CHAPTER 1 Basic VLSI Design - WBUTHELP.COM · 2012. 6. 26. · CHAPTER 1 Basic VLSI Design + DRAIN...
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CHAPTER 1 Basic VLSI Design
+ DRAIN Vdd - n Type Silicon SOURCE Figure 1.1: The beginning of the n-channel JFET
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Figure 1.3 : p-channel JFET
Figure 1.2
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Fig.1.4 Schematic Symbols .
Figure 1.5 Physical structure of MOS transistors and their schematic icons
p+ p+
n substrate
channel
Source Drain
p transistor
G
S
D
SB
Polysilicon Gate SiO2
Insulator L W
G
substrate connected to V DD
Source
n transistor substrate connected
Polysilicon Gate SiO2 Insulator
n+ n+
p substrate channel
Drain G
S
D
SB
L W
G
S
D
to GND
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Figure 1.6(a): NMOS-transistor
Figure 1.6(b): P-transistor .
Figure 1.6 (c ): C-switch .
N
D
S
G
D
S
G
P
D
S
G
D
S
G
C D S
-G
G
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.
Figure 1.7: Transistor schematic of a static complementary inverter.
vdd
a b
vdd
a o/p
a o/p
b b
vss
a b
vss Fig. 19. NAND gate schematic
Fig 1.8 NOR gate schematic
VDD
Out
Gnd
In
Inverter
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Figure 1.10: A dynamic latch circuit.
.
Figure 1.11(a): Wires and wire segments.
Figure 1.11(b): Schematic symbols for transistors
D
F 1
F
Cg
Q1
Wire segments
n-type p-type
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Figure 1.12: General CMOS Layout structure, Circuit and the Layout diagram of CMOS Inverter.
VDD
Out
Gnd
VDD
Out
Gnd
Pullup Network
(p-transistors)
Pulldown Network
(n-transistors)
InInputs
Inverter
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Figure 1.13: Stick diagram
Table 1.1 Rules for possible interactions between layers.
Figure 1.15: The inverter circuit used for delay analysis
VDD In VSS
Out
Metal p-diff n-diff poly
Figure 1.14: Stick diagram symbols
VDD
CL
Gnd
In
Inverter
t
Input voltage
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Figure 1.16: Circuit used for power consumption analysis
Figure 1.17: A pseudo-nMOS NOR gate
Figure 1.18: A circuit model for stuck-open faults.
VDD
t1
t2 b a CL
VDD
CL
Gnd
In
Inverter
t
VDD
CL
Gnd
Id,p IL
Id,n
a b
output
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Figure1.19: Testing for combinational faults.
A
B
E
G
C
F
D
i1
i2
i3 i4
i5
i6 i7
i8
W1
W2 O1
O2
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Fig. 1.20 Commercially available FPGA architectures
1 PO 2 PO 3 PO
4 PI 5 PI 6 7
8 PI 9PI 10PI 11PI
Fig 1.21 Initial 3-restricted DAG
1 2 3
Symmetrical Array Row-based Interconnect
Interconnect
Logic Block
Logic Block
Interconnect
Interconnect Overlayed on Logic Blocks
Sea-of-Gates Hierarchical PLD
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4 5 10 11
8 9
Fig. 1.22 Mapping of the 3-restricted DAG by four 3-LUTs connection between wire segments in x and y axes and also vias.
Fig.1.23 3-D FPGA architecture
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CHAPTER 2 VLSI CAD
Figure 2.1: Y-chart
System
Register transfer
Logic
Circuit
BEHAVIOR
Algorithms, flowcharts
Register Transfer
Boolean expression
Transfer function
STRUCTURAL
Processors, Memories
Registers, flipflops, MUX
Gates
Transistors
Cell layout
Modules
Boards
PHYSICAL
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CHAPTER 3
Partitioning in High Level Synthesis
Figure: 3.1 Example: Behavioral description of a 4 bit Shift multiplier
.
A_PORT B_PORT Architecture SHIFT_MULT of MULT is begin START begin process variable A,B,M: BIT_VECTOR CLK variable COUNT: INTEGER begin M_OUT DONE wait until (START =1) A:= A_PORT; COUNT :=0; Entity MULT is B:=B_PORT; DONE<=’ 0 ’ Port (A_PORT, M:=B”0000”; B_PORT: in bit _ vector(3 down to 0); while (COUNT <4) loop M_PORT: out bit _vector (7 down to 0); if (A(0)=’1’) then M:=M+B; CLK: in BIT end if; START: in BIT A:=SHR(A,M(0)); DONE: out BIT; M:=SHR(M,’0’); ); COUNT:=COUNT+1 end MULT; end loop; M_OUT <=M & A; DONE <=’1’; End process; End SHIFT_MULT;
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Figure: 3.2 CDFG for the shift-multiplier example
0 1
B1
0 1
B4 0 1
B2
0 1
B3
Control-flow graph
Read START ‘1’
=
Read A_PORT Read B_PORT ‘0’
Write A Write B Write COUNT
‘0’
Write DONE
B”0000”
Write A
Read A[0] ‘1’
=
Read COUNT ‘4’
<
Read M Read A
&
Write M_OUT
‘1’
Write DONE
Read M Read B
+
Write M
Read A Read M[0]
Write A
Write COUNT
‘1’
Write M
Read M SHR Read
COUNT
+
‘0’
SHR
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Figure : 3.3 Scheduled CDFG for the shift multiplier
START=1
A=A_PORT; COUNT=0; B=B_PORT; DONE <= 0 M=B” 0000” ;
COUNT <4
A(0) = ‘1’
M = M + B;
ENDIF
M_OUT <= M & A; DONE <=’1’;
A=SHR(A,M(0)); COUNT=COUNT + 1; M=SHR(M,’0’);
S0
S1
S2
S3
0
1
1
B10
0 B4
0 B2
B3
1
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Figure: 3.4 Initial unit selection for the shift-multiplier design
Mult Count_Reg B_Reg A_Reg
Shift1 Shift2 Compar Adder
A_PORT B_PORT
START
CLK
DONE M_OUT
Concat enator
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Figure 3.5 Synthesized design for the shift-multiplier example
A= S0 & START=1 B= S0 & ~(START=1) C= S1 & COUNT < 4 D= S1 & ~(COUNT < 4) E= S2 & A(0)=1 F= S2 & ~ (A(0)=1) G= S3 Control Unit A B C D E F G Mux1 - - - - 1 - 0
Mux2 1 - - - - - 0
Mux3 - - - - 0 - 0
Mux4 - - - - 0 - 1
Load A_Reg 1 - - - - - 1
Load B_Reg 1 - - - - - -
Clear Count_Reg
1 - - - - - -
Load Count_Reg
- - - - - - 1
Clear Multiplier
1 - - - - - -
Load Multiplier
- - - - 1 - 1
Adder - - - - 1 - 1
Shift1 - - - - - - 1
Shift2 - - - - - - 1
DONE 0 - - 1 - - -
Next State S1 S0 S2 S0 S3 S3 S1
Multiplier Count_Reg
B_Reg A_Reg
Mux1
Comp
Adder
A_PORT B_PORT
START
CLK DONE M_OUT
Mux2
Shift2 Shift1
0
Mux3 Mux4
0001
0100
State Reg
A_Reg(0)
Comp LT
Concat
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3.2 PARTITIONING
Figure 3.6 Circuit Partitioning: (a) an example (b) graph and its physical representations
FF1
REG
FF2 Chip1
Chip2
a b d e f g
c
nj ni
a b
a
b
G1
G2 v
G
c v
d v
e f
g
a
e25
e24 v
e36 v
v1 v2 v3
v4 v5
V6
ni nj
c
d e f g
(a) (b)
(b)
Cutline
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3
V(24135)
5
1
3
5
1
3
4
3
V1 V1 V2 V3 V4 V5
Graphical Representation Closeness measurement Cluster Tree Representation
V5
V2413
V2413 V5
V2413 -- --
V5 3 --
V(24)
V(241)
V(2413)
3
V1 V2 V4 V3 V5
V3
V5
V2
V4
4
6
V1 -- -- -- -- -- V2 5 -- -- -- -- V3 4 1 -- -- -- V4 0 6 0 -- -- V5 0 3 0 0 --
V1 V2 V4 V3 V5
V(24)
V1
V3
V5
4
V24
V1 V24 V3 V5
V1 -- -- -- -- V24 5 -- -- -- V3 4 1 -- -- V5 0 3 0 --
V1 V2 V4 V3 V5
V(24)
V(241)
V3
V5
V241 V241 V3 V5
V241 -- -- -- V3 4 -- -- V5 3 0 --
V1 V2 V4 V3 V5
V(24)
V(241)
V(2413)
(a)
(b)
(c)
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3 4 1 2 5
c e f b a d b
Criterion B a b c 3
2 1 5 4
Figure 3.7 : Cluster tree formation a b c f c a e d b
(d)
d e f
First cutline
(a)
d e f
(b)
{ f, c}
{ d }
{ b }
{ a, e}
5
3
2
1
{ a, e}
{ f,c}
{ b }
{ d}
(c)
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f c a e d b
Figure 3.8 Clustering based on a) criterion A only, b) criterion B only, c) Criterion A below the first cut-line, then criterion B, d) criterion B below the first cut-line, then criterion A e) criterion A below the second cut-line, then criterion B
{ c, e}
{ a, d }
{ b }
{f }
5
4
1
{ c, e}
{ f }
{a ,d}
{ b }
(d)
Second Cutline
{f, c}
{a,e,d}
{ b}
5
3 2
{a,e,d}
{f, c}
{ b}
(e)
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1 2 3 4 5 6 7 8 9 10
40 20 10 10
Figure 3.9 Two-way partition
Figure 3.10 Interconnection reduction by node interchanging: a)before interchanging vi and vj, b) after interchanging vi and vj
Figure 3.11: Kernigham-Lin Search Strategy
vi G1
vj G2
Cutline
vj G1
vj G2
Cutline
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Figure 3.12 (a) two cluster partition
Figure 3.12 (b) three cluster partition
G1
O2
(+) o1 (+)
O3 (*)
a b c
G3
e13 e23
O2
(+) o1 (+)
O3 (*)
a b c
G3
e13 e23
o1 (+)
o2 (+)
e13 e23
mult1 G2
add1 G1
e13 e23
mult1 G3
add1 G1
add2 G2
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e10,11
v4 e4,9 v9
v2 e2,5
v5 e5,7
v7 v8
v3 e3,6 v6 e6,8
CHAPTER 4 Scheduling in High level Synthesis
Figure 4.1(a) Text description
Figure 4.1 (b) DFG (Data Flow Graph)
While (x<a) do { x1:= x + dx; u1:= u – (3 * x * u * dx) – (3 * y * dx); y1:= y + (u * dx); x:= x1; u:=u1; y:=y1; }
u dx 3 x u dx x dx
* * * +
* * +
y y
* -
-
dx u
<
c
a
v10
v11
v1
e1,5
e7,8
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V1 V2 V3 V4 V10 E=1 E=2 V5 V6 V9 V11 E=3 V7 E=4 V8 (a)
V1 V2 L=1 L=2 V5 V3 L=3 V7 V6 V4 V10 L=4 V8 V9 V11 (b)
1 2 3 4 5 6 7 8 9 10 11 S1 S2 S3 S4 (a)
V1 V2 S1 S2 V5 V3 V10 S3 V7 V6 V4 S4 V8 V9 V11 (b)
Figure 4.2: (a) ASAP schedule, (b) ALAP schedule.
Figure 4.3: An ILP scheduling example: (a) ranges for operations, (b) final schedule,
* * *
+
*
*
+
*
-
-
<
* *
* +
* *
+
* -
- <
* *
*
+ * *
+
* -
- <
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S1 2.33 1 2
S2 2.33 5 3 S3 1.33 7 6 4 10 S4 0.00 8 9 11 (c) (d)
-------------------------------------------------------- ---------------------------------------
S1 1 2 3 4 10 2.83
S2 5 2.33
S3 7 6 0.83
S4 8 9 11 0.00
(a) (b)
Figure 4.4: Force-directed scheduling example: (a) probability of scheduling operations into control steps, (b) operator cost for multiplications in a, (c) probability of scheduling operations into control steps after operation o3 is scheduled to step s2, (d) operator cost for multiplications in 4.4c. '
* *
*
+
*
*
+
*
-
-
<
* *
*
+
* *
+
*
-
-
<
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S1 S2 S3 S4
S1 S2 S3 S4
* * - + < S1 1 2 10 S2 5 3 11 S3 6 4 7 S4 8 9
Figure 4.5: Rescheduling: (a) initial schedule where three operations are movable to five control steps (dashed arrows), (b) after operation 6 is moved and locked.
Plist* = 1<0>, 2<0>,3<1>, 4<2>
<0> <0> <2> <2> Plist+ =10<2> Plist- = NIL <0> <1> <2> <2> Plist< =NIL (b) <0> <1>
Resources* = 2 Resources+ = 1 <0> Resources- = 1 Resources< = 1 (c) Figure 4.6: List scheduling: (a) a DFG with mobility labeling (inside < > ), (b) the list of ready operations for control state s1, (c) the resource constraints, (d) the scheduled .DFG
1 2 3 4 10
5 6 9 11
7
8
(a)
1 2 3 4 10
5 6
9 11
7
8
(b)
* * * +
*
* + < *
-
-
(a)
* *
*
+
*
*
+
< *
-
-
(d)
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2 4 10 1 5 3 9 11
7 6 8 (a) (b) 2 1 10 S1 2 1 10 3 5 S2 3 5 11
S3 4 6 7 S4 8 9 (c ) (d) Figure 4.7: Static-list scheduling: (a) a DFG (b) priority list, (c) partial schedule of five nodes, (d) the final schedule.
Node 8 9 11 7 6 4 10 5 3 1 2
ALAP 1 1 1 2 2 2 2 3 3 4 4 ASAP 4 2 2 3 2 1 1 2 1 1 1 Priority 1 2 3 4 5 6 7 8 9 10 11
*
*
-
-
*
*
*
+
+
+
<
*
*
*
*
+
<
*
-
*
+
-
* *
* *
*
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S1 S2 (a)
S1 S2 (b)
S1 (c)
S1 S2 S3 (d)
Figure 4.8: Scheduling with arbitrary-delay units
Figure 4.9: CDFG for a behavioral description with a conditional construct.
a:=a+1; if(a>100) then b:=a/c; else b:=d/c; endif c:=c-g;
+
* -
+ *
-
+ *
-
*
*
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ALU1 ALU2 ALU3 S1 S2 S3 (a) ALU1 ALU2 ALU3 S1 S2 S3 (b)
v1=v2+v3 v4= v2*v3 v5=v1+v4 v6=v4/v1 v2=v4*v5
v4=v2*v3 v1= v2+v3 v5=v1+v4 v6=v4/v1 v2=v4-v5
1 2 3 4 5 7 8 12 11 10 9 6
b
time
10,11, 12 7, 8, 9 4, 5, 6 1, 2, 3
u
(a)
(b)
1
2
3
4
5
7 10
8 11
6 9 12
m
p
(c)
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ALU1 ALU2 ALU3 S1 S2 S3 ( c ) Figure 4.11: Scheduling using simulated annealing : (a) an initial schedule, (b) after swapping two operations, (c) after displacing an operation.
v4=v2*v3 v1= v2+v3 v5=v1+v4 v2=v4-v5 v6=v4/v1
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Figure 4.12: Path-based scheduling: (a) an example CDFG, (b) a path in the CDFG with constraint intervals, (c) scheduled CDFG.
4.5.3 DFG Restructuring
2
3
1
9
8
5 4
10
7
6
ipp<=pc ipo<=oldpc outbus,=inbus + 8 if( jump = ‘1’) then pc<= jumppc endif wait until (cond=’T’) oldpc<= pc pc< = pc + 8
2
3
1
9
8
5 4
10
7
6
2
3
1
9
8
5 4
10
7
6
write
jump
loop
write
i1
i2
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Figure 4.13: DFG restructuring : (a) DFG (b) DFG after tree-height reduction
+
+
+
+
+
a b c d e f
1
2
3
4
5
(((a + b) + c) + d) + (e + f) (a)
+
+
+
+
+
a b c d e f
1
2 3
4
5
((a + b) + c) + (d + (e + f)) (b)
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Figure 4.13: DFG restructuring: (c) DFG (d) DFG after redundant operation insertion.
+
+
+
+
a b d c
1
2
3
4
5
d (a + b + c) + (a+b) + (a+b) (c)
*
+
+ +
+
a b d c
1
2
3
45
d (a + b + c) + 2(a+b) (d)
*
+ 6
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CHAPTER 5 Data Path Allocation in High Level Synthesis
a b c d o1 o2 r1 r2 r3 r4 S1 e f S2 o3 o4 g h Add1 Add2 Figure 5.1: Mapping of behavioral objects into RT components.
+ +
+ +
a b ,e, g c ,f, h d
+1 +3 +2 +4
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+
+
+
+
O1
O2
O3
O4
a b c d
e f
g h
S1
S2
r1 r2 r3 r4
+1 +4 +2 +3
a b, e, g c, f, h d
ADD1 ADD2
r1 r2 r3 r4
+1 +3 +2 +4
a ,g b, e c, f d,h
ADD1 ADD2
r1 r2 r3 r4
+1 +4 +2 +3
a ,g b, e c, f d,h
ADD1 ADD2
(a) (b)
(c)
(d)
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S1 S2 Edge Common Neighbor e1
1,3 1 e1
1,4 1 e1
2,3 0 S3 S4 S5 e1
2,5 0 e1
3,4 1 e1
4,5 0 (b)
S13 S2 Edge Common Neighbor e1
13,4 0 e1
2,5 0 e1
4,5 0 S4 S5 (c)
S134 S2 Edge Common Neighbor e1
2,5 0 S5 (d)
v2
v5
S134 S25 Cliques: S134 = { V1, V3, V4 } S25 = { V2, V5} (e) (f)
v1
v3 v4
Figure 5.2: Interdependence of functional-unit and storage binding
(a)
Figure 5.3: Clique partitioning example
v1 v2
v3 v4 v5
v1 v2
v3 v4 v5
v1
v3 v4
v2
v5
v1
v3 v4
v2
v5
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V1 V2
S1 V6 V4
V3 S2 V10 V5
V7 S3
V11 V8 V9 S4
V1 V2 (a)
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 R W R W R W R W (b)
Cliques: {v1,v8}=r1 {v2,v3,v9}=r2 {v4,v5,v11}=r3 {v6,v7}=r4 {v10}=r5 (d)
*
/ +
* - -
- +
(c)
v3
v8
v10 v1
v9 v2
v7
v5
v6 v4
v11
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V1 V10 V4 V6 V2 V3 V5 V7 V8 V9 V11 V11 V1
2 S1
S2
S3 S4
Cluster 1 Cluster 2 Cluster 3 Cluster 4 (a)
Figure 5.4: Register allocation using clique partitioning: (a) a scheduled DFG, (b) lifetime intervals of variables, (c) the graph model for register allocation, (d) a clique-partitioning solution
V1 V10 V4 V6 V2 V3 V5 V7 V8 V9 V11 V1’ V2’ r1 r2 r3 r4 r5
S1 V1 V10 V4 V6 V2 V3 S2 V5 V7 S3 S4 V8 V9 V11 V1 V2 Figure 5.5: Register allocation using the left-edge algorithm: (a) sorted variable lifetime intervals, (b) five-register allocation result.
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r1 v3
r1 = { v1 , v8 , v11}
r2 r2 = { v9 , v10 } r3 = { v4 , v5 , v11} v5 r4 = { v6 , v7 }
r3 r5 = { v2 , v3 , v12}
r4 v7
r5
Set R Set V (b) (c)
Figure 5.6: Weighted bipartite-matching for register allocation: (a) sorted lifetime intervals with clusters, (b)
bipartite graph for binding of variables in Cluster2 after Cluster1 has been assigned to the registers, (c)
final binding of all variables to the set of registers.
v1
v10
v4
v6
v2
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CHAPTER 6 LOGIC SYNTHESIS
(a) (b)
( c) Figure 6.1 Cubic representation of a boolean function of (a) one variable (b) two variables and ( c) three
variables.
10
00
11
01
0 1
001 m1
011 m3
010 m2
110 m6
100 m4
101 m5
000 m0
111 m7
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FIGURE 6.2 A cubic representation of the function F(A, B, C) = ? m(0, 2, 3, 4, 7).
FIGURE 6.3 A cubic representation of the function G(A, B, C) = A1C1 + B1C1 + ABC.
m3
m2
m4
m0
m7
A
C
B
m2
m4
m0
m7
A
C
B
x00
0x0
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A m6 X1X m7 m2 B m3 C Figure 6.4: A cubic representation of the function H(A, B, C) = B.
F(xi) xi F= xi F(xi) + x1
i F(x1i)
F(x1i)
x1
i (a) F1(xi) x1
i F= [x1i + F1(xi)][ xi +F1(x1
i)] F1(x1
i)
xi (b)
Figure 6.5 An expanded function F, represented (a) in NAND-NAND logic, and (b) in NOR-NOR
logic.
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Figure 6.6: A binary tree representation of the function F = A(BD + B1C1) + A1( BC1 + B1CD).
(a) (b)
(c) Figure 6.7 Binary decision diagram of the functions (a) AB (b) A+B and (c) A(+) B.
A
B B
C C C D
D
F
0
0 0
1
1
1
1
A
B
Y=AB
0
0
1
1
Y=0
Y=0 Y=1
A
B
Y=A+B
0
0
1
Y=0
Y=1
Y=1 Y=
1
A
B
Y
0
0
1
Y=0 Y=1
B
0
1 0 1
0
1 1 0 0
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1 0
0 0
0 0
1 1
1 1
2 3
4,7 5,6
(a) (b) FIGURE 6.9: Realization of the function Y = A (+) B (+) C (a) The binary tree; (b) the tree reduced to the
BDD,
B
C
0
0
1
1
m0 m1 m2 m3 m4 m5 m6 m7
C0
1 1
B
C
0
0
1
1 C
0
A 1 0
1 2 3
7 6 5 4
B
C
0
0
1
1
0 1 1 0 1 0 0 1
C0
1 1
B
C
0
0
1
1 C
0
A 1 0
1 2 3
7 6 5 4
A
B B
C C
0 1
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(a)
B
C
0
0
1
1
1 0 1 0 0 0 1 1
C0
1 1
B
C
0
0
1
1 C
0
A 1 0
1 2 3
7 6 5 4
B
C
0
0
1
1
1 0 1 0 1 0 (b)
C0
1 4,5
B
0
1
C
A0
Y
2
5 4
A
Y
0
C
A
Y
0
01
1 0
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(c) Figure 6.10 Realization of the function, Y(A, B, C) = ? m(0, 2, 6, 7) (a) The binary tree (b) reducing the tree(c) the BDD.
B
A
D
F
E
C
0 (a) 1
1
1
0
1
1
1
1
0
0
0 0
0
F
BC
A
Y
0 1
0
1 1 0 0
0 1 1
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Figure 6.11: BDD illustrating (a) Advantages of a good ordering, (b) Drawbacks of a bad ordering
C
A
D
F
E
C
0 (b) 1
F
E E E
B B B B
D
B
D
0
0
1
1
0 1 0 1 0 1 1 1 (a)
D0
1 1
B
D
0
0
1
1 D
0
A 1 0
1 2 3
7 6 5 4
Y
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Y (c) (d) FIGURE 6.12: Realization of the function Y = AB + D. (a) The binary tree; (b) reducing the tree; (c) the
BDD; (d) counting the paths to an output.
B
0 1
0 1 0 1 (b)
D0
1 1
B
0 1
1 D
0
A 1 0
1
1
B
0 1
0-
D
0
A 1
Y
0 1 1
B
1 1
1-
D
0
A 1
Y
2 2
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1 0
0
1
0
1
0 1
1 1
2
1
1
2
2 2
(a) (b)
FIGURE 6.13: The BDD for the function Y = AB + D, with D the most significant bit. (a) The binary tree; (b) BDD.
(a) (b)
FIGURE 6.14: Realization of the function Y = AB + CD. (a) The BDD; (b) the number of paths to an
out put.
B
D
0
0
1
1
0 0 0 1 1 1 1 1
D0
1 1
B
D
0
0
1
1 D
0
A 1 0
1 2 3
7 6 5 4
Y
A
B
0
0
1
1 0 0
D 1
1
Y
1
A
B C
D
0 1
A
B C
D
0 1
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THEN ELSE
ELSE
FIGURE 6.15: If-then-else diagrams of (a) AB, (b) A + B, and (c) A (+) B. FIGURE 6.16: If-then-else diagrams of (a) AB + A1C and (b) ABD
B
A
0
THEN ELSE
IF
B
A
1
THEN ELSE
IF
B
ATHEN ELSE
IF
B
B
ATHEN ELSE
IF
A
1
IF
D
THEN
B C
IF
0
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b
a BTHEN
ELSE
F
THEN ELSE
1 0
1 c
a CTHEN
ELSE
G
THEN ELSE
1 0
0
d
b DTHEN
ELSE
H
THEN ELSE
1 0
1 b
a THEN
ELSE
I
THEN ELSE
0 D
C
F 2 F 1
Inputs Outputs
AND plane
OR plane
Register Register
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VDD VDD GND GND VDD GND P0
P1 P2 P3 GND VDD F 2 F 2 F 1 F 1 I0 I1 I2 Y0 Y1 Y2
FIGURE 6.18: The basic floor plan of a PLA structure.
FIGURE 6.19: A stick drawing of an NMOS NOR-NOR PLA realization.
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A A1 B B1 C1 C D1 D Y1 Y2 Y3 P1=A1BC Y1=P1+P2
Y2=P1+P3+P4 P2=AB1D1 Y3=P2+P3 Y4=P4+P5 P3=A1C1D1 Y5=P5+P6 Y6=P4+P6 P4=CD1E P5=CEF1
P6=E1FG1
E1 E F1 F G1 G D1 D Y4 Y5 Y6
Inputs Outputs Inputs I1 I2 I3 Y1 Y2 Y3 Y4 I7 I8 I9 I10 P1 P5 P2 P6 P3 P7 P4 P8 I1 I4 I5 I6 Y5 Y6 Y2 Y7 Y3 Y8 I11 I12 I9 I10 AND Plane OR Plane AND Plane
FIGURE 6.20: A column custom-folded PLA. (a) AND-plane column-folding; (b) OR-plane column-
folding.
FIGURE 6.21: A row or product-line folded PLA.
. .
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1 2 3 4 5 6 7 8 9 10 P1 AB1
P2 AC
P3 D P4 A1B
P5 B1C A1 A B1 B C1 C D1 D Y1 Y2 (a)
A B1 C D P1 AB1
P2 AC P3
D P5 B1C P4 A1B A1 B C D Y1 Y2
(b)
Figure 6.22: A simple PLA implemented (a) directly, and (b)optimized
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A B1
C D E1
2i 3i
(b) FIGURE 6.23 (a): Multilevel NOR diagram of the function Y = A’B’ + C’(D + E’) (b) a typical NMOS NOR gate.
?
d ? ß
V (a)
W X
Y
1i
VDD
GND
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Figure 6.25 An FSM with redundant states and its minimized version.
0/0
0/0
1/1
0/0
1/0
1/1
1/1 0/0
1/1
0/0
0/0
0/0
0/0
1/1
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CHAPTER 7
PHYSICAL SYNTHESIS
Figure 7.1: Physical design cycle
Circuit Design
Partitioning
Floorplanning & Placement
Routing
Compaction
Extraction & Verification
Fabrication
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(a)
(b)
(c )
A
D
E
B 8 C
F G
H I
6 1 7
2
5 4
3
1
2 3
4 7 5 6
F G H I D E A
B C
H
V
H
V V V V
H
F G H I D E A
B C
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( d) Figure 7.2: Floorplan with slicing tree and a non— slicing floorplan.
Figure 7.3: Interconnection topologies.
Figure 7.4: Phases of routing.
(a) Global Routing (b) Detailed Routing
A a
D d
b B
c C
Fig 7.3 (a) Steiner tree (b) minimum spanning tree (c) complete graph
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Figure 7.5: A net routed by Lee’s algorithm. obstacle T S Figure 7.6: A net routed by Mikami-Tabuchi’s Algorithm obstacle T S Figure 7.7: A net routed by Hightower’s Algorithm
6 5 4 3 4 5 6 7
5 4 3 2 3 4 5 6
4 3 2 1 2 3 4 5
5 4 3 2 3 4 5 6
6 5 4 3 4 5 6 7
7 6 5 4 5 6 7 8
8 7 6 5 6 7 8 9
9 8 7 6 7 8 9 10
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1 Switchbox 1
2 2 (c) (d)
1 3 3 4 2 2 1 (a) (b)
Figure 7.8: Channels and Switchboxes 7.4.2.1 Problem Formulation
(a) (b)
Figure 7.9: (a) Grid-based. (b) Gridless
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Layer1 Layer2 Track 1 Layer3 Via Unreserved Layer Model
1 4 2 0 2 1 1 0 3 4 0 upper boundary lower boundary Terminal 3 0 1 2 0 3 4 0 0 2 3 Net list: 1 4 2 0 2 1 1 0 3 4 0 3 0 1 2 0 3 4 0 0 2 3
Track2 Track 3 Track1 Track 2 Track 1 Figure 7.10: A comparison between HVH, VHV, and unreserved layer models.
Figure 7.11: A channel and its associated net list.
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upper boundary terminals via Tracks Dogleg Lower boundary trunks branches
1 5 2 0 2 1 1 0 3 4 0 3 0 1 2 0 3 4 0 0 2 3 (a) 1 5 2 4 3 (b)
Figure 7.12: Terminology for channel routing problems.
Figure 7.13: A routing problem and its HCG .
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1 5 2 0 2 1 1 0 3 4 0 3 0 1 2 0 3 4 0 0 2 3 (a) 1 5 2 4 3 (b)
4 1 2 3 1 2 3 4 (c)
Figure 7.14: A channel routing problem and its VCG.
. The figure 7.15 (a) shows a channel routing problem with a vertical constraint
cycle while figure 7.15 (b) shows how a dogleg can be used to break a vertical constraint cycle. Figure 7.15(c) shows vertical constraint cycle involving four nets. In figure 7.15(d), we show one possible routing for the example in figure 7.15(c).
1 2 1 2 2 1 2 1 (a) (b)
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4 1 2 3 1 2 3 4 (d)
Figure 7.15: A cyclic vertical constraint.
1 5 2 4 3 Figure 7.16: A combined constraint graph (CCG) 7.4.2.5 Left-edge Channel Routing Algorithm
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7.5 Compaction
Figure 7.17: Constraint graph generation
v3 ? 1 v2 ? 1 5 ? v4 2
v0 ? 4 1 v1 ? 2 ? v5 Fig 7.18: Input DAG
Q P1 P2 P3 P4 P5 x1 x2 x3 x4 x5 “not initialized”
{v0} {v1}
{v2,v5} {v3,v5}
{v5} {v4}
1 2 1 2 1 0 1 1 2 1 0 0 1 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 5 0 0 0 1 5 0 0 3 1 5 6 6 3 1 5 6 6 3 1 5 6 7 3 1 5 6 7 3
Table 7.2:Results of Longest Path algorithm
A
B
C
D
F
E
A
C
F
B D
E
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. v3 ?
1 v2 ? -1 1 5 ? v4 2 -3
v0 ? 4 -4 1 v1 ? 2 v5 ?
Fig 7.19: DAG with a few backward edges
Step x1 x2 x3 x4 x5
Initialize Forward 1
Backward 1 Forward 2
Backward 2 Forward 3
Backward 3
-8 -8 -8 -8 -8 1 5 6 7 3 2 5 6 7 3 2 5 6 8 4 2 5 7 8 4 2 5 7 8 4 2 5 7 8 4
Table 7.3:Results of Liao-Wong algorithm
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APPENDIX A VHDL BASICS
Figure A.1(a) (b) Figure A.1: Example of structural description.
A Y
F B
?
?
?
F A Y
G B
?
?
?
A Y
H B
?
?
?
A Y
I B
?
?
?
?
?
?
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Figure A.2 Structure of count2 .
Graph Theory Basics
A B C D E Fig. B.1 A graph 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 Fig. B.2 Adjacency matrix representation
COUNT2 BIT_0 Q0 CLK FF0 BIT_1 INV Q1 INV_FF0 FF1
T_FLIPFLOP CLK Q
? ?
INVERTER A Y
T_FLIPFLOP CLK Q
?
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A B E NULL B A C D NULL C B E NULL D B E NULL E A C D NULL Fig.B.3 Adjacency list representation
V5 V2 V3 V2 V4 V5 V4
V1 V3 V3
(a) (b) Fig B.4: A directed graph (a) and its adjacency list representation(b). When this algorithm is applied on graph shown in Fig B.4, the algorithm takes different steps as shown in table BT.2
Q W Edges processed (V1) (V1 , V2)
(V3 , V4, V5 )
(V4, V5 )
(V5)
V1
V2
V3
V4
V5
(V1 , V2) ,(V1 , V3) (V2, V4) ,(V2 , V5) NULL (V4 , V3)
NULL
V1
V2
V3
V4
V5
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Table BT.2: The different steps of the breadth-first search algorithm applied to the graph of figure B.4 V1 2 V6 6 1 3 1 V2 V5 2 1 1
1 V4 V3 5 Fig B.5 : An edge-weighted directed graph.
Iteration T vi .distance, for i = 1 2 3 4 5 6
1 2 3 4 5 6
{ V1} { V1 , V4}
{ V1 , V4, V5} { V1 , V4 ,V5 ,V6}
{ V1 ,V4 ,V5 ,V6 ,V2} { V1 ,V4 ,V5 ,V6 ,V2 ,V3}
6 8 1 3 8 6 6 2 8 6 6 3 4 6 5
Table BT.3: The evolution of the distance attributes in Dijkstra’s algorithm when applied to the graph with vs = v1 and vt=v2 . 2 V2 2 V2 1 5 1 V1 4 V3 2 V5 2 V1 V3 2 V5 2 1 1 3 V4 V4 Fig B.6 An edge-weighted undirected graph(a) and its minimum spanning tree (b).
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Iteration U Vi .distance, vi .via_edge, for i =
1 2 3 4 5 0 1 2 3 4
V1 V2
V3 V4
V5
2, (V1 ,V2) 4, (V1, V3) 3, (V1, V4 ) +8 ,? 1, (V2, V3 ) 2, (V2, V4 ) 5, (V2, V5 ) 1, (V3, V4 ) 2, (V3, V5 ) 2, (V3, V5 )
Table BT.4: The evolution of Prim’s algorithm when applied to the graph of figure B.6a.