Homework
• Reading
– Tokheim Chapter 9.1 – 9.6
• Machine Projects
– Continue on mp3
• Labs
– Continue in labs with your assigned section
1
Sequential Circuits
• A sequential circuit is constructed using a
combinational circuit with memory circuits
• Similar to a C function with static internal
variables (state memory)
• One additional input is a clock signal
Input(s)
Clock
Combinational
Logic
Output(s)
Memory
Elements
2
Simple Memories (Flip-Flops)
• Simplest is Reset-Set (R-S type)
• Note the inverted signal inputs
• Can buy a standard TTL R-S flip-flop (279)
S
0
1
1
0
R
1
0
1
0
Q
Q
1
0
0
1
no change
prohibited
S
R
S
Q
R
Q
NAND
Q
NAND
Q
3
Simple Memories (Flip-Flops)
• Timing Diagram
Hold
Set
Hold
No
Reset
Effect
Hold
No
Effect Hold
1
S
0
1
R
0
1
Q
0
1
Q
0
4
Synchronous Flip-Flops
• Use of a clock to make the circuit synchronous
• Syn (with) + chronous (clock) => with a clock
• Level-triggered (changes state while clock high)
S
NAND
S
R
Q
R-S
Flip Flop
Clock
NAND
Q
R
TRUTH TABLE
S
R Clock
Q
0
1
0
1
0
1
0
0
1
1
No Chg
Prohibited
5
The D-Type Flip-Flop
• Single data input and edge-triggered clock
• Also called a “Delay” flip-flop (D-type)
• Changes state on either rising or falling edge
D
(Data)
NAND
S
D
R-S
Flip Flop
Q
NAND
Clock
A
C
AND
B
R
TRUTH TABLE
Q
Clock
Q
0
0
1
1
Edge To Pulse Converter
A B
C
0 1
0
1 1
1 (Due to delay through inverter)
1 0
0
6
Actual D-Type Flip-Flop
• Has preset (PR) and clear (CLR) inputs which can
be set asynchronously (but not both at same time)
• Nomenclature use > for an edge-triggered input
D PR Q
> Clk
Q
CLR
7
Reset Circuitry
• When power is turned on, there is a time
delay for power to reach each part of the
circuit and to stabilize at the rated voltage
• We need to apply a reset signal for longer
than that time delay to all memories
• Reset signal presets (to 1) or clears (to 0)
every flip-flop in the system as needed
• Reset signal is released after a time delay
• Reset button causes reset signal to be
asserted and released again after time delay
8
Example Reset Circuitry
Power
R
To All
Flip-Flops
Reset
Button
V
C
Time Constant = R * C
Time
Ground
9
Timing Diagrams for D Flip-Flop
10
Clock - Divide by Two Counter
• Connect Q output back to D input
D PR Q
> Clk
Q
CLR
• Timing Diagram (after starting with Q = 0)
Clk
Q
Q is an output clock at ½ the frequency of the input clock
11
Shift Registers
• Serial in, Parallel out:
Four Bit Parallel Output Available After Four Clocks/Shifts
Serial
Data In
D
Q
FF3
D
Q
FF2
D
Q
FF1
D
Q
FF0
Clock In
12
Shift Registers
• Parallel in, Serial out:
Four Bit Parallel Input Presented for One Clock Edge while “Load” Signal is True
Load/Shift#
1
M
U
x
D
Q
FF3
M
U
x
D
Q
FF2
M
U
x
D
Q
FF1
M
U
x
D
Q
Serial
Data Out
FF0
Clock In
13
The J-K or Universal Flip-Flop
•
•
•
•
•
Named for Jack Kilby (TI Engineer / Inventor of IC)
Three synchronous inputs (plus preset and clear)
J-K flip-flop is available as a 7473 chip
Can be edge-triggered or level-triggered
Example shown is falling “edge triggered”
TRUTH TABLE
J PR Q
>Clk
K
Q
CLR
J
0
0
1
1
K
0
1
0
1
Clock
Q
Stays same
0
1
Toggles
14
J-K Flip-Flop Internals
• Avoids an invalid input such as 0 0 to the R-S Flip Flop
K
Clock
J
AND
S
Q
R-S
Flip Flop
Edge
Detect
Q
AND
R
15
Using J-K Flip-Flops
• Primary use is for storage registers and counters
• Mod-16 counter also known as a ripple counter
X3 X2 X1 X0 counts 0x0 ... 0xF (Hexadecimal) sequentially
X1
X0
Clk
J
>
K
Q
J
>
K
Q
X2
J
>
K
Q
X3
J
>
K
Q
Vcc
(+5 V)
16
Timing diagram for Mod-16
Counter
Note that the counter actually serves to divide down the input clock!
17
Counter Range != 2N
X0
X1
X2
NAND
Vcc
(+5 V)
J
>
K
Q
J
>
K
Q
J
>
K
Q
Reset
Clk
Can we we make it count to something different than 2N?
Ans. Yes, using a combinational logic (a NAND Gate in this case)
Counts: 0, 1, 2, 3, 4, 5, 0, 1, …
18
Synchronous BCD up/down counter
• BCD Up/Down Counter is available as a 74192
• BCD stands for Binary Coded Decimal
• Counts 0000 -1001, then carries LED Bit Display
D
QD
C
QC
B
A
Load Data
Count Up
Count Down
Clear
74192
BCD
Up/Down
Counter
QB
QA
Borrow
Carry
19
Describing Sequential Circuits
• In general,
– Next state = f(inputs, current state)
– Outputs = f(inputs, current state)
• Example:
Clock
A
D
SET
CLR
Q
D
SET
Q
Truth Table
Q
CLR
Q
Last
Next
State State
A Q1 Q2 Q1 Q2 X
State = (Q1, Q2) [2 bits]
4 states: (0,0), (0,1), (1,0), (1,1)
• State diagram:
X
A=0
(1,0)
(0,0)
(1,1)
A=1
(0,1)
A=0
0
0
0
0
1
0
1
0
0
1
0
0
0
0 1
0
0
0
.
.
.
.
.
.
.
.
.
.
.
.
0
1
1
0
1
1
1
1
1
1
1
1
A=0
20
Digital Logic Summary
• Combinational circuits:
–Made from gates without feedback
–Have no internal states
–Outputs depend only on current inputs
–Fully defined by truth table on the inputs
–Passes clocks (if any) as wave trains
–Output states constantly change with inputs
21
Digital Logic Summary
• Sequential circuits:
–Have feedback among the gates
–Can have internal states
–Outputs depend on inputs and past inputs (via
values of internal states)
–Not completely described by pure truth table on
inputs
–Usually one input is a clock signal
–Outputs usually change on one clock edge only
22