1. Asynchronous Circuit Design
Introduction
Analysis
Synthesis
Races
Static and dynamic hazards
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2. Fundamental Mode Asynchronous Circuit
Output
Input
Single Input Change
Comb
Secondary
State
Excitation
State
Delay
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3. Asynchronous Sequential Circuit
Analysis

4. Example 1- Logic Diagram
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5. Dr. Tri Caohuu © 2006 Andy Davis
Example 1- Excitation/Transition Table Y1 = x2’y1 +x1’y1+x1’x2y2 Y2 = x1y1+x2y1y2+x1y2+x1x2 z = x2’y1 +x1’y1y2+x1x2‘y2 PS
y1 y2
Excitation
Y1 Y2
Output z
Input State x1x2
Input State x1x2 00 01 10 11 00 01 10 11 00 00 10 00 01 01 00 01 00 01 10 10 10 11 01 11 11 11 01 10
Dr. Tri Caohuu © 2006 Andy Davis

6. Dr. Tri Caohuu © 2006 Andy Davis
The State Table
Next State
Output z PS
Input State x1x2
Input State x1x2 00 01 10 11 00 01 10 11 A
00  A
01  B
10  C
11  D 00 C A B 01 A B A B 10 C C D B 11 C D D B
Dr. Tri Caohuu © 2006 Andy Davis

7. Dr. Tri Caohuu © 2006 Andy Davis
The Flow Table
Next State
Output z PS
Input State x1x2
Input State x1x2 00 01 10 11 00 01 10 11 00 A C A B 01 A B A B 10 C C D B 11 C D D B
Dr. Tri Caohuu © 2006 Andy Davis

8. Dr. Tri Caohuu © 2006 Andy Davis
The Flow Diagram A B C D
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9. Asynchronous Sequential Network - SYNTHESIS
Races, Cycles, and Hazards

10. Synthesis of Asynchronous Sequential Circuit2 2
x1x2
z1z2
When x1x2=00, then z1z2=00
Sequence x1x2= , then z1z2=10. Output remains at 10 until x1x2=00, then z1z2=00
Sequence x1x2= , then z1z2=01. Output remains at 01 until x1x2=00, then z1z2=00
Dr. Tri Caohuu © 2006 Andy Davis

11. A. Partially completed Primitive Flow Table
x1x2 00 01 11 10 1
1 /00
-/- 2
2 /00 3
3 /10 4
4 /01 5
5 /10 6
6 /01 7
7 /00 8
8 /10 9
9 /01
Before output
changes from 00
After output
changes from 00
Two successful
sequences
Dr. Tri Caohuu © 2006 Andy Davis

12. Dr. Tri Caohuu © 2006 Andy Davis
B. Primitive Flow Table
x1x2 00 01 11 10 1
1 /00
2/00
-/dd
7/00 2
1/00
2 /00
5/d0 3
1/d0
3 /10
5/10 4
1/0d
4 /01
6/01 5
3/10
5 /10
8/10 6
4/01
6 /01
9/01 7
6/0d
7 /00 8
8 /10 9
9 /01
Changes from
1 to 0
Changes from
0 to 1
No change
on output
Dr. Tri Caohuu © 2006 Andy Davis

13. Dr. Tri Caohuu © 2006 Andy Davis
C. Reduced Flow Table 9 2 3 4 5 6 7 8 9  56 8 1 2 7 3 6 4 5
a c b d
Dr. Tri Caohuu © 2006 Andy Davis

14. C. Reduced Flow Table Cont.00 01 11 10 a
a /00
b/d0
c/00 b
a/d0
b /10 c
c /00
a/00
d/0d d
c /0d
d /01
Dr. Tri Caohuu © 2006 Andy Davis

15. Dr. Tri Caohuu © 2006 Andy Davis
D. Race Free Assignment
a = 00
b = 01
c = 10
d = 11 a b a 00
11, 00 ac ab 01 10 10 c b 01 d c
00,11
d=11
Dr. Tri Caohuu © 2006 Andy Davis

16. E. Excitation and Output Tables
x1x2 00 01 11 10 d0
y1y2 0d
z1z2
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17. E. Excitation and Output Tables Cont.
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18. Dr. Tri Caohuu © 2006 Andy Davis
F. Circuit
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19. Dr. Tri Caohuu © 2006 Andy Davis
Race & Critical Race
Race Definition: Two or more secondary state (yi) variables change during a transition between stable state. Depending on which variables change firstly, we may end up in an incorrect stable state (critical race). However, if the circuit ends up in a correct state irrespect of which variable changes firstly, we have a case of non-critical race.
Dr. Tri Caohuu © 2006 Andy Davis

20. Dr. Tri Caohuu © 2006 Andy Davis
Race – Example
x1x2 00 01 11 10 1
y1y2 z
Dr. Tri Caohuu © 2006 Andy Davis

21. Dr. Tri Caohuu © 2006 Andy Davis
Race – Example Cont.
x1 x2 y1 y2
< >
<0000>
δ 1> δ 2 => 1011 => 0011 => 0010 => 0000
δ 2> δ 1 => 1011 => 0011 => 0001 => 0000
δ 1> δ 2 => 1001 => 1101 => 1100 => 1100
We want to go from 01 to 10, but this change first before y1 change from 0 to 1
δ 2> δ 1 => 1001 => 1101 => 1111 => 1110
Non Critical
Not Correct
Correct
Dr. Tri Caohuu © 2006 Andy Davis

22. Dr. Tri Caohuu © 2006 Andy Davis
Avoidance 00 01 11 10 a
a/0
b/0
a/1
b/1 b
c/0 c
c/1
d/0 d
d/1
Critical Race
Col 01 => b, c
Col 11 => a, c
Col 10 => d, b
Dr. Tri Caohuu © 2006 Andy Davis

23. Dr. Tri Caohuu © 2006 Andy Davis
Avoidance Cont. 01 10 00 01 10 a b a b 00 11 11 11 00 11 10 d c 10 d c
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24. Dr. Tri Caohuu © 2006 Andy Davis
Avoidance Cont.
Let a = 00
ab => b = 01
bc = 01 => c = 11
cd => d = 10
Dr. Tri Caohuu © 2006 Andy Davis

25. Dr. Tri Caohuu © 2006 Andy Davis
Avoidance Cont. 00 01 11 10
Connected nodes of transition diagram differed by only one (1) bit
Dr. Tri Caohuu © 2006 Andy Davis

26. Race-Free State Assignment00 01 11 10 a
a/0
b/0
c/- b c
a/-
c/1 a 01 b 11 10 c
a=00 => b=01, c=10 => b≠c
Dr. Tri Caohuu © 2006 Andy Davis

27. Method One (adding cycles)
-> d -> c -> (c) 00 01 11 10 a
a/0
b/0
d/- b
c/- c
c/1 d
a/- 01 a b 11 10 11 d c
y1 y2 a b c d
Dr. Tri Caohuu © 2006 Andy Davis

28. Dr. Tri Caohuu © 2006 Andy Davis
Method One Cont.
x1x2 00 01 11 10 dd
y1y2
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29. Method Two: Universal state assignment
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30. Dr. Tri Caohuu © 2006 Andy Davis
Method Two Cont.
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31. Dr. Tri Caohuu © 2006 Andy Davis
Method Two Cont.
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32. Dr. Tri Caohuu © 2006 Andy Davis
Method Two Cont.
Dr. Tri Caohuu © 2006 Andy Davis