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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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?
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
EE 3563 Sequential Logic Design Principles
 Clock Signal
Fall 2004
EE 3563 Digital Systems Design
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?
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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)
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
triangle
indicates
edge-triggered
behavior
 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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
EE3563 Latches and Flip-Flops
 Negative edge-triggered D-FF
Fall 2004
EE 3563 Digital Systems Design
EE3563 Latches and Flip-Flops
 Edge-triggered D-FF with Preset and Clear
Fall 2004
EE 3563 Digital Systems Design
EE3563 Latches and Flip-Flops
 Edge triggered D-FF with enable
 This can be used to hold a value despite the clock signal
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
EE3563 Latches and Flip-Flops
 Scan flip-flops
Fall 2004
EE 3563 Digital Systems Design
EE3563 Latches and Flip-Flops
 Master/Slave S-R Flip-Flops
 Used when we want an S-R FF to change only in
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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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
S-R Flip-Flop
EE 3563 Digital Systems Design
EE3563 Latches and Flip-Flops
 Master/Slave J-K Flip-Flop
 Solves the problem of when both S and R are asserted
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
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

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
Fall 2004
EE 3563 Digital Systems Design
EE3563 Latches and Flip-Flops
 Master/Slave J-K flip-flop
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design
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
Fall 2004
EE 3563 Digital Systems Design