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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
  adjacency requirements


        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
    Additional Permanent States

         0 1                y1y2   00 01 11 10
                            y3y4
    00 a     a              00     a   b   e   e
    01 b d                  01     a   b   f   f
    11 b d                  11     c   c   e   f
    10 c     c              10     d   d   e   f

Chapter 4: Asynchronous Circuits               25

								
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