Download Implementing Processes, Threads, and Resources

Sequential Circuits
• Prelim on delays and performance
• Sequential circuits
– CLU with feedback loops
– Bi-stable (aka S-R flip-flop)
– Next time:
• Application of flip-flops
• Clocked flip-flops, clocked D-flip-flops
• Level-triggered, edge-triggered, master-slave flipflops
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-1
The Inverter at the Transistor
Level
Slide 1-2
Output voltage vs. Input voltage
VCC
VCC = +5 V
A
RL
VCC
Vout
Vin
A
Collector
Emitter
Base
A
A
Vout – Output voltage – V
4.0
3.5
VCC = 5 V
RL = 400 W
3.0
2.5
2.0
1.5
1.0
0.5
0
GND = 0 V
0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6 1.8
2
Vin– Input voltage– V
(a)
Power
terminals
(b)
(c)
(d)
Transistor A transistor
Inverter transfer
symbol
used
function
as an inverter
(Compare to our relay implementation of the inverter.)
Slide 1-3
Assignments of Logical 0
and Logical 1 to Voltage Ranges
+5 V
+5 V
Logical 1
2.4 V
Logical 1
2.0 V
Forbidden range
Forbidden range
0.8 V
0.4 V
0V
Logical 0
(a) At the output of a
logic gate
Logical 0
0V
(b) At the input to a
logic gate
Slide 1-4
Assignments of Logical 0
and Logical 1 to Voltage Ranges
+5 V
+5 V
Logical 1
2.4 V
Logical 1
2.0 V
Forbidden range
Forbidden range
0.8 V
0.4 V
0V
Logical 0
(a) At the output of a
logic gate
Logical 0
0V
(b) At the input to a
logic gate
Speed and Performance
• The speed of a digital system is
governed by
– the propagation delay through the logic
gates and
– the propagation across
interconnections.
Slide 1-5
Propagation Delay for a NOT Gate
+5V
The NOT
Output changes
From 1 to 0
0V
10%
50%
(2.5V)
Slide 1-6
(Fall time)
90%
Propagation Delay
(Latency)
+5V
The NOT
Output changes
From 0 to 1
0V
(Rise time)
10%
Time
90%
50%
(2.5V)
If you don’t believe in delays:
think again (“nothing” is
instantaneous)
Switches in series => AND
Input 1
Input 2
Current / no current
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-7
Sequential Logic
Slide 1-8
• The combinational logic circuits we have been studying so
far have no memory. The outputs always follow the
inputs.
• There is a need for circuits with a memory, which behave
differently depending upon their previous state.
• An example is the vending machine, which must remember
how many and what kinds of coins have been inserted, and
which behave according to not only the current coin
inserted, but also upon how many and what kind of coins
have been deposited previously.
• These are referred to as finite state machines, because they
can have at most a finite number of states.
...
ik
...
Inputs
Combinational
logic unit
fo
Outputs
fm
...
io
...
Classical Model of a Finite State
Machine
State bits
Q0 D 0
...
s0
Qn D n
sn
Synchronization
signal
Delay elements (one per state bit)
Slide 1-9
Feedback paths in a logic circuit
X
Y
Y
X
Z
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-10
Feedback paths in a logic circuit
S
R
Q
Q
A
B
A B
F
0
0
1
1
1
0
0
0
0
1
0
1
F = A+ B
NOR
Slide 1-11
Slide 1-12
S-R flip-flop (aka bi-stable)
• In which state can the S-R flip-flop
be?
– S=0 & R=0
• Q=0, Q` = 0 ?
• Q=0, Q` = 1 ?
• Q=1, Q` = 0 ?
• Q=1 , Q` =1 ?
– S=0 & R=1
• Q=0, Q` = 0 ?
• Q=0, Q` = 1 ?
• Q=1, Q` = 0 ?
• Q=1 , Q` =1 ?
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-13
S-R flip-flop (aka bi-stable)
• In which state can the S-R flip-flop
be?
– S=1 & R=0 (use symmetry)
• Q=0, Q` = 0 ?
• Q=0, Q` = 1 ?
• Q=1, Q` = 0 ?
• Q=1 , Q` =1 ?
– S=1 & R=1
• Q=0, Q` = 0 ?
• Q=0, Q` = 1 ?
• Q=1, Q` = 0 ?
• Q=1 , Q` =1 ?
Digital Techniques Fall 2007 André Deutz, Leiden University
S-R flip-flop (aka bi-stable)
Slide 1-14
• S and R are predominantly 0
• Summary: When setting S to 1 momentarily, the latch ends
up in state Q=1, regardless of the previous state; when S
drops back to 0 state will stay Q=1. Likewise, setting R to
1 momentarily forces the latch to Q=0. (When R=S=0,
then Q=1 or Q=0 (both are stable) – if you never allow
R=S=1, then Q=1 in case S was the most recent input set to
1; otherwise R was the most recent input set to 1.
• Thus S-R is a rudimentary 1-bit memory
• S == set; R == reset (aka clear)
• We have tacitly assumed that the NOR gate has delays!
• State S=R=1 and Q=Q’=0 is stable – one of the troubles
with this is that we cannot predict anymore what happens
when S and R return to 0.
Digital Techniques Fall 2007 André Deutz, Leiden University
A NOR Gate with a Lumped
Delay
A
A
B
Dt
B
A+B
1
0
1
0
1
A+B
0
Dt
Timing behavior
This delay between input and output is at the basis of the
functioning the flip-flop (= important memory element)
Slide 1-15
Slide 1-16
An S-R Flip-Flop (a bi-stable)
S
Q
R
Q
Qt
St
Rt
Qi+1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
(disallowed)
1
0
1
1
1
1
(disallowed)
S
R
Q
Q
Dt
Dt
2Dt
2Dt
Timing behavior
The S-R flip-flop is an active-high (positive logic) device.
Slide 1-17
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-18
Converting a NOR S-R to an NAND
S-R
S
R
Q
Q
Active-high
NOR
Implementation
S
R
Q
Q
Push bubbles
(DeMorgan’s)
S
R
Rearrange
bubbles
Q
Q
R
S
Q
Q
Convert
from bubbles
to active-low
signal names
A Circuit with a Hazard
A
B
C
AB
C
S
S
Q
Dt
B
A
Glitch caused by
a hazard
R
AB
R
Q
Q
Q
It is desirable to be able to “turn off”
the flip-flop so it does not respond to
such hazards.
Dt
2Dt
Timing behavior
Slide 1-19
Slide 1-20
Amplitude
A Clock Waveform
Time
Cycle time = 25 ns
In a positive logic system, the “action” happens when the clock is high, or
positive. The low part of the clock cycle allows propagation between
subcircuits, so their inputs are stable at the correct value when the clock next
goes high.
Slide 1-21
A Clocked S-R Flip-Flop
S
R
S
Q
CLK
CLK
Q
Q
R
Q
2Dt
3Dt
Timing behavior
The clock signal, CLK, turns on the inputs to the flip-flop.
A Clocked D (Data) Flip-Flop
Slide 1-22
Circuit
D
D
Q
CLK
CLK
Q
Q
Q
Dt
D
2Dt
Symbol
C
Dt
Q
Q
2Dt
Timing behavior