Sequential logic - University of Washington · 2006-10-24 · Sequential logic Sequential circuits...
Transcript of Sequential logic - University of Washington · 2006-10-24 · Sequential logic Sequential circuits...
Autumn 2006 CSE370 - IV - Sequential Logic 1
Sequential logic
Sequential circuitssimple circuits with feedbacklatchesedge-triggered flip-flops
Timing methodologiescascading flip-flops for proper operationclock skew
Basic registersshift registerssimple counters
Hardware description languages and sequential logic
Autumn 2006 CSE370 - IV - Sequential Logic 2
X1X2•••
Xn
switchingnetwork
Z1Z2•••
Zn
Circuits with feedback
How to control feedback?what stops values from cycling around endlessly
Autumn 2006 CSE370 - IV - Sequential Logic 3
"remember"
"load""data" "stored value"
"0"
"1"
"stored value"
Simplest circuits with feedback
Two inverters form a static memory cellwill hold value as long as it has power applied
How to get a new value into the memory cell?selectively break feedback pathload new value into cell
Autumn 2006 CSE370 - IV - Sequential Logic 4
R
S
Q
Q'
RS
Q
R'S'
Q'
S'
R'
Memory with cross-coupled gates
Cross-coupled NOR gatessimilar to inverter pair, with capability to force output to 0 (reset=1) or 1 (set=1)
Cross-coupled NAND gatessimilar to inverter pair, with capability to force output to 0 (reset=0) or 1 (set=0)
Autumn 2006 CSE370 - IV - Sequential Logic 5
Reset Hold Set SetReset Race
R
S
Q
\Q
100
Timing behavior
R
S
Q
Q'
Autumn 2006 CSE370 - IV - Sequential Logic 6
S R Q0 0 hold0 1 01 0 11 1 unstable
State behavior or R-S latch
Truth table of R-S latch behavior
Q Q'0 1
Q Q'1 0
Q Q'0 0
Q Q'1 1
R
S
Q
Q'
Autumn 2006 CSE370 - IV - Sequential Logic 7
Theoretical R-S latch behavior
State diagramstates: possible valuestransitions: changesbased on inputs
Q Q'0 1
Q Q'1 0
Q Q'0 0
Q Q'1 1
SR=10SR=00SR=01
SR=11
R
S
Q
Q'
Autumn 2006 CSE370 - IV - Sequential Logic 8
Theoretical R-S latch behavior
State diagramstates: possible valuestransitions: changesbased on inputs
Q Q'0 1
Q Q'1 0
Q Q'0 0
Q Q'1 1
SR=10
SR=01SR=00SR=10
SR=00SR=01
SR=11 SR=11
R
S
Q
Q'
Autumn 2006 CSE370 - IV - Sequential Logic 9
Theoretical R-S latch behavior
State diagramstates: possible valuestransitions: changesbased on inputs
Q Q'0 1
Q Q'1 0
Q Q'0 0
Q Q'1 1
SR=00
SR=10
SR=01SR=00SR=10
SR=00SR=01
SR=11 SR=11
SR=01 SR=10
SR=11
R
S
Q
Q'
Autumn 2006 CSE370 - IV - Sequential Logic 10
Theoretical R-S latch behavior
State diagramstates: possible valuestransitions: changesbased on inputs
Q Q'0 1
Q Q'1 0
Q Q'0 0
Q Q'1 1
SR=00SR=11SR=00
SR=10
SR=01SR=00SR=10
SR=00SR=01
SR=11 SR=11
SR=10SR=01
SR=01 SR=10
SR=11
possible oscillationbetween states 00 and 11
R
S
Q
Q'
Autumn 2006 CSE370 - IV - Sequential Logic 11
Observed R-S latch behavior
Very difficult to observe R-S latch in the 1-1 stateone of R or S usually changes first
Ambiguously returns to state 0-1 or 1-0a so-called "race condition"or non-deterministic transition
SR=00SR=00
Q Q'0 1
Q Q'1 0
Q Q'0 0
SR=10
SR=01SR=00SR=10
SR=00SR=01
SR=11 SR=11
SR=01 SR=10
SR=11
R
S
Q
Q'
Autumn 2006 CSE370 - IV - Sequential Logic 12
Q(t+∆)
RS
Q(t)
S R Q(t) Q(t+∆)0 0 0 00 0 1 10 1 0 00 1 1 01 0 0 11 0 1 11 1 0 X1 1 1 X
hold
reset
set
not allowed characteristic equationQ(t+∆) = S + R’ Q(t)
R-S latch analysis
Break feedback path
R
S
Q
Q'
0 0
1 0
X 1
X 1Q(t)
R
S
Autumn 2006 CSE370 - IV - Sequential Logic 13
R’
S’ Q
Q'
Activity: R-S latch using NAND gates
characteristic equationQ(t+∆) =
Q(t)
R
S
S R S’ R’ Q(t) Q(t+∆)0 0 1 1 00 0 1 1 10 1 1 0 00 1 1 0 11 0 0 1 01 0 0 1 11 1 0 0 01 1 0 0 1
Autumn 2006 CSE370 - IV - Sequential Logic 14
R’
S’ Q
Q'
Activity: R-S latch using NAND gates
characteristic equationQ(t+∆) = S + R’ Q(t)
R’S’
Q(t)
0 0
1 0
X 1
X 1Q(t)
R
S
S R S’ R’ Q(t) Q(t+∆)0 0 1 1 0 00 0 1 1 1 10 1 1 0 0 00 1 1 0 1 01 0 0 1 0 11 0 0 1 1 11 1 0 0 0 X1 1 0 0 1 X
hold
reset
set
not allowed
Autumn 2006 CSE370 - IV - Sequential Logic 15
enable'
S'Q'
QR' 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
Autumn 2006 CSE370 - IV - Sequential Logic 16
period
duty cycle (in this case, 50%)
Clocks
Used to keep timewait long enough for inputs (R' and S') to settlethen allow to have effect on value stored
Clocks are regular periodic signalsperiod (time between ticks)duty-cycle (time clock is high between ticks - expressed as % of period)
Autumn 2006 CSE370 - IV - Sequential Logic 17
clock’
R’ and S’
changing stable changing stablestable
Clocks (cont’d)
Controlling an R-S latch with a clockcan'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 propagatesignals must be stable for the other half of clock period
clock’
S’Q’
QR’ R
S
Autumn 2006 CSE370 - IV - Sequential Logic 18
clock
R
S Q
Q’ R
S Q
Q’R
S
Cascading latches
Connect output of one latch to input of anotherHow to stop changes from racing through chain?
need to be able to control flow of data from one latch to the nextmove one latch per clock periodhave to worry about logic between latches (arrows) that is too fast
Autumn 2006 CSE370 - IV - Sequential Logic 19
Master-slave structure
Break flow by alternating clocks (like an air-lock)use positive clock to latch inputs into one R-S latchuse negative clock to change outputs with another R-S latch
View pair as one basic unitmaster-slave flip-floptwice as much logicoutput changes a few gate delays after the falling edge of clockbut does not affect any cascaded flip-flops
master stage slave stage
P
P’
CLK
R
S Q
Q’ R
S Q
Q’R
S
Autumn 2006 CSE370 - IV - Sequential Logic 20
10 gates
D flip-flop
Make S and R complements of each othereliminates 1s catching problemcan'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-flopcan make R-S flip-flop by adding logic to make D = S + R’ Q
D Q
Q’
master stage slave stage
P
P’
CLK
R
S Q
Q’ R
S Q
Q’
Autumn 2006 CSE370 - IV - Sequential Logic 21
Q
D
Clk=1
R
S
0
D’
0
D’ D
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 equationQ(t+1) = D
holds D’ whenclock goes low
holds D whenclock goes low
Edge-triggered flip-flops using gates
Only 6 gatessensitive to inputs only near edge of clock signal (not while high)
D Q
Autumn 2006 CSE370 - IV - Sequential Logic 22
Edge-triggered flip-flops using transistors
Only 8 transistors
D Q
D Q
D
clk
Q
clk’
clk’ clk
D
clk’
Q
clk
clk clk’
Autumn 2006 CSE370 - IV - Sequential Logic 23
positive edge-triggered FF
negative edge-triggered FF
DCLK
QposQpos’QnegQneg’
100
Edge-triggered flip-flops (cont’d)
Positive edge-triggeredinputs sampled on rising edge; outputs change after rising edge
Negative edge-triggered flip-flopsinputs sampled on falling edge; outputs change after falling edge
Autumn 2006 CSE370 - IV - Sequential Logic 24
Timing methodologies
Rules for interconnecting components and clocksguarantee proper operation of system when strictly followed
Approach depends on building blocks used for memory elements
we'll focus on systems with edge-triggered flip-flopsfound in programmable logic devices
many custom integrated circuits focus on level-sensitive latchesBasic 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
Autumn 2006 CSE370 - IV - Sequential Logic 25
there is a timing "window" around the clocking event during which the input must remain stable and unchanged in order to be recognized
clock
datachangingstable
input
clock
Tsu Th
clock
dataD Q D Q
Timing methodologies (cont’d)
Definition of termsclock: periodic event, causes state of memory element to change
can be rising edge or falling edge or high level or low levelsetup 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)
Autumn 2006 CSE370 - IV - Sequential Logic 26
behavior is the same unless input changeswhile the clock is high
D Q
CLK
positiveedge-triggered
flip-flop
D QG
CLK
transparent(level-sensitive)
latch
D
CLK
Qedge
Qlatch
Comparison of latches and flip-flops
Autumn 2006 CSE370 - IV - Sequential Logic 27
Type When inputs are sampled When output is valid
unclocked always propagation delay from input changelatch
level-sensitive clock high propagation delay from input changelatch (Tsu/Th around falling or clock edge (whichever is later)
edge of clock)
master-slave clock hi-to-lo transition propagation delay from falling edgeflip-flop (Tsu/Th around falling of clock
edge of clock)
negative clock hi-to-lo transition propagation delay from falling edgeedge-triggered (Tsu/Th around falling of clockflip-flop edge of clock)
Comparison of latches and flip-flops (cont’d)
Autumn 2006 CSE370 - IV - Sequential Logic 28all measurements are made from the clocking event (the rising edge of the clock)
Typical timing specifications
Positive edge-triggered D flip-flopsetup and hold timesminimum clock widthpropagation delays (low to high, high to low, max and typical)
D
Clk
Q
T su1.8ns
T h 0.5ns
T w 3.3 ns
T pd3.6 ns 1.1 ns
T su1.8ns
T h 0.5 ns
T pd3.6 ns 1.1 ns
T w 3.3 ns
Autumn 2006 CSE370 - IV - Sequential Logic 29
IN
Q0
Q1
CLK
100
Cascading edge-triggered flip-flops
Shift registernew value goes into first stagewhile previous value of first stage goes into second stageconsider setup/hold/propagation delays (prop must be > hold)
CLK
INQ0 Q1
D Q D Q OUT
Autumn 2006 CSE370 - IV - Sequential Logic 30
timing constraintsguarantee proper
operation ofcascaded components
assumes infinitely fast distribution of the clock
Cascading edge-triggered flip-flops (cont’d)
Why this workspropagation delays exceed hold timesclock width constraint exceeds setup timethis guarantees following stage will latch current value before it changes to new value
Tsu1.8ns
Tp1.1-3.6ns
Th0.5ns
In
Q0
Q1
CLK
Tsu1.8ns
Tp1.1-3.6ns
Th0.5ns
Autumn 2006 CSE370 - IV - Sequential Logic 31
original state: IN = 0, Q0 = 1, Q1 = 1due to skew, next state becomes: Q0 = 0, Q1 = 0, and not Q0 = 0, Q1 = 1
CLK1 is a delayedversion of CLK0
InQ0Q1
CLK0CLK1
100
Clock skew
The problemcorrect behavior assumes next state of all storage elementsdetermined by all storage elements at the same timethis is difficult in high-performance systems because time for clockto arrive at flip-flop is comparable to delays through logiceffect of skew on cascaded flip-flops:
Autumn 2006 CSE370 - IV - Sequential Logic 32
Summary of latches and flip-flops
Development of D-FFlevel-sensitive used in custom integrated circuits
can be made with 8 switchesedge-triggered used in modern programmable logic devicesgood choice for data storage register
Historically J-K FF was popular but now never usedsimilar to R-S but with 1-1 being used to toggle output (complement state)good in days of TTL/SSI (more complex input function: D = J Q’ + K’ Qcan always be implemented using D-FF
Preset and clear inputs are highly desirable on flip-flopsused at start-up or to reset system to a known state
Autumn 2006 CSE370 - IV - Sequential Logic 33
Flip-flop features
Reset (set state to 0) – Rsynchronous: Dnew = R' • Dold (when next clock edge arrives)asynchronous: doesn't wait for clock, quick but dangerous
Preset or set (set state to 1) – S (or sometimes P)synchronous: Dnew = Dold + S (when next clock edge arrives)asynchronous: doesn't wait for clock, quick but dangerous
Both reset and presetDnew = R' • Dold + S (set-dominant)Dnew = R' • Dold + R'S (reset-dominant)
Selective input capability (input enable or load) – LD or ENmultiplexor at input: Dnew = LD' • Q + LD • Doldload may or may not override reset/set (usually R/S have priority)
Complementary outputs – Q and Q'
Autumn 2006 CSE370 - IV - Sequential Logic 34
R S R S R SD Q D Q D Q D Q
OUT1 OUT2 OUT3 OUT4
CLK
IN1 IN2 IN3 IN4
R S
"0"
Registers
Collections of flip-flops with similar controls and logicstored values somehow related (for example, form binary value)share clock, reset, and set linessimilar logic at each stage
Examplesshift registerscounters
Autumn 2006 CSE370 - IV - Sequential Logic 35
D Q D Q D Q D QIN
OUT1 OUT2 OUT3 OUT4
CLK
Shift register
Holds samples of inputstore last 4 input values in sequence4-bit shift register:
Autumn 2006 CSE370 - IV - Sequential Logic 36
clear sets the register contentsand output to 0
s1 and s0 determine the shift function
s0 s1 function0 0 hold state0 1 shift right1 0 shift left1 1 load new input
left_inleft_out
right_out
clearright_in
output
input
s0s1
clock
Universal shift register
Holds 4 valuesserial or parallel inputsserial or parallel outputspermits shift left or rightshift in new values from left or right
Autumn 2006 CSE370 - IV - Sequential Logic 37
Nth cell
DQ
CLK
Q[N-1](left)
Q[N+1](right)
Input[N]
to N-1th cell
to N+1th cell
clear s0 s1 new value1 – – 00 0 0 output0 0 1 output value of FF to left (shift right)0 1 0 output value of FF to right (shift left)0 1 1 input
Design of universal shift register
Consider one of the four flip-flopsnew value at next clock cycle:
s0 and s1control mux0 1 2 3
CLEAR
Autumn 2006 CSE370 - IV - Sequential Logic 38
parallel inputs
parallel outputs
serial transmission
Shift register application
Parallel-to-serial conversion for serial transmission
Autumn 2006 CSE370 - IV - Sequential Logic 39
D Q D Q D Q D QIN
OUT1 OUT2 OUT3 OUT4
CLK
OUT
Pattern recognizer
Combinational function of input samplesin this case, recognizing the pattern 1001 on the single input signal
Autumn 2006 CSE370 - IV - Sequential Logic 40
D Q D Q D Q D QIN
OUT1 OUT2 OUT3 OUT4
CLK
Counters
Sequences through a fixed set of patternsin this case, 1000, 0100, 0010, 0001if one of the patterns is its initial state (by loading or set/reset)
Autumn 2006 CSE370 - IV - Sequential Logic 41
Activity
How does this counter work?
D Q D Q D Q D QIN
OUT1 OUT2 OUT3 OUT4
CLK
Autumn 2006 CSE370 - IV - Sequential Logic 42
Activity
How does this counter work?
D Q D Q D Q D QIN
OUT1 OUT2 OUT3 OUT4
CLK
Counts through the sequence: 1000, 1100, 1110, 1111, 0111, 0011, 0001, 0000
Known as Mobius (or Johnson) counter
Autumn 2006 CSE370 - IV - Sequential Logic 43
D Q D Q D Q D Q
OUT1 OUT2 OUT3 OUT4
CLK
"1"
Binary counter
Logic between registers (not just multiplexer)XOR decides when bit should be toggledalways for low-order bit,only when first bit is true for second bit,and so on
Autumn 2006 CSE370 - IV - Sequential Logic 44
EN
DCBALOADCLKCLR
RCOQDQCQBQA
(1) Low order 4-bits = 1111
(2) RCO goes high
(3) High order 4-bits are incremented
Four-bit binary synchronous up-counter
Standard component with many applicationspositive edge-triggered FFs w/ synchronous load and clear inputsparallel load data from D, C, B, Aenable inputs: must be asserted to enable countingRCO: ripple-carry out used for cascading counters
high when counter is in its highest state 1111implemented using an AND gate
Autumn 2006 CSE370 - IV - Sequential Logic 45
EN
DCBALOADCLKCLR
RCOQDQCQBQA
"1"
"0""0""0""0"
"0"
EN
DCBALOADCLKCLR
RCOQDQCQBQA
"1"
"0""1""1""0"
Offset counters
Starting offset counters – use of synchronous loade.g., 0110, 0111, 1000, 1001,1010, 1011, 1100, 1101, 1111, 0110, . . .
Ending offset counter – comparator for ending valuee.g., 0000, 0001, 0010, ..., 1100, 1101, 0000
Combinations of the above (start and stop value)
Autumn 2006 CSE370 - IV - Sequential Logic 46
Hardware Description Languages and Sequential Logic
Flip-flopsrepresentation of clocks - timing of state changesasynchronous vs. synchronous
Shift registersSimple counters
Autumn 2006 CSE370 - IV - Sequential Logic 47
module dff (clk, d, q);
input clk, d;output q;reg q;
always @(posedge clk)q = d;
endmodule
Flip-flop in Verilog
Use always block's sensitivity list to wait for clock edge
Autumn 2006 CSE370 - IV - Sequential Logic 48
module dff (clk, s, r, d, q);input clk, s, r, d;output q;reg q;
always @(posedge clk)if (r) q = 1'b0;else if (s) q = 1'b1;else q = d;
endmodule
module dff (clk, s, r, d, q);input clk, s, r, d;output q;reg q;
always @(posedge r)q = 1'b0;
always @(posedge s)q = 1'b1;
always @(posedge clk)q = d;
endmodule
More Flip-flops
Synchronous/asynchronous reset/setsingle thread that waits for the clockthree parallel threads – only one of which waits for the clock
Synchronous Asynchronous
Autumn 2006 CSE370 - IV - Sequential Logic 49
module dff (clk, d, q);
input clk, d;output q;reg q;
always @(clk)q = d;
endmodule
Incorrect Flip-flop in Verilog
Use always block's sensitivity list to wait for clock to change
Not correct! Q willchange whenever theclock changes, notjust on an edge.
Autumn 2006 CSE370 - IV - Sequential Logic 50
always @(posedge CLK)begin
temp = B;B = A;A = temp;
end
always @(posedge CLK)begin
A <= B;B <= A;
end
Blocking and Non-Blocking Assignments
Blocking assignments (X=A)completes the assignment before continuing on to next statement
Non-blocking assignments (X<=A)completes in zero time and doesn’t change the value of the target until a blocking point (delay/wait) is encountered
Example: swap
Autumn 2006 CSE370 - IV - Sequential Logic 51
Register-transfer-level (RTL) Assignment
Non-blocking assignment is also known as an RTL assignmentif used in an always block triggered by a clock edgeall flip-flops change together
// B,C,D all get the value of Aalways @(posedge clk)
beginB = A;C = B;D = C;
end// implements a shift register always @(posedge clk)
beginB <= A;C <= B;D <= C;
end
Autumn 2006 CSE370 - IV - Sequential Logic 52
Shift register in Verilog
module shift_register (clk, in, out);
input clk;input in;output [0:3] out;
reg [0:3] out;
initial beginout = 0; // out[0:3] = {0, 0, 0, 0};
end
always @(posedge clk) beginout = {in, out [0:2]};
end
endmodule
Autumn 2006 CSE370 - IV - Sequential Logic 53
Activity: express in Verilog
always @(posedge clk)begin
end
D Q D Q D Q D QIN
OUT1 OUT2 OUT3 OUT4
CLK
Autumn 2006 CSE370 - IV - Sequential Logic 54
Mobius Counter in Verilog
initialbegin
A = 1’b0;B = 1’b0;C = 1’b0;D = 1’b0;
end
always @(posedge clk)begin
A <= ~D;B <= A;C <= B;D <= C;
end
{A, B, C, D} <= {~D, A, B, C};
D Q D Q D Q D QIN
OUT1 OUT2 OUT3 OUT4
CLK
Autumn 2006 CSE370 - IV - Sequential Logic 55
Binary Counter in Verilog
module binary_counter (clk, c8, c4, c2, c1);
input clk;output c8, c4, c2, c1;
reg [3:0] count;
initial begincount = 0;
end
always @(posedge clk) begincount = count + 4’b0001;
end
assign c8 = count[3];assign c4 = count[2];assign c2 = count[1];assign c1 = count[0];
endmodule
module binary_counter (clk, c8, c4, c2, c1, rco);
input clk;output c8, c4, c2, c1, rco;
reg [3:0] count;reg rco;
initial begin . . . end
always @(posedge clk) begin . . . end
assign c8 = count[3];assign c4 = count[2];assign c2 = count[1];assign c1 = count[0];assign rco = (count == 4b’1111);
endmodule
Autumn 2006 CSE370 - IV - Sequential Logic 56
Sequential logic summary
Fundamental building block of circuits with statelatch and flip-flopR-S latch, R-S master/slave, D master/slave, edge-triggered D flip-flop
Timing methodologiesuse of clockscascaded FFs work because propagation delays exceed hold timesbeware of clock skew
Basic registersshift registerscounters
Hardware description languages and sequential logic