Datorteknik TopologicalSort bild 1 To verify the structure Easy to hook together combinationals and flip-flops Harder to make it do what you want
Datorteknik TopologicalSort bild 1 To verify the structure Easy to hook together combinationals and flip-flops Harder to make it do what you want.
Apr 01, 2015
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Datorteknik TopologicalSort bild 1
To verify the structure
Easy to hook together combinationals and flip-flops
Harder to make it do what you want
Datorteknik TopologicalSort bild 2
To verify the structure
We want to check:
Does my structure contain combinatorial loops?
We want to compute:
What values are being computed
by the structure right now? (simulation)
We will need to estimate:
How fast can we clock this structure (timing analysis)
Datorteknik TopologicalSort bild 3
To verify the structure
These three problems are all related to each other
The underlying concepts are graphtheoretical
We use topological sort
Datorteknik TopologicalSort bild 4
Answer:
Impossible to be sure by “inspection”
We need a procedure
Datorteknik TopologicalSort bild 5
Where do we begin?
...... At the primary inputs
But ...
What is an input to the circuit?
Datorteknik TopologicalSort bild 6
Inputs
Here’s one!
It’s a “break”. There is nothing “upstream”
As far backwards as we can go
&
Datorteknik TopologicalSort bild 7
Is there a path through this?
D Q
Datorteknik TopologicalSort bild 8
The D- flip flop
Combinationally, the D-flip flop is like this:
D Q
Datorteknik TopologicalSort bild 9
Branch
logic
Sgn/Ze
extend
Zero ext.
ALU
A
B
31
0
4+
+
Datorteknik TopologicalSort bild 10
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
Datorteknik TopologicalSort bild 11
+
-
1
2
43
Add one
Equal?Left shiftone bit
B
Datorteknik TopologicalSort bild 12
The procedure
Visit_line (p);
Mark line
For each component connected
Visit_component (p)
End;
Visit_component (q)
Mark input [save q]
If all inputs marked then
Calculate output
For all outputs
Visit_line (output)
End;Main
For all inputs
Visit_line (value)
If all lines visited then OK
Else Combinatorial loop
End;
Datorteknik TopologicalSort bild 13
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
M
Datorteknik TopologicalSort bild 14
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
M
M
Datorteknik TopologicalSort bild 15
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
M
M
M
Datorteknik TopologicalSort bild 16
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
M
M
M
2
M M
Datorteknik TopologicalSort bild 17
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
M
M
M
2
M M
3
M
M
M
Datorteknik TopologicalSort bild 18
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
M
M
M
2
M M
3
M
M
M
4
M
M
Datorteknik TopologicalSort bild 19
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
M
M
M
2
M M
3
M
M
M
4
M
M
5
M
M
M
M
Datorteknik TopologicalSort bild 20
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
M
M
M
2
M M
3
M
M
M
4
M
M
5
M
M
M
M
M
M
Datorteknik TopologicalSort bild 21
+
-
1
2
43
Add one
Equal?Left shiftone bit
B
1
M M
M
Datorteknik TopologicalSort bild 22
+
-
1
2
43
Add one
Equal?Left shiftone bit
B
1
M M
M
2
M M
Datorteknik TopologicalSort bild 23
+
-
1
2
43
Add one
Equal?Left shiftone bit
B
1
M M
M
2
M M
3
M
M
Datorteknik TopologicalSort bild 24
+
-
1
2
43
Add one
Equal?Left shiftone bit
B
1
M M
M
2
M M
3
M
M
4
M
M
M
Datorteknik TopologicalSort bild 25
+
-
1
2
43
Add one
Equal?Left shiftone bit
B
1
M M
M
2
M M
3
M
M
4
M
M
M
Combinational loop
Datorteknik TopologicalSort bild 26
Static timing analysis
Use the topological sort procedure
Use max delay as component output
Datorteknik TopologicalSort bild 27
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
32
15
26
20
18
8
0
00
0
0
Datorteknik TopologicalSort bild 28
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
0
8
8
32
15
26
20
18
8
0
00
0
0
Datorteknik TopologicalSort bild 29
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
20
0
8
8
32
15
26
20
18
8
0
00
0
0
0
Datorteknik TopologicalSort bild 30
0
8
8
32
15
26
20
18
8
0
00
0
0
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
0 20
3
40
40
0
Datorteknik TopologicalSort bild 31
0
8
8
32
15
26
20
18
8
0
00
0
0
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
0 20
3
40
40
0
4
00
Datorteknik TopologicalSort bild 32
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
3
4
5
0
15
5581
0
8
8
32
15
26
20
18
8
0
00
0
0
0 2040
40
0
00
0
26
Datorteknik TopologicalSort bild 33
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
3
4
5
15
8140
0
26
Datorteknik TopologicalSort bild 34
Compiled simulation
Use the topological sort procedure
Use logic function as component output
Datorteknik TopologicalSort bild 35
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
5
47
11
1
Datorteknik TopologicalSort bild 36
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
12
5
47
11
1
2
2
Datorteknik TopologicalSort bild 37
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
655
47
11
112
2
2
Datorteknik TopologicalSort bild 38
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
3
-9
-9
11
5
47
11
1
65
12
2
2
Datorteknik TopologicalSort bild 39
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
3
4
7
5
47
11
1
-9
-9
11
65
12
2
2
7
Datorteknik TopologicalSort bild 40
+
-
1
2
5
3
4
Add one
Equal?Left shiftone bit
A
1
2
3
4
5
4
4
4
77
4
5
47
11
1
-9
-9, N=1
11
65
12
2
2
4, Propagate NEG INPUT
1010
0
NEG
POS
Datorteknik TopologicalSort bild 41
+
-
1
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Add one
Equal?Left shiftone bit
A
1
2
3
4
5
4
10-9
7
0
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