Announcements
• Assignment 7 posted, due Friday 18th
• All project components ordered
• Dates
– Thursday 12/1 review lecture
– Tuesday 12/6 project demonstrations in the lab
(no presentations)
– Sunday 12/11 project reports due to me by
email
– Tuesday 12/13 final exam, 1pm-3pm here.
Lecture 20 Overview
• Sequential Logic
• Timing Methodology
• Registers and counters.
Sequential Logic
• So far we have dealt mainly with combinational logic arrays of gates which have an output determined by the
present state of the inputs
• output=f(present inputs)
• Sequential logic deals with devices with memory - where
the output depends on the present and past states of the
inputs and outputs
http://fac-web.spsu.edu/cs/faculty/bbrown/web_lectures/sequential/
Principal of sequential circuits
• A simple example: This thermostat system has loops. The output of the temperature
changing functions affects the input of the temperature-checking function. Its output
affects the operation of the temperature changing function(s).
• Sequential circuits use feedback – results (outputs) are fed back as input
• outputs=f(present inputs, past inputs, past outputs)
• This means the logic circuit has "memory”
Summary of latches and flip-flops
• Flip-flops come in two main types
– Level sensitive; usually called a latch simplest type, can be made with as few as
four switches (two cross-coupled logic gates)
– Edge-triggered (e.g. master-slave, D-type)
• A clock or enable input is used to specify
when a change to the input matters
Compare Latches and Flip-Flops
Note the inversion
symbols at the
CLK inputs
The behaviour is the same unless the input changes
while the clock is low. The latch is transparent when
the clock is low - any change on the input is reflected
on the output. The edge-triggered FF is only affected
by the input present at the clock edge
http://fac-web.spsu.edu/cs/faculty/bbrown/web_lectures/sequential/
Edge triggered Flip-Flops
• Two basic types
• Positive-edge triggered: Inputs are sampled on the rising edge of the clock
pulse. Outputs change after the rising edge
• Negative-edge triggered: Inputs are sampled on the falling edge of the clock
pulse. Outputs change after the falling edge
Timing methodologies
• What are TSU, TH, Propagation time?
• Timing specifications describe the rules for
interconnecting components and clocks
– They guarantee correct operation of the system when
strictly followed
• The correct approach depends on which building
blocks are used as memory elements
– i.e. edge-triggered flip-flops or level sensitive latches
• Basic rules for correct timing
– correct inputs, with respect to time, must be provided
to the flip-flops
– No flip-flop changes state more than once per
clocking event
• Definitions
Timing Methodologies
– Clock event:
• a periodic event. Causes state of memory element to change. Can be a
rising edge, falling edge or a high level or low level.
– Setup Time:
• Minimum time before the clocking event during which the input to the flip-flop
must be stable (Tsu)
– Hold Time:
• Minimum time after the clocking event during which the input to the flip-flop
must remain stable (Th)
– Propagation Delay:
• Time take for an input change to be reflected on the output
Typical Timing Specifications
• Example: A positive edge-triggered D flip-flop will have
specified
– setup and hold times (Tsu and Th)
– minimum clock pulse width (Tw)
– propagation delays (low to high (Tplh), high to low (Tphl), max and
typical)
All measurements are made from the clocking event - in this case the rising
edge of the clock.
www.onsemi.com/pub_link/Collateral/74HC74.PDF
Dealing with Timing Specifications
Divide circuit into combinational
logic and flip-flop
Combinational
Logic
D
Q
FF
Q
FF
Q
D
D
FF
Xn
Xn+1
T
CLK
Dealing with Timing Specifications
Logic(TP)
Divide circuit into combinational
logic and flip-flop
Xn+1
Xn+2
Combinational
Logic
D
Q
FF
Q
FF
Q
D
D
FF
T
Xn+1 FF(TP)
CLK
Xn+2 must be
ready FF(TSU)
before clock
edge
Dealing with Timing Specifications
Logic(TP)
Divide circuit into combinational
logic and flip-flop
Xn+1
Xn+2
Combinational
Logic
D
Q
FF
Defines minimum clock period:
T > FF(TP) + Logic(TP) + FF(TSU)
Q
FF
Q
D
D
FF
T
Xn+1 FF(TP)
CLK
Xn+2 must be
ready FF(TSU)
before clock
edge
Other Flip-flop features
• As well as input (D), clock (C) and output
(Q, Q'), often have additional features:
• Reset – forces output state to 0: R
– Synchronous: Q=R'·D (when next clock edge
arrives)
– Asynchronous: Doesn't wait for next clock edge;
quick but dangerous
• Preset (or Set) - forces state to 1: S (or P)
– Synchronous: Q=D+S (when next clock edge
arrives)
– Asynchronous
• Both Reset and Preset
– Q=R'·D+S
– Q=R'·D+R'·S
(set-dominant)
(reset-dominant)
Other Flip-flop features
•
Selective input capability (input enable or load): LD or EN
– multiplexer at input: Qnew=LD'·Qold+LD·D
– So, LD=0 : Qnow=Qold
– LD=1: Qnow=D
– load may or may not override reset/set (usually R/S have priority)
•Note: all unused inputs should be tied either HIGH or LOW.
Using Flip-Flops: Registers
• Collections of flip-flops with similar controls and logic
– Stored values are somehow related (for example, they form a binary
number)
– Share clock, reset and set lines
– A register is a group of memory elements read or written as a unit
• Examples
– storage register
– shift register
– Counters
Parallel Output
This is the simplest form of
register: a parallel
input/output register.
A Clock signal causes the
inputs to be read and
stored and made available
at the outputs.
Stores bits, but does
nothing with them
Parallel Input
Shift Register
• Often, however, the bits will not arrive in parallel but in
serial - one bit at a time
– Use a shift register
– Input is applied to first flip-flop and shifted along one at each
clock event
– This example is a 4-bit shift register
– It accepts serial input, stores the last 4 bits in the sequence and
makes them available as parallel output
Parallel Output
Serial Input
Shift Register
• Often, however, the bits will not arrive in parallel but in
serial - one bit at a time
– Use a shift register
– Input is applied to first flip-flop and shifted along one at each
clock event
– This example is a 4-bit shift register
– It accepts serial input, stores the last 4 bits in the sequence and
makes them available as parallel output
Parallel Output
Serial Input
http://www.ee.usyd.edu.au/tutorials/digital_tutorial/part2/register03.html
Universal Shift Register
• Holds 4 values
– serial or parallel inputs
– serial or parallel outputs
– permits shift right or left
– new values can be applied from left or right
Shift Register Application
•
Often only one line is available for data transmission (eg computer networks)
– Shift register can perform parallel to serial conversion at one end
– serial to parallel conversion at the other
Another Application: Pattern recognizer
• Performs some combinational function of input samples
– In this case, recognizing the pattern 1001 on the single input line
01001
Digital counters: Ripple (Asynchronous) Counters
Counters are sequential logic circuits that proceed through a welldefined sequence of states.
For a "divide-by-2" counter, simply connect the Q' output to the D input
and feed an external clock signal in as the input:
+'ve edge-triggered D flipflop
Output
Input
Input
Output
For a "divide-by-4" counter, connect 2 flipflops together in a chain:
Input
Input
Output
Output
• For a "divide-by-n" : connect 2n flipflops together.
• Note that the FF outputs do not change at exactly the same time because of
the propagation delay in each FF.
• These counters are known as ripple or asynchronous counters.
Synchronous Counters
• Connect all flip-flops to the same clock
• All flipflops change state at the same time (synchronous)
• A counter is a device which sequences through a fixed set of patterns
• in this case, 1000, 0100, 0010, 0001 (if one of these patterns is the
initial state, defined by set/reset)
• Counts to n (n=number of flipflops) before repeating
• Mobius (or Johnson) Counter
• in this case, get 1000, 1100, 1110, 1111, 0111, 0011, 0001, 0000
• counts to 2*n before repeating
http://www.ee.usyd.edu.au/tutorials/digital_tutorial/part2/register07.html
Binary Counter
D
• We normally want to count in a more useful fashion: e.g.
binary
• This requires combinational logic between the flipflops
• Need a rule for binary counting
•"The least significant bit always changes"
• "A bit changes state if all less significant bits are
HIGH"
• Can implement this with an XOR gate
• Note Xxor1=X'
A
So
A+=Axor1,
B+=BxorA,
B
C+=CxorAB,
C
D+=DxorABC
D
A
Decimal
Binary
Hex
0
0000
0
1
0001
1
2
0010
2
3
0011
3
4
0100
4
5
0101
5
6
0110
6
7
0111
7
8
1000
8
9
1001
9
10
1010
A
11
1011
B
12
1100
C
13
1101
D
14
1110
E
15
1111
F
Binary Down Counter
A
D
• How do you modify this circuit to count down?
• The rule is
• "The least significant bit always changes"
• "A bit changes state if all less significant
bits are LOW"
• Note AXOR1=A'
AXNOR0=A'
A
So
A+=Axor1,
B+=BxnorA,
B
C
C+=CxnorAB,
D
D+=DxnorABC
Decimal
Binary
Hex
0
0000
0
1
0001
1
2
0010
2
3
0011
3
4
0100
4
5
0101
5
6
0110
6
7
0111
7
8
1000
8
9
1001
9
10
1010
A
11
1011
B
12
1100
C
13
1101
D
14
1110
E
15
1111
F
Binary Counters
• Counters can be bought pre-packaged: e.g. a synchronous four-bit binary upcounter
• Standard component with many applications
•Typical features:
• Positive edge-triggered FFs with synchronous LOAD and CLEAR inputs
• LOAD input allows parallel load of data from D, C, B, A
• CLEAR input resets outputs to 0000
• EN input: must be asserted to enable counting
• RCO: ripple-carry output used for cascading counters
• High when counter is in its highest state 1111
• Implemented using an AND gate: RCO= QA·QB·QC·QD
EN
D
C
RCO
B
QD
A
QC
LOAD QB
QA
CLK
CLR
Binary Counters
• For an 8-bit synchronous binary up counter, cascade two
4-bit devices together
• Connect RCO from the first to EN of the second
Offset Counters
• Two types; for a "starting offset counter" use the
synchronous LOAD input.
• The counter counts like this:
•0110,0111,1000,1001,1010,1011,1100,1101,1111,0110,...
Load value 0110
• For an "ending offset counter" use a comparator for the
ending value
• The counter counts like this:
•0000,0001,0010, ... , 1100,1101,0000, ....
Sequential Logic Summary
• Fundamental building blocks of circuits with memory
– latch and flipflop
– R-S latch, R-S master-slave flipflop, D master-slave flipflop,
edge-triggered D flipflop
• Timing Methodologies
– use of clocks
• Basic registers
–
–
–
–
Storage register
Shift registers
pattern detectors
counters