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# Asynchronous Circuits by aax58232

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```									         Asynchronous Circuits

M. Balakrishnan
Dept. of Comp. Sci. & Engg.
I.I.T. Delhi

Chapter 4: Asynchronous Circuits         1
Terminology
• Input State
x              z
• Secondary or                     Comb.
Logic
internal state
• Secondary or               y                   Y

internal variables                 Delay

• Fundamental mode

Chapter 4: Asynchronous Circuits             2
Illustrative Example
Consider a circuit with 2 inputs (x1 and x2)
and 1 output (z). The output is “1” only
when x1 and x2 are “1” with x1 being “1”
first.
x1

x2

z

Chapter 4: Asynchronous Circuits          3
Total States

x1

x2

z

1      2     3     4      1   4   5   1

Chapter 4: Asynchronous Circuits                   4
Primitive Flow Table
x1,x2         00         01      11     10
1        1 ,0          4       -      2
2          1           -       3     2 ,0
3           -          4      3 ,1    2
4          1         4 ,0      5      -
5           -          4      5 ,0    2

Chapter 4: Asynchronous Circuits           5
Merger Graph
• Identify compatibility
1
• Identify cliques
4                    2
A      (1,2,3)
B      (4,5)
3
5

Chapter 4: Asynchronous Circuits               6
Reduced Flow Table
x1, x2       00          01      11     10
A         1 ,0          4      3 ,1   2 ,0
B           1        4 ,0      5 ,0    2

Chapter 4: Asynchronous Circuits               7
Final State Table
x1, x2        00          01       11     10
0         0 ,0        1 ,0      0 ,1   0 ,0
1         0 ,0        1 ,0      1 ,0   0 ,0

z = y’x1x2

y = x1’x2 + yx2
Chapter 4: Asynchronous Circuits            8
Asynchronous Circuit

z = y’x1x2
y = x1’x2 + yx2

Chapter 4: Asynchronous Circuits   9
Asynchronous Sequential Circuit
Design

M. Balakrishnan
Dept. of Comp. Sci. & Engg.
I.I.T. Delhi

Chapter 4: Asynchronous Circuits         10
Another Example
Consider a circuit with 1 input (x ) and 1
output (z). The output should suppress
every alternate pulse on the input starting
with the first.
x

z

Chapter 4: Asynchronous Circuits            11
Total States

x

z

1   2   3     4    1

Chapter 4: Asynchronous Circuits   12
Primitive Flow Table
x          0           1
1        1 ,0          2
2          3         2 ,0
3        3 ,0          4
4          1         4 ,1

Chapter 4: Asynchronous Circuits   13
State Encoding
• Let us choose the following encoding

1    :      00
2    :      01
3    :      10
4    :      11

Chapter 4: Asynchronous Circuits         14
Final State Table
y1        y2        x           Y1   Y2   z
0         0        0            0    0   0
0         0        1            0    1   0
0         1        0            1    0   0
0         1        1            0    1   0
1         0        0            1    0   0
1         0        1            1    1   1
1         1        0            0    0   0
1         1        1            1    1   1

Chapter 4: Asynchronous Circuits             15
Asynchronous Circuit

z = y1.x
Y1 = y1’.y2.x’ + y1.y2’+y1.x
Y2 = x

Chapter 4: Asynchronous Circuits   16
Races & Cycles
State assignment of secondary states could
result in races and cycles.

• Races
– Critical
– Non-critical
• Cycles
Chapter 4: Asynchronous Circuits         17
State Assignment in
Asynchronous Circuits
M. Balakrishnan
Dept. of Comp. Sci. & Engg.
I.I.T. Delhi

Chapter 4: Asynchronous Circuits         18
Illustration for Races & Cycles
x1x2         00         01      11   10
y1y2
00          11         00      10   01
01          11         00      10   01
11          11         00      10   11
10          11         10      10   11

Chapter 4: Asynchronous Circuits        19
State Assignment
x      0      1             x   0    1
1      1      2            00   00   01
2      3      2            01   10   01
3      3      4            10   10   11
4      1      4            11   00   11

Chapter 4: Asynchronous Circuits             20
Alternative State Assignment
x      0      1             x   0    1
1      1      2            00   00   01
2      3      2            01   10   01
3      3      4            11   11   10
4      1      4            10   00   10

Chapter 4: Asynchronous Circuits             21
Transition Graph
Transition Graph is drawn to capture

1            2             3   4

Chapter 4: Asynchronous Circuits           22
Another Transition Table
x1x2   00 01 11 10                    (01) (10)
y1y2
1               2
1      3     1    4     2
2      3     1    4     2     (01)   (11)            (11)
3      3     1    4     3                      4
3   (11) (10)
4      3     4    4     3

Chapter 4: Asynchronous Circuits                  23
Transition Diagram
(01) (10)
1               2     x1x2 00      01 11 10
0    1       3 4 4
(11)
1        2         4
3   (11) (10)
4

Chapter 4: Asynchronous Circuits             24