NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
Topics covered in this
presentation
What is Row Reduction.
What are the reasons for doing Row Reduction
What are state variables and external inputs.
Algorithms used for row reduction
For completely specified state machines.
Pairchart
For incompletely
NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
Taking Column represented by state 1
 From pairchart, state 1 goes to state 2 with input A
and to state 3 with input B.
1
 So we will write 2 and 3 in each block in
column 1 and Row 1 as shown.
X
2
3
2
3
X
5
X
X
1
5
X
3
2
6
4
X
4
1
2
3
6
B
2,0
4,1
2,0
3
NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
Increasing Order
A
Figure2
1
1
2
3
2
4
3
5
4
6
2,0
4,1
2,0
3,1
6,0
4,1
B
3,1
1,0
1,1
6,0
5,1
5,0
5
6
1
2
3
4
Increasing Order
5
6
1
Step 3 of Pairchart Algorithm
Lets start filling the Table in Figure 2.
Output Compatibility
We will take one column at
NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
Definition
Given a sequential machine, our aim is to
find the finite state machine which have
same behavior as the given machine but has
reduced states.
1
Advantages of Row Reduction
Cost Reduction
We know Flip Flops used as memory elements are costly
NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
1
X
2
3
2
3
2
1
1
 State 3 goes to 2 and 1 so we write it in
column 3 and also in row 3 > 2 and 1
2
3
 So we will write 2 and 1 in each block in
4
column 2 and Row 2 (if no X) as shown.
X
4
X
4
Taking next Column represented by state 3
3
2
X
1
1
4
1
2
NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
Given CSSM
A
B
1
2,0
3,1
2
4,1
1,0
3
2,0
1,1
4
3,1
6,0
6,0
5,1
4,1
5,0
5
6
Figure 1
1
How to read CSSM
1
2
3
4
5
6
A
B
2,0
3,1
4,1
1,0
2,0
1,1
3,1
6,0
6,0
5,1
4,1
5,0
If you are in State 1 and input is A you go to State 2 with output 0.
If you are in St
NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
Completely Specified Machines.
A machine which has no dont cares in its
table is called a completely specified state
machine (CSSM).
Lets see an example to find out what do we
mean by having no dont cares.
1
Completely Specified State Machine
(CSSM)
Sta
NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
Column 1
check if 1 is output compatible
with 3 for both input A and B
1
2
Answer: Yes.
For same Input A and B
State 1 and State 3 has
same output.
So we dont do
anything with the
block at the inter
section of 1 and 3.
X
3
4
1
2
3
4
5
6
A
B
2,0
4,1
2,0
NED University of Engineering & Technology, Karachi
AST
CISE 503

Fall 2016
Implementation of Step 1 of Pairchart Algorithm
Increasing Order
1
2
3
4
5
6
1
2
3
4
Increasing Order
5
6
1
Step 2 of Pair Chart Algorithm
We can remove half of the pairchart
(diagonally) because it is symmetric along
the diagonal.
So we are effectively