Lecture 9
Registers, Counters and Shifters
Hai Zhou
ECE 303
Advanced Digital Design
Spring 2002
ECE C03 Lecture 9
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Outline
•
•
•
•
•
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Registers
Register Files
Counters
Designs of Counters with various FFs
Shifters
READING: Katz 7.1, 7.2, 7.4, 7.5, 4.7 Dewey
10.2, 10.3, 10.4, Hennessy-Patterson B26
ECE C03 Lecture 9
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Building Complex Memory Elements
• Flipflops: most primitive "packaged" sequential circuits
• More complex sequential building blocks:
Storage registers, Shift registers, Counters
Available as components in the TTL Catalog
• How to represent and design simple sequential circuits: counters
• Problems and pitfalls when working with counters:
Start-up States
Asynchronous vs. Synchronous logic
ECE C03 Lecture 9
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Registers
• Storage unit. Can hold an n-bit value
• Composed of a group of n flip-flops
– Each flip-flop stores 1 bit of information
• Normally use D flip-flops
D
Q
Dff
clk
D
Q
Dff
clk
D
Q
Dff
clk
D
Q
Dff
clk C03 Lecture 9
ECE
4
Controlled Register
Reset
0
1
0
Load
0
0
1
Action
Q = old Q
Q=0
Q=D
D
Q
Dff
clk
D
Q
Dff
clk
D
Q
Dff
clk
D
Q
Dff
clk
ECE C03 Lecture 9
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Registers
Group of storage elements read/written as a unit
4-bit register constructed from 4 D FFs
Shared clock and clear lines
Schematic Shape
171
12
13
CLK
CLR
11
D3
5
D2
4
D1
14
D0
Q3
Q3
Q2
Q2
Q1
Q1
Q0
Q0
9
10
7
6
2
3
1
15
TTL 74171 Quad D-type FF with Clear
(Small numbers represent pin #s on package)
ECE C03 Lecture 9
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Shift Registers
Storage + ability to circulate data among storage elements
\Reset
Shift Direction
Shif t
J Q
K Q
J Q
K Q
J Q
K Q
J Q
K Q
Q1
Q2
Q3
Q4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
Shif t
Shif t
Shift
\Reset
Shift
Shift from left storage
element to right neighbor
on every lo-to-hi transition
on shift signal
Q1
Q2
Q3
Q4
Wrap around from rightmost
element to leftmost element
Master Slave FFs: sample inputs while
clock is high; change outputs on
falling
edge
ECE C03 Lecture
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Shift Registers I/O
Serial vs. Parallel Inputs
Serial vs. Parallel Outputs
Shift Direction: Left vs. Right
QD
QC
QB
QA
74194 4-bit Universal
Shift Register
Serial Inputs: LSI, RSI
Parallel Inputs: D, C, B, A
Parallel Outputs: QD, QC, QB, QA
Clear Signal
Positive Edge Triggered Devices
S1,S0 determine the shift function
S1 = 1, S0 = 1: Load on rising clk edge
synchronous load
S1 = 1, S0 = 0: shift left on rising clk edge
LSI replaces element D
S1 = 0, S0 = 1: shift right on rising clk edge
RSI replaces element A
S1 = 0, S0 = 0: hold state
Multiplexing logic on input to each FF!
Shifters well suited for serial-to-parallel conversions,
ECE C03
Lecture 9
such as terminal
to computer
communications
8
Application of Shift Registers
Parallel to Serial Conversion
D7
D6
D5
D4
Clock
Parallel
Inputs
D3
D2
D1
D0
Sender
Receiver
S1
S0 194
LSI
D
QD
C
QC
B
QB
A
QA
RSI
CLK
CLR
S1
S0 194
LSI
D
QD
C
QC
B
QB
A
QA
RSI
CLK
CLR
D7
D6
D5
D4
S1
S0 194
LSI
D
QD
C
QC
B
QB
A
QA
RSI
CLK
CLR
S1
S0 194
LSI
D
QD
C
QC
B
QB
A
QA
RSI
CLK
CLR
D3
D2
D1
D0
Parallel
Outputs
Serial
transmission
ECE C03 Lecture 9
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Counters
Proceed through a well-defined sequence of states in response to
count signal
3 Bit Up-counter: 000, 001, 010, 011, 100, 101, 110, 111, 000, ...
3 Bit Down-counter: 111, 110, 101, 100, 011, 010, 001, 000, 111, ...
Binary vs. BCD vs. Gray Code Counters
A counter is a "degenerate" finite state machine/sequential circuit
where the state is the only output
ECE C03 Lecture 9
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Counter Design Procedure
This procedure can be generalized to implement ANY finite state
machine
Counters are a very simple way to start:
no decisions on what state to advance to next
current state is the output
Example: 3-bit Binary Upcounter
00
0
0
0
1
Present
State
C B A
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
Next
State
Flipflop
Inputs
C+ B+ A+ TC TB TA
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
State Transition
Table
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
Flipflop
Input Table
ECE C03 Lecture 9
Decide to implement with
Toggle Flipflops
What inputs must be
presented to the T FFs
to get them to change
to the desired state bit?
This is called
"Remapping the Next
State Function"
11
Example Design of Counter
K-maps for Toggle
Inputs:
Resulting Logic Circuit:
CB
A
00
11
10
11
10
01
0
1
TA =
CB
A
00
01
0
1
TB =
CB
A
00
01
11
10
0
1
TC =
ECE C03 Lecture 9
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Resultant Circuit for Counter
K-maps for Toggle
Inputs:
+
C
CB
A
Resulting Logic Circuit:
00
01
11
10
0
1
1
1
1
1
1
1
1
1
TSQ
CLK Q
R
B
TA = 1
QA
T SQ
CLK Q
R
QB
QC
T SQ
CLK Q
R
\Reset
C
CB
00
01
11
10
0
0
0
0
0
1
1
1
1
1
A
Count
Timing Diagram:
100
B
TB = A
\Reset
QC
C
CB
00
01
11
10
0
0
0
0
0
1
0
1
1
0
A
QB
QA
Count
B
TC = A • B
ECE C03 Lecture 9
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More Complex Counter Design
Step 1: Derive the State Transition Diagram
Count sequence: 000, 010, 011, 101, 110
Present
State
Next
State
Step 2: State Transition Table
000
010
011
101
110
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
ECE C03 Lecture 9
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Complex Counter Design (Contd)
Step 1: Derive the State Transition Diagram
Count sequence: 000, 010, 011, 101, 110
Present
State
Next
State
Step 2: State Transition Table
000
001
010
011
100
101
110
111
0 1 0
XXX
0 1 1
1 0 1
XXX
1 1 0
0 0 0
XXX
Note the Don't Care conditions
ECE C03 Lecture 9
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Counter Design (Contd)
Step 3: K-Maps for Next State Functions
CB
A
00
01
11
CB
10
A
0
0
1
1
C+ =
00
01
11
10
B+ =
CB
A
00
01
11
10
0
1
A+ =
ECE C03 Lecture 9
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Counter Design (contd)
Step 4: Choose Flipflop Type for Implementation
Use Excitation Table to Remap Next State Functions
Q Q+
T
0
0
1
1
0
1
1
0
0
1
0
1
Toggle Excitation
Table
Present
State
Toggle
Inputs
CBA
TC TB TA
000
001
010
011
100
101
110
111
0 1 0
XXX
0 0 1
1 1 0
XXX
0 1 1
1 1 0
XXX
Remapped Next State
Functions
ECE C03 Lecture 9
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Resultant Counter Design
Remapped K-Maps
CB
A
00
01
11
CB
10
A
0
0
1
1
00
TC
01
11
10
TB
CB
A
00
01
11
10
0
1
TA
TC = A C + A C = A xor C
TB = A + B + C
TA = A B C + B C
ECE C03 Lecture 9
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Resultant Circuit for Complex Counter
Resulting Logic:
5 Gates
13 Input Literals +
Flipflop connections
TC
Count
T
S Q C
TB
CLK Q
\C
R
B
T S Q
CLK Q
\B
R
TA
A
T S Q
CLK Q
\A
R
\Reset
A
C
TC
A
\B
C
Timing Waveform:
TB
\A
B
C
\B
C
TA
100
Count
\Reset
0
0
0
0
1
1
0
B
0
0
1
1
0
1
0
A
0
0
1
0
0
C
ECE
C03 Lecture
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Implementing Counters with Different FFs
• Different counters can be implemented best with different
FFs
• Steps in building a counter
– Build state diagram
– Build state transition table
– Build next state K-map
• Implementing the next state function with different FFs
• Toggle flip flops best for binary counters
• Existing CAD software for finite state machines favor D
FFs
ECE C03 Lecture 9
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Implementing 5-state counter with RS FFs
Continuing with the 000, 010, 011, 101, 110,
000, ... counter example
Q Q+ R S
0
0
1
1
0
1
0
1
X
0
1
0
0
1
0
X
Q+ = S + R Q
RS Exitation Table
Present
State
000
001
010
011
100
101
110
111
Next
State
0 1 0
XXX
0 1 1
1 0 1
XXX
1 1 0
0 0 0
XXX
Rmepped next state
RC SC RB SB RA SA
X
X
X
0
X
0
1
X
0
X
0
1
X
X
0
X
0
X
0
1
X
0
1
X
1
X
X
0
X
1
0
X
X 0
X X
0 1
0 X
X X
1 0
X 0
X X
Remapped Next State Functions
ECE C03 Lecture 9
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Implementation with RS FFs
RS FFs Continued
CB
A
CB
00
01
11
X
X
1
X
X
0
X
0
0
1
10
00
01
11
10
0
0
0
0
X
1
X
1
X
X
A
RC
CB
SC = A
CB
00
01
11
10
0
0
0
1
X
1
X
1
X
0
A
00
01
11
10
0
1
X
0
X
1
X
0
X
1
A
RB
0
1
01
X
X
0
0
RA
11
X
X
10
X
1
A
0
1
SB = B
SA = B C
CB
00
RB = A B + B C
RA = C
SB
CB
A
RC = A
SC
00
01
0
X
1
X
11
0
X
ECE C03 Lecture
SA 9
10
X
0
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Implementation With RS FFs
\A
A
R
Q
CLK
Q
S
C
RB
R
Q
CLK
Q
S
\B
\C
Count
A
C
B
B
C
SA
R
Q
CLK
Q
S
\B
RB
A
\A
B
\C
SA
Resulting Logic Level Implementation:
3 Gates, 11 Input Literals + Flipflop connections
ECE C03 Lecture 9
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Implementing with JK FFs
Continuing with the 000, 010, 011, 101, 110,
000, ... counter example
Q Q+ J
K
0
0
1
1
X
X
1
0
0
1
0
1
0
1
X
X
Q+ = S + R Q
RS Exitation Table
Present
State
000
001
010
011
100
101
110
111
Next
Rmepped next state
State JC KC JB KB JA KA
0 1 0
XXX
0 1 1
1 0 1
XXX
1 1 0
0 0 0
XXX
0
X
0
1
X
X
X
X
X
X
X
X
X
0
1
X
1
X
X
X
X
1
X
X
X
X
0
1
X
X
1
X
0 X
X X
1 X
X 0
X X
X 1
0 X
X X
Remapped Next State Functions
ECE C03 Lecture 9
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Implementation with JK FFs
CB
A
CB
00
01
11
10
A
0
0
1
1
00
JC
11
10
JC = A
KC
CB
A
01
KC = A/
CB
00
01
11
10
A
00
01
11
10
0
0
JB = 1
1
1
KB = A + C
JB
CB
A
JA = B C/
KB
KA = C
CB
00
01
11
10
A
0
0
1
1
JA
00
01
11
10
KA
ECE C03 Lecture 9
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Implementation with JK FFs
+
A
\A
J Q C
CLK
K Q
KB
\C
J Q B
CLK
K Q
\B
JA
C
J Q A
CLK
K Q
\A
Count
A
C
KB
B
\C
JA
Resulting Logic Level Implementation:
2 Gates, 10 Input Literals + Flipflop Connections
ECE C03 Lecture 9
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Implementation with D FFs
Simplest Design Procedure: No remapping needed!
DC = A
DB = A C + B
DA = B C
A
D
Q
CLK Q
C
\ C
DB
D
Q
CLK Q
B
\ B
DA
D
Q
CLK Q
A
\ A
Count
\C
\A
DB
\ B
B
\ C
DA
Resulting Logic Level Implementation:
3 Gates, 8 Input Literals + Flipflop connections
ECE C03 Lecture 9
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Comparison with Different FF Types
• T FFs well suited for straightforward binary counters
But yielded worst gate and literal count for this example!
• No reason to choose R-S over J-K FFs: it is a proper subset of J-K
R-S FFs don't really exist anyway
J-K FFs yielded lowest gate count
Tend to yield best choice for packaged logic where gate count is key
• D FFs yield simplest design procedure
Best literal count
D storage devices very transistor efficient in VLSI
Best choice where area/literal count is the key
ECE C03 Lecture 9
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Summary
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•
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•
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Registers
Register Files
Counters
Designs of Counters with various FFs
NEXT LECTURE: Memory Design
READING: Katz 7.6
ECE C03 Lecture 9
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