where an input data change travels through multiple latches during their transparent phase Amirtharajah/Parkhurst, EEC 116 Fall

19 Safest Edge-Triggered Flip-Flop Master Slave Amirtharajah/Parkhurst, EEC 116 Fall

20 Edge-Triggered Flip-Flop Timing Diagram D Amirtharajah/Parkhurst, EEC 116 Fall

21 Dynamic Positive Edge-Triggered FF D I0 I1 C0 C1 No feedback devices Data stored on input capacitances of inverters I0 and I1 Dynamic logic issues apply: leakage, capacitive coupling, charge sharing Amirtharajah/Parkhurst, EEC 116 Fall

22 Timing definitions: Clocked Circuit Timing Clock-to- or Propagation Delay (t clk ): delay of flip-flop from clock edge to output Setup Time (t setup ): amount of time before clock edge that data has to be stable. If data arrives after this time, it will not be latched correctly. Hold Time (t hold ): amount of time after clock edge that data has to be stable. It is possible to trade off setup and hold time with flip-flop circuit design Modify data and clock timing relationship by delaying one of the two signals Amirtharajah/Parkhurst, EEC 116 Fall

23 Flip-Flop: Timing Definitions φ t In t setup t hold DATA STABLE t Out t pff DATA STABLE t From Digital Integrated Circuits Jan Rabaey Notes Amirtharajah/Parkhurst, EEC 116 Fall

24 Maximum Clock Frequency In LOGIC t p,comb Out t pff + t p Φ + t < T =, comb setup Signals must propagate out of flip-flop, through combinational logic, and be stable before next clock edge (clock period = T, clock frequency = f) Amirtharajah/Parkhurst, EEC 116 Fall f

25 Staticized Dynamic Positive Edge-Triggered FF I1 I3 D I0 I2 C0 C1 Use weak feedback inverters to enhance robustness Returns to reduced clock load static flip-flop with same sizing issues Amirtharajah/Parkhurst, EEC 116 Fall

26 Clock Overlap Failures B D A 1. Both high simultaneously, race condition from D to 2. Node A can be driven simultaneously by D and B Amirtharajah/Parkhurst, EEC 116 Fall

27 Race Through and Feedback Paths B D A 1. Both high simultaneously, race condition from D to 2. Node A can be driven simultaneously by D and B Amirtharajah/Parkhurst, EEC 116 Fall

28 Nonoverlapping Clocks Methodology PHI0 B D A PHI1 PHI1 PHI0 PHI0 PHI1 Guarantee nonoverlap period long enough Note: internal nodes left high Z during nonoverlap Amirtharajah/Parkhurst, EEC 116 Fall

29 C 2 MOS Edge Triggered Flip-Flop D C0 C1 Tristate inverters eliminate clock overlap race condition Amirtharajah/Parkhurst, EEC 116 Fall

30 Zero-Zero Overlap Condition Gnd Gnd D C0 C1 Both phases low simultaneously enables opposite nets Amirtharajah/Parkhurst, EEC 116 Fall

31 High-High Overlap Condition D V DD V DD C0 C1 Both phases high simultaneously enables opposite nets Amirtharajah/Parkhurst, EEC 116 Fall

32 C 2 MOS Design Clock overlap problems eliminated as long as rise and fall times remain fast Slow rise / fall times imply pullup and pulldown nets on simultaneously resulting in potential errors, static power Dynamic flip-flop style leaves output high Z Must take care when using since output wire could be exposed to many more noise sources than internal nodes Mix and match styles by using C 2 MOS as master and other types of latch as slave Clock load small, but potentially larger than transmission gate dynamic latches due to PMOS sizing Amirtharajah/Parkhurst, EEC 116 Fall

33 Pipelining a REG a REG φ. log REG Out φ REG. REG log REG Out b REG φ φ b REG φ φ Non-pipelined version Pipelined version φ φ From Digital Integrated Circuits Jan Rabaey Notes Amirtharajah/Parkhurst, EEC 116 Fall

34 Next Topic: Latchup and Layout Guidelines Latchup Minimizing area Managing complexity Amirtharajah/Parkhurst, EEC 116 Fall

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