MSc Thesis KwasiAduBoahenOpare 20th October 2010
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Transcript of MSc Thesis KwasiAduBoahenOpare 20th October 2010
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7/31/2019 MSc Thesis KwasiAduBoahenOpare 20th October 2010
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7/31/2019 MSc Thesis KwasiAduBoahenOpare 20th October 2010
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7/31/2019 MSc Thesis KwasiAduBoahenOpare 20th October 2010
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S
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(1)
T 4
T 4
T 5
T 5
T 6
T 6
T 7 T 8
T 8 T 9
T 9
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T 11
T 11
A (1)
T 2 A
S A ( p)
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w
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7/31/2019 MSc Thesis KwasiAduBoahenOpare 20th October 2010
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m n
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n
m
C in = n (m + 1)
C out = m − 1
C clk = n (m + 1) + m − 1
n
m
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AND OR NOT NAND NOR XOR
0 1 w
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w
(abc) = (001)
0 w 1
Z 1
0
w
NOR
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Q 1 Q 2
Q 3
Q 4 d
Q 1 Q 1
(w1, w2) = (0 , 0), (0, 1), (1, 0), (1, 1) (0, 0) Q 3
Q 4 F 1 (0, 1)
F 0 Q 2
(1, 0) Q 1 F V ss
F 0(1, 1) Q 2 F
0
Q 1
(1, 0) F
F (0, 0)
(0, 0), (1, 0) Q 1 F
NAND d
Q 4 (1, 1)
Q 1 Q 2 Q 4
Q 2
(1, 0)
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Q 1 Q 2 Q 4
Q 2 Q 4
AND OR
AND OR
AND OR
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(x n − 1, ..., x 2, x1, x0)
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( pn − 1, ..., p 2, p1, p0)
2n − 1
(x3, x2, x1, x0)
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p
(x3, x2, x1, x0)
( p3, p2, p1, p0) (x3, x2, x1, x0)
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x1, x 2, ...x n z1, z2, ...z n
y1, y2, ...y k Y 1, Y 2, ...Y k
F F l Y l yl
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D C D S A
B D S
A B
D
A B
D S C
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Y 1, Y 2, ...Y k
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n
m n (m + 1)
n (m + 1) + m − 1
n
m
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B
A B
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
A B
A
B
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A
B B
A B
A B
n
m in =
n (m + 1)
n m
m m
in = n (m + 1)
m n
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˜A ( p)
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r
S
s = m − r
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S
A
A( p) p
A( p)
p
k
x
y
A ≡ [T ], m n [t ij ]
[T ] ≡ [T j ], 1 ≤ j ≤ n T j j th
T k ≡ [t ik ], 1 ≤ i ≤ m, j = k
[T j ]T (r )
k ⊂ T k , r = T k
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S
T (r )k ⊂ T k T k ≡ [t ik ], 1 + r ≤ i ≤ m, j = k
T k ≡ T (0)k
T (− r )
k ⊂ T k T k ≡ [t ik ], 1 ≤ i ≤ m − r, j = k
S
S =n
j =1
S j , S j skip, S, j th A ( p) .
A( p)
S
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•
•
T (r )k T (− r )k+ x
t ik T (r )k , 1 + r ≤ i ≤ m
t ik + x T (− r )
k+ x , 1 ≤ i ≤ m − r,
t ik = t ik + x t ik + x
p = 1 p T pm n
p ≤ n ? A ( p) S A( p) p A ( p)
A
T ( r )k + x + y − 1
T (− r )k + x + y
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T p S p
T p S = 0 T p pivotFound = 1
k = p r = 0 x = 0 y = 0T p initExist = 1
k > 1 1 k + y y + 1 k = 1 + yx y = 0
k < n
S A ( p) p
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T (r )k T (
− r )k+ x
T (0)k+ x
initExist 1
y r = 0
r < mr = 0
T (r )k+ x + y− 1 T
(− r )k+ x + y
pivotF ound = 0 r
pivotF ound = 1 S T k+ x + y
T k+ x + y
initExist = 0
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r = 0 y = 0
r < m x = 1 r = 0
k + x > n(n )
r
T k+ x
pivotF ound = 0 x
T (r )k T (
− r )k+ x
pivotF ound = 0 x
pivotF ound = 1 S T k+ x
T k+ x
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initExist = 1
k +1 k + x + y y+1 x > 1 k = k + y+1x = 1 y = 0
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s s
s
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Q 3 Q 4 Q 7 Q 8
Q 3 Q 4 Q 7 Q 8
A i d
m
n
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A
p = 1 k = p k = 1
x y r x = 0 y = 0 r = 6
T 1
S = 0 T 1
x > 1
k y = 0 xk < 12 T k
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T 1
r y
r = 0 y = 0 r < 6
T k+ x k + x > nT k+ x T 2
T (r )1 T (
− r )2 r = 0 pivotFound =
0 x 2
T 1 T 3 x
x T k+ x
T 3, T 4 T 9 T 12
pivotF ound = 0 x T 12
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(1)
k + x > n T 1
r 1
x 1
T (1)k T (
− 1)k+ x T 2 T 12
r 2 x
1 r = 2 T 6
x = 5 pivotFound 1
S = 4 T 6 T 6
T 2 T 6
T 6 2 k
k = 2 x y x = 1 y = 0
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k < n T 2
T 2
T (r )2 T (
− r )2+ x
r = 0 r = 1 T 11 r = 2 x = 9
S = 4 T 11 pivotFound 1
T 11 initExist 1
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initExist = 1 y
1 r 0 r < m
T (r )k+ x + y− 1 T (
− r )k+ x + y T (r )
11 T (− r )
12 T 12
T 11 pivotFound = 0 r
1 1
r = 5 pivotFound 1 T 12
S = 1
initExist = 0
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T 3 T 12 y + 1 2 T 11
T 12
k 4 x y x = 1 y = 0
T 4
k < n T 4
T 4
T 7 T (r )4
T (− r )
4+ x T 9 r = 2 x = 5
pivotF ound 1 S = 4 T 9
T 5 T 9 T 9
k k = 5 x y x = 1 y = 0
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T 4
T 5
k < n T 5
T 5
T (r )5 T (
− r )5+ x
T 12 r = 3 x = 7 pivotFound
1 S = 3 T 12
initExist = 0
T 6 T 12 T 12
k k = 6 x y x = 1y = 0
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T 5
T 6
k < n T 6
T 6
T (r )6 T (
− r )6+ x
T 7 r = 3 x = 1 pivotFound
1 S = 3 T 7
initExist = 1
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T 6
y 1 r
0 r < m T (r )k+ x + y− 1 T (
− r )k+ x + y
T (r )7 T (
− r )8 T 8 T 7
r = 2 T 8 S = 4
y
2 r 0 T (r )8 T
(− r )9
r = 1 T 9
S = 5 T 9
T 7 T 8
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T 8 T 9
x > 1 T 9
k 9 k = k + y +1
x = 1 y = 0
k < n T 9
T 9
T (r )
9 T (− r )
9+ x
r = 0 r = 5 5
1
r = 6 r < m x r 1
0 pivotF ound 1 S = 0
T k+ x T 10 x = 1 x > 1
k k = 10 k = k + y + 1
x y x = 1 y = 0
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T 9
k < n T 10
T 10
T (r )10 T
(− r )10+ x T 11
r = 0 x = 1 T 11 S = 6
T 11 initExist = 1
T 11
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initExist = 1 y 1 r 0 T (r )11
T (− r )
12 r = 5
T 12 S = 1 T 12
T 11
x > 1 k
k = 12 k = k + y + 1 x = 1 y = 0
k = 12 k < n S
A(1)
p 2 T 2
A
S = 0 T 2
S A (2)
A T 3 T 12
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A(1)
S = 35 A(1)
T 3 T 4 T 9 T 12
S
T 2 A
A
A (1)
A(5) S
A(1) p
84
5
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T k
T j
T k T j
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