EE 3563 Sequential Logic Design Principles

1. EE 3563 Sequential Logic Design Principles • A sequential logic circuit is one whose outputs depend not only on the current inputs, but also on the past sequence of inputs, possibly arbitrarily far back in time • The book gives the example of changing channels on a TV • A TV with a remote – the old manual dial doesn’t count • A computer would be a more complex example • Can not describe the behavior of a sequential circuit with a simple truth table – output as a function of input • Must know the “state” of the circuit • Collection of state variables whose values at any one time contain all the information necessary to determine the future behavior • In the TV example, the current channel must be known in order to increment/decrement the channel EE 3563 Digital Systems Design

2. EE 3563 Sequential Logic Design Principles • A state variable describes the value of a particular element of a sequential circuit • In the TV example, a state variable would be needed to store the current channel • Could be stored internally any number of ways • 3-digit BCD • Binary number • In digital circuits a state variable has two values • The total number of possible states is 2n where n is the number of binary state variables • You can see that this number can grow large very quickly, but it is finite • Sequential circuits often called finite-state machines • Often, it is impractical to test every possible state transitioning to every other possible state • Say a 3-digit BCD is used for the TV, that’s 12 bits or 4096 states • Would not test every channel change combination EE 3563 Digital Systems Design

3. EE 3563 Sequential Logic Design Principles • State changed occur when the internal clock transitions • The clock is active high when the state change occurs on the rising edge or at a high value • The clock is active low when the state change occurs on the falling edge or when the clock is low • More on rising/falling edges later • Some circuits are designed so some elements are triggered by an active high clock while other elements are triggered by an active low • The clock period (T) is the time between successive changes • The clock frequency is the inverse of the period (f = 1/T) • Frequency of 44.1 KHz has a period of 22.58 μs EE 3563 Digital Systems Design

4. EE 3563 Sequential Logic Design Principles • The first edge in a clock pulse is called the clock tick • State changes occur in lock-step with the clock • Some circuits, called asynchronous circuits, do not completely change state on the tick of the clock, but rather various elements “signal” other elements when they are ready • How do you suppose the TV example implements a clock? EE 3563 Digital Systems Design

5. EE 3563 Sequential Logic Design Principles • The first edge in a clock pulse is called the clock tick • State changes occur in lock-step with the clock • Some circuits, called asynchronous circuits, do not completely change state on the tick of the clock, but rather various elements “signal” other elements when they are ready • How do you suppose the TV example implements a clock? • It doesn’t! Not all sequential circuits require a clock! • The duty cycle is the percentage of time a clock signal is asserted • Does NOT have to be symmetrical EE 3563 Digital Systems Design

6. EE 3563 Sequential Logic Design Principles • Clock Signal EE 3563 Digital Systems Design

7. EE 3563 Sequential Logic Design Principles • Bistable elements have two stable states • The simplest bistable circuit element is shown below • Upon power up, what will be the outputs? EE 3563 Digital Systems Design

8. EE 3563 Sequential Logic Design Principles • Bistable elements have two stable states • The simplest bistable circuit element is shown below • Upon power up, what will be the outputs? • It is analogous to flipping a coin, which could have 1 of 3 possible outcomes, not all equally likely • Heads, Tails, on its side EE 3563 Digital Systems Design

9. EE 3563 Sequential Logic Design Principles • Graph shows behavior of the inverters • Two stable states, one metastable state • In the metastable state, a little noise or power spike could cause the outputs to transition to one of the stable states • Just like a little vibration could cause the coin that landed on its side to fall over EE 3563 Digital Systems Design

10. EE 3563 Sequential Logic Design Principles • Another metastable example • All sequential circuits are susceptible to metastable behavior • This situation manifests itself in situations when the triggering actions for latches and flip flops are marginal • For example, if the clock speed is too high for a particular circuit EE 3563 Digital Systems Design

11. EE3563 Latches and Flip-Flops • Latches and flip-flops are the basic building blocks of most sequential circuits • Flip-flops use a clocking signal to change state • Latches change output at any time , independent of a clocking signal • This is the distinction made by the text • Some texts have been known to use the terms incorrectly, calling a flip-flop a latch • The distinction is important for correct operation of some sequential circuits EE 3563 Digital Systems Design

12. EE3563 Latches and Flip-Flops • S-R (Set-Reset) Latch implemented with NOR gates • S sets Q to one, R resets (clears) Q to zero • Function Table describes the behavior • Doesn’t tell the whole story • Metastable behavior not indicated • Use the functional behavior timing diagram • Note: QN is not always the complement of Q EE 3563 Digital Systems Design

13. EE3563 Latches and Flip-Flops • Functional behavior of an S-R latch • Note the (undesirable) metastable behavior • May enter that state if S and R are negated simultaneously • Since nothing is perfectly “simultaneous” the designers often specify how “close” is considered simultaneous • Usually specified as within 20 ns, but may be different for faster/slower circuits EE 3563 Digital Systems Design

14. EE3563 Latches and Flip-Flops • The S’-R’ Latch – called the S-bar R-bar latch • I don’t have an “overline” in MS Word • Similar to S-R latch, except it has active low sets/resets • May be built from NAND gates • Remembers its state when both inputs are one • When both inputs go to zero, outputs both go to one EE 3563 Digital Systems Design

15. EE3563 Latches and Flip-Flops • The S-R Latch with enable • When the enable input “C” is asserted, behaves just like an S-R latch • When C is deasserted, it remembers its current values • May become metastable if both inputs are one and C goes to zero (deasserted) EE 3563 Digital Systems Design

16. EE3563 Latches and Flip-Flops • The D (data) latch allows the storage of data • Avoids the metastable problem better than the S-R latch • It is essentially an S-R latch with enable and the S input tied to an inverter feeding the R input • The “C” enable input may also be a clock input • When enabled, the latch is transparent EE 3563 Digital Systems Design

17. EE3563 Latches and Flip-Flops • The D latch does not eliminate the metastability problem • Four delay parameters are shown • tpLH(CQ) – time propagation from L to H of Q due to input C • When C is transitioning to zero, the data must be stable for tsetup and thold to avoid metastability problems EE 3563 Digital Systems Design

18. EE3563 Latches and Flip-Flops • Once you use the enable input with a clocking signal, you are working with a flip-flop instead of a latch • We can construct a positive-edge-triggered D flip-flop with a pair of D latches as shown below • It will only change output on the rising edge of the clock • If the input changes while the clock is high, the output will not change triangle indicates edge-triggered behavior EE 3563 Digital Systems Design

19. EE3563 Latches and Flip-Flops • The edge-triggered D flip-flop also has a setup and hold time • If the setup/hold time is not met, the edge-triggered FF will usually become stable (though in an unpredictable state) • It can go metastable or oscillate • Can also have a negative edge-triggered FF • Some D flip-flops have separate set/reset inputs to force the output to a particular state EE 3563 Digital Systems Design

20. EE3563 Latches and Flip-Flops • Negative edge-triggered D-FF EE 3563 Digital Systems Design

21. EE3563 Latches and Flip-Flops • Edge-triggered D-FF with Preset and Clear EE 3563 Digital Systems Design

22. EE3563 Latches and Flip-Flops • Edge triggered D-FF with enable • This can be used to hold a value despite the clock signal EE 3563 Digital Systems Design

23. EE3563 Latches and Flip-Flops • A scan flip-flop is used for testing • Use an alternate source of data during testing • When in testing mode, a pattern can be scanned into all the flip-flops • After loading the test pattern, the flip-flops are put into normal mode and clocked as usual • Two extra inputs are used • Test enable which is simply a pin used to choose between the normal input and the test input • Test input – the alternate D input • All the different flip-flops could be designed with a scan capability EE 3563 Digital Systems Design

24. EE3563 Latches and Flip-Flops • Scan flip-flops EE 3563 Digital Systems Design

25. EE3563 Latches and Flip-Flops • Master/Slave S-R Flip-Flops • Used when we want an S-R FF to change only in synchronization with a clock • Can use S-R latches in place of D latches of the negative edge-triggered flip-flop • Resulting device is not edge triggered because the output depends on the value during the entire time the clock is high • A short pulse can set or reset the master latch • The final output depends upon whether the master latch was set/reset while the clock was high • Changes output to final latched value – value at falling edge of clock • Called a pulse-triggered flip-flop EE 3563 Digital Systems Design

26. EE3563 Latches and Flip-Flops • Master/Slave S-R pulse triggered flip-flop • Metastable behavior occurs if pulsed when both S-R are high postponed output indicator Master Slave S-R Flip-Flop S-R Flip-Flop EE 3563 Digital Systems Design

27. EE3563 Latches and Flip-Flops • Master/Slave J-K Flip-Flop • Solves the problem of when both S and R are asserted simultaneously • J & K inputs are analogous to S-R inputs • However, asserting J asserts the master’s S input only as long as the QN output is one (Q is zero) • Asserting K asserts the master’s R input only if Q is one • If both are asserted at the same time, the flip-flop goes to the opposite of its current state • problem: it is possible for the output to change to a one even though K and not J is asserted at the end of the triggering pulse • Called 1’s catching • Also may have a 0’s catching • J-K inputs MUST be held valid during entire period clock is 1 EE 3563 Digital Systems Design

28. EE3563 Latches and Flip-Flops • Master/Slave J-K flip-flop EE 3563 Digital Systems Design

29. EE3563 Latches and Flip-Flops • Edge-triggered J-K flip-flop • Solves the 1’s catching and 0’s catching problem (as well as the simultaneous input change problem) • Inputs sampled at the rising edge • Have obsoleted the pulse-triggered types • 74x109 is a positive edge-triggered J-K’ flip-flop • K is active low EE 3563 Digital Systems Design

30. EE3563 Latches and Flip-Flops • A T (toggle) flip-flop changes state upon every tick of the clock • May be pos/neg edge-triggered and have an enable • Can be used as a frequency divider • Use one T-FF to divide by two, cascade them for larger divisions EE 3563 Digital Systems Design