Asynchronous sequential circuit analysis

The presentation covers asynchronous sequential circuit analysis; Map, transition table, flow table. It also covers asynchronous circuit design process and race conditions

1. Asynchronous Sequential Circuit Analysis
4/5/2019
Dr Naim R Kidwai, Professor, Integral University
lucknow, www.nrkidwai.wordpress.com
1
Learning Objectives:
1.To learn analysis of asynchronous Sequential Circuits
2.To learn map, transition table and flow table
3.To learn Design of asynchronous Sequential Circuit
4.To race conditions in asynchronous Sequential Circuit

2. Asynchronous Sequential Circuit
4/5/2019
Dr Naim R Kidwai, Professor, Integral University
lucknow, www.nrkidwai.wordpress.com
2
•It do not use clock pulses, so change of state occurs whenever input changes
•Memory element used are latch or time delay elements
•A combinational circuit with feedback is asynchronous sequential circuit
Combination
al circuit
Delay element
Delay element
Input
variables
secondary
variables
excitation
variables
Output
variables
Block diagram of Asynchronous sequential circuit

3. Asynchronous Sequential Circuit Analysis
4/5/2019
Dr Naim R Kidwai, Professor, Integral University
lucknow, www.nrkidwai.wordpress.com
3
Steps of Analysis
1.In the circuit look for feedback
2.Assign excitation variable to output that is fed-back (Capital Letter)
3.Assign secondary variable at the input where feedback ends (small letters)
4.Write the Boolean expression for excitation variable221
212
211
yxYYz
yxyxY
yxxyY



y
1
y
2
Y
2
Y
1
z
x
The circuit in example
has two feedback
paths Input
variable
secondary
variable
excitation
variable

4. Asynchronous Sequential Circuit Analysis
4/5/2019
Dr Naim R Kidwai, Professor, Integral University
lucknow, www.nrkidwai.wordpress.com
4
x
y
1y
201
0000
0110
1111
1001
Map of Y
1
Map: are similar to k-map with value of secondary variables (present state) labelling rows and
value of input variable labelling columns, and each cell displays value of excitation variable as
per Boolean function
Transition Table: is a combined map of all excitation variables Y=Y
1Y
2... (next state), merging of
secondary variable maps. The cells where excitation variable are same as secondary variable
are called stable state and are marked with circle
x
y
1y
201
0001
0111
1110
1000
Map of Y
2
x
y
1y
2 0 1
00 00 01
01 11 01
11 11 10
10 00 10
Transition table Y
1Y
2
x
y
1y
201
0000
0110
1110
1000
Map of z221
212
211
yxYYz
yxyxY
yxxyY




5. Asynchronous Sequential Circuit Analysis
4/5/2019
Dr Naim R Kidwai, Professor, Integral University
lucknow, www.nrkidwai.wordpress.com
5
x
y
1y
201
0000
0110
1111
1001
Map of Y
1
Flow table: In the design representation of asynchronous sequential circuit it is more
convenient to represent the state with letter symbols rather than binary symbols. Such a
table is referred as flow table.
Output may be included in flow /transition table with state separated by a comma, giving
complete description of the circuit
x
y
1y
201
0001
0111
1110
1000
Map of Y
2
x
y
1y
2 0 1
00 00 01
01 11 01
11 11 10
10 00 10
Transition table Y
1Y
2
x
y
1y
201
0000
0110
1110
1000
Output Map (z)
x
y
1y
2 0 1
a a, 0 b, 0
b c, 1b, 0
c c, 1d, 0
d a, 0d, 0
Flow table with output221
212
211
yxYYz
yxyxY
yxxyY




6. Design from Flow table
4/5/2019
Dr Naim R Kidwai, Professor, Integral University
lucknow, www.nrkidwai.wordpress.com
6
00 01 11 10
aa , 0a , 0a , 0b , 0
ba, 0a, 0b, 1b, 0
Flow table with output
1. The circuit has two input variables (let x
1and x
2), one
excitation variable Y (corresponding secondary variable y)
and one output z.
2.Assign binary values to state . a=0, b=1, then flow table
changes to transition table with output
x
1x
2
y 00 01 11 10
00 , 00 , 00 , 01 , 0
10, 00, 01, 11, 0
transition table with output
3. Separate map of Y and output map and find binary expression
for Y and z using k map
4.Implement the Boolean expressions using gates
x
1x
2
y00011110
000 01
10011
Map of Y
x
1x
2
y00011110
00000
10010
Output mapyxxxY
121
 yxxY
21

y
x
2
Y
z
x
1

7. Race Conditions
Araceconditionexistswhentwoormorestatevariables(excitation)changeinresponseto
inputvariablechanges.
Noncriticalrace:iffinalstablestatedoesnotdependontheorderofstatevariablechanges
Criticalrace:iffinalstablestatedependsontheorderofstatevariablechanges
4/5/2019
Dr Naim R Kidwai, Professor, Integral University
lucknow, www.nrkidwai.wordpress.com
7
x
y
1y
20 1
000011
011011
110111
110001
Non critical race
Y
1Y
2=00, and x=0 to x=1
then possible transitions are
Y
1Y
2: 00→11
Y
1Y
2: 00→01→11
Y
1Y
2: 00→10→01→11
x
y
1y
20 1
000011
011001
110001
100111
Non critical race
Y
1Y
2=00, and x=0 to x=1
then possible transitions are
Y
1Y
2: 00→11→01
Y
1Y
2: 00→01
Y
1Y
2: 00→10→11 →01
x
y
1y
20 1
000011
011001
110011
100110
Critical race
Y
1Y
2=00, and x=0 to x=1
then possible transitions are
Y
1Y
2: 00→11
Y
1Y
2: 00→01
Y
1Y
2: 00→10
x
y
1y
20 1
000011
011011
110011
100110
Critical race
Y
1Y
2=00, and x=0 to x=1
then possible transitions are
Y
1Y
2: 00→11
Y
1Y
2: 00→01→11
Y
1Y
2: 00→10