ÿþ / 3 3
1
I m i N a z w i s k o n r i n d e k s u p k t o c e n a
1 . ( 3 p ) D r z e w o C S A u y t e d o r e d u k c j i a r g u m e n t ó w w d o d a w a n i u 6 3 l i c z b 6 4 - b i t o w y c h w k o d z i e U 2 m a c o
n a j m n i e j 1 0 p o z i o m ó w . Z a w i e r a o n o 6 1 Å"
Å"6 4 + 2 = 3 9 0 6 s u m a t o r ó w ( T ( 3 , 2 ) = 4 ) , a m i n i m a l n y c z a s o b l i c z e n i a
Å"
Å"
s u m y w y n o s i T C S A + 2 îøl o g 2 n ùø + 3 = 1 0 Å" Å"6 = 5 5 . ( 6 3 = 1 0 0 0 0 0 1 U 2 , w i c 6 3 + 1 a r g 1 0 p o z i o m ó w )
Å"4 + 3 + 2 Å"
Å" Å"
Å" Å"
2 . ( 4 p ) U z u p e Bn i j s c h e m a t d r z e w a C S A z l i c z a j c e g o j e d y n k i ( 3 p ) U z u p e Bn i j p o n i s z y g r a f p r e f i k s o w y .
Z a z n a c z w z e B w y t w a r z a j c y G 8 : 0
( 9 ) ( 0 )
s u m a t o r k o Dc o w y
3 . ( 3 p ) W R N S ( 3 , 4 , 5 , 7 ) w a r t o c i l i c z b y { 1 , 2 , 2 , 6 } * { 2 , 3 , 4 , 5 } = { 2 , 2 , 3 , 2 } j e s t 2 + | { 0 , 0 , 1 , 0 } | = 3 3 8 ( 8 2 )
1 9 7 m o d Õ( 3 3 ) 1 9 7 m o d 2 0
Õ
Õ
Õ
4 . ( 3 p ) 6 4 1 9 7 m o d 3 3 = ( 6 4 m o d 3 3 ) m o d 3 3 = ( 2 ) m o d 3 3 = ( 2 ) 3 m o d 3 3 = 4
5 . ( 2 p ) W 8 - b i t o w y m d o d a w a n i u l i c z b 1 1 0 1 0 1 0 0 U 2 + 0 1 0 1 0 1 1 1 U 2 n a d m i a r n i e w y s t p i , a l o g i c z n e w a r t o c i
f u n k c j i g e n e r a c j i i p r o p a g a c j i p r z e n i e s i e n i a w y n o s z G 6 : 0 = 1 o r a z P 3 : 1 = 0 ( t a k e H 3 : 1 = 0 ) .
6 . ( 5 p ) C i g 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 j e s t z m i e n n o p r z e c i n k o w z n o r m a l i z o w a n
r e p r e z e n t a c j l i c z b y x ( w y k Ba d n i k w k o d z i e + 1 2 7 ) . O b l i c z x 1 i z a p i s z g o w t y m s a m y m f o r m a c i e
z z a o k r g l e n i e m d o 3 . c y f r y u Ba m k a . W a r t o d z i e s i t n a o d w r o t n o c i w y n o s i o k o Bo 1 , | 3 | 1 | 2 | × 2 4 8 . .
| 0 | | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | | 0 | 1 | 0 | 1 | 1 | 0 | 0 | & & | 0 | 0 |
7 . ( 4 p ) O b l i c z , s t o s u j c p r z e k o d o w a n i e B o o t h a - M c S o r l e y a ( 2 p ) o b l i c z w s y s t e m i e U 1 0
A U 2
1 0 1 1 0 1
X U 2
×
×
×
×
1 0 0 1 0 0 1 1 9 9 9 9 9 8 3 7
X S D - 1 0 0 1 0 1 0 - 1
×
×
×
×
9 7 2 3
0 0 0 0 0 0 0
0 1 0 0 1 1 9 9 9 9 9 5 1 1
1 1 1 1 1
1 0 1 1 0 1 9 9 9 9 6 7 4
1 1 1
1 0 1 1 0 1 9 9 8 8 5 9
0 1 0 0 1 1 0 0 1 6 3
0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 4 5 1 5 1
8 . ( 4 p ) W y k o n a j z d o k Ba d n o c i d o 3 c y f r z n a c z c y c h d z i e l e n i e n i e o d t w a r z a j c e l i c z b d a n y c h w k o d z i e N B
1 0 , 1 0 1 1 - D
= -
= -
= -
=
k = - 2
X = 0 1 0 0 , 1 0 1 : 0 1 , 0 1 0 1 = + D
= +
= +
= +
- D 1 0 , 1 0 1 1
q 0 = 0
1 1 1 0 1 1
0 1 0 1 0 1
q 1 = 1
0 1 0 0 0 0 0
1 1 0 , 1 0 1 1
q 2 = 1
0 0 0 1 0 1 1
I l o r a z j e s t r ó w n y Q = 0 , 1 1 . . . 2 Å"2 2
A R Y T M E T Y K A K O L O K W I U M 2 1 9 s t y c z n i a 2 0 0 7 © J a n u s z B i e r n a t
/ 3 3
2
I m i N a z w i s k o n r i n d e k s u p k t o c e n a
1 . ( 3 p ) R e d u k c j i l o c z y n ó w c z c i o w y c h w m n o e n i u 3 2 - b i t o w y m w k o d z i e N B m o n a w y k o n a w d r z e w i e
C S A o 8 . p o z i o m a c h . Z a w i e r a o n o 3 2 Å"
Å"3 0 = 9 6 0 s u m a t o r ó w ( T ( 3 , 2 ) = 4 ) , a m i n i m a l n y c z a s o b l i c z e n i a
Å"
Å"
i l o c z y n u w y n o s i T C S A + 2 îøl o g 2 n ùø + 3 = 8 Å" Å"5 = 4 5 .
Å"4 + 3 + 2 Å"
Å" Å"
Å" Å"
2 . ( 4 p ) U z u p e Bn i j s c h e m a t d r z e w a C S A z l i c z a j c e g o j e d y n k i ( 3 p ) U z u p e Bn i j p o n i s z y g r a f p r e f i k s o w y .
Z a z n a c z w z e B w y t w a r z a j c y G 7 : 0
( 8 ) ( 0 )
s u m a t o r k o Dc o w y
3 . ( 3 p ) W R N S ( 3 , 4 , 7 , 1 3 ) w a r t o c i l i c z b y { 2 , 3 , 4 , 7 } * { 2 , 3 , 2 , 8 } = { 1 , 1 , 1 , 4 } j e s t 1 + | { 0 , 0 , 0 , 3 } | = 5 8 9 ( 5 0 3 )
2 3 8 m o d Õ( 3 9 )
Õ
Õ
Õ
4 . ( 3 p ) 4 3 2 3 8 m o d 3 9 = ( 4 3 m o d 3 9 ) m o d 3 9 = 4 2 3 8 m o d 2 4 m o d 3 9 = 4 2 m o d 3 9 = 1 0 2 m o d 3 9 = 2 2
5 . ( 2 p ) W 8 - b i t o w y m d o d a w a n i u l i c z b 1 1 0 1 0 1 0 0 U 2 + 1 0 0 1 0 0 0 1 U 2 n a d m i a r n i e w y s t p i , a l o g i c z n e w a r t o c i
f u n k c j i g e n e r a c j i i p r o p a g a c j i p r z e n i e s i e n i a w y n o s z G 5 : 2 = 0 o r a z P 2 : 0 = 0 ( t a k e H 2 : 0 = 0 ) .
6 . ( 5 p ) C i g 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 j e s t z m i e n n o p r z e c i n k o w z n o r m a l i z o w a n
r e p r e z e n t a c j l i c z b y x ( w y k Ba d n i k w k o d z i e + 1 2 7 ) . O b l i c z x 1 i z a p i s z g o w t y m s a m y m f o r m a c i e
z z a o k r g l e n i e m d o 3 . c y f r y u Ba m k a . W a r t o d z i e s i t n a o d w r o t n o c i w y n o s i o k o Bo 1 , | 5 | 0 | 3 | × 2 1 1 0
| 0 | | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 0 | 1 | 0 | 0 | & & | 0 | 0 |
7 . ( 4 p ) O b l i c z , s t o s u j c p r z e k o d o w a n i e B o o t h a - M c S o r l e y a ( 2 p ) o b l i c z w s y s t e m i e U 1 0
A U 2
1 0 1 0 1 1
X U 2
×
×
×
×
1 0 1 1 0 0 1 1 9 9 9 9 9 8 5 3
X S D 0 - 1 0 - 1 0 1 0 - 1
×
×
×
×
6 2 1
0 0 0 0 0 0 0
0 1 0 1 0 1 9 9 9 9 9 8 5 3
1 1 1 1 1
1 0 1 0 1 1 9 9 9 9 7 0 6
0 0 0
0 1 0 1 0 1 9 9 9 1 1 8
0
0 1 0 1 0 1 0 0 1 4 7
0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 5 5 7 1 3
8 . ( 4 p ) W y k o n a j z d o k Ba d n o c i d o 3 c y f r z n a c z c y c h d z i e l e n i e n i e o d t w a r z a j c e l i c z b d a n y c h w k o d z i e N B
1 0 1 1 1 , 1 - D
= -
= -
= -
=
k = 2
X = 0 0 1 , 0 1 1 0 1 : 0 1 0 0 0 , 1 = + D
= +
= +
= +
1 0 1 1 1 , 1
q 0 = 0
1 1 1 0 1 0 0
0 1 0 0 0 1
q 1 = 1
0 0 0 1 0 1 1
1 0 1 1 1 1
q 2 = 0
1 1 1 0 1 0
I l o r a z j e s t r ó w n y Q = . 0 , 1 0 . . . 2 Å"2 2
A R Y T M E T Y K A K O L O K W I U M 2 1 9 s t y c z n i a 2 0 0 7 © J a n u s z B i e r n a t
/ 3 3
3
I m i N a z w i s k o n r i n d e k s u p k t o c e n a
1 . ( 3 p ) D r z e w o C S A u y t e d o r e d u k c j i a r g u m e n t ó w w d o d a w a n i u 7 2 l i c z b 3 2 - b i t o w y c h w k o d z i e U 2 m a c o
n a j m n i e j 1 0 p o z i o m ó w . Z a w i e r a o n o 7 1 Å"
Å"3 2 + 4 = 2 2 7 6 s u m a t o r ó w ( T ( 3 , 2 ) = 4 ) , a m i n i m a l n y c z a s o b l i c z e n i a
Å"
Å"
s u m y w y n o s i T C S A + 2 îøl o g 2 n ùø + 3 = 1 0 Å" Å"5 = 5 3 . ( 7 2 = 1 0 1 1 1 0 0 0 U 2 , w i c 7 2 a r g 1 0 p o z i o m ó w )
Å"4 + 3 + 2 Å"
Å" Å"
Å" Å"
2 . ( 4 p ) U z u p e Bn i j s c h e m a t d r z e w a C S A z l i c z a j c e g o j e d y n k i ( 3 p ) U z u p e Bn i j p o n i s z y g r a f p r e f i k s o w y .
Z a z n a c z w z e B w y t w a r z a j c y G 9 : 0 ( ! ! b r a k )
( 8 ) ( 0 )
s u m a t o r k o Dc o w y
3 . ( 3 p ) W R N S ( 4 , 5 , 7 , 1 1 ) w a r t o c i l i c z b y { 1 , 4 , 3 , 2 } * { 3 , 2 , 4 , 7 } = { 3 , 3 , 5 , 3 } j e s t 3 + | { 0 , 0 , 2 , 0 } | = 6 6 3 ( 8 8 7 )
2 6 2 m o d Õ( 3 5 ) 2 6 2 m o d 2 4
Õ
Õ
Õ
4 . ( 3 p ) 6 7 2 6 2 m o d 3 5 = ( 6 7 m o d 3 5 ) m o d 3 5 = ( 3 ) m o d 3 5 = ( 3 ) 2 m o d 3 3 = 9 1 m o d 3 5 = 4
5 . ( 2 p ) W 8 - b i t o w y m d o d a w a n i u l i c z b 0 1 1 0 0 1 0 0 U 2 + 1 0 1 1 1 1 1 1 U 2 n a d m i a r n i e w y s t p i , a l o g i c z n e w a r t o c i
f u n k c j i g e n e r a c j i i p r o p a g a c j i p r z e n i e s i e n i a w y n o s z G 7 : 1 = 1 o r a z P 4 : 3 = 1 ( t a k e H 4 : 3 = 1 ) .
6 . ( 5 p ) C i g 0 0 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 j e s t z m i e n n o p r z e c i n k o w z n o r m a l i z o w a n
r e p r e z e n t a c j l i c z b y x ( w y k Ba d n i k w k o d z i e + 1 2 7 ) . O b l i c z x 1 i z a p i s z g o w t y m s a m y m f o r m a c i e
z z a o k r g l e n i e m d o 3 . c y f r y u Ba m k a . W a r t o d z i e s i t n a o d w r o t n o c i w y n o s i o k o Bo 1 , | 0 | 0 | 3 | × 2 8 2 .
| 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | | 0 | 0 | 0 | 0 | 1 | 0 | 0 | & & | 0 | 0 |
7 . ( 4 p ) O b l i c z , s t o s u j c p r z e k o d o w a n i e B o o t h a - M c S o r l e y a ( 2 p ) o b l i c z w s y s t e m i e U 1 0
A U 2
1 0 1 1 0 1
X U 2
×
×
×
×
1 0 0 1 0 1 1 1 9 9 9 9 9 7 3 7
X S D - 1 0 0 1 1 0 0 - 1
×
×
×
×
9 8 3 2
0 0 0 0 0 0 0
0 1 0 0 1 1 9 9 9 9 9 4 7 4
1 1 1 1
1 0 1 1 0 1 9 9 9 9 2 1 1
1 1 1
1 0 1 1 0 1 9 9 7 8 9 6
0 1 0 0 1 1 0 0 2 6 3
0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 4 4 1 8 4
8 . ( 4 p ) W y k o n a j z d o k Ba d n o c i d o 3 c y f r z n a c z c y c h d z i e l e n i e n i e o d t w a r z a j c e l i c z b d a n y c h w k o d z i e N B
1 0 , 1 0 1 1 - D
= -
= -
= -
=
k = - 3
X = 0 0 1 1 1 , 1 0 1 : 0 1 , 0 1 0 1 = + D
= +
= +
= +
- D 1 0 , 1 0 1 1
q 0 = 0
1 1 1 0 1 0 0
0 1 0 1 0 1
q 1 = 1
0 0 1 0 0 1 1
1 0 1 0 1 1
q 2 = 0
1 1 1 1 1 0
I l o r a z j e s t r ó w n y Q = . 0 , 1 0 . . . 2 Å"2 3
A R Y T M E T Y K A K O L O K W I U M 2 1 9 s t y c z n i a 2 0 0 7 © J a n u s z B i e r n a t
/ 3 3
4
I m i N a z w i s k o n r i n d e k s u p k t o c e n a
1 . ( 3 p ) R e d u k c j i l o c z y n ó w c z c i o w y c h w m n o e n i u 2 4 - b i t o w y m w k o d z i e N B m o n a w y k o n a w d r z e w i e
C S A o 7 p o z i o m a c h . Z a w i e r a o n o 2 4 Å"
Å"2 2 = 5 2 8 s u m a t o r ó w ( T ( 3 , 2 ) = 4 ) , a m i n i m a l n y c z a s o b l i c z e n i a
Å"
Å"
i l o c z y n u w y n o s i T C S A + 2 îøl o g 2 n ùø + 3 = 7 Å" Å"5 = 4 1 .
Å"4 + 3 + 2 Å"
Å" Å"
Å" Å"
2 . ( 4 p ) U z u p e Bn i j s c h e m a t p o n i s z e g o s u m a t o r a C S A ( 7 x 2 b ) ( 3 p ) U z u p e Bn i j p o n i s z y g r a f p r e f i k s o w y .
Z a z n a c z w z e B w y t w a r z a j c y G 8 : 0
( 1 0 ) ( 0 )
3 . ( 3 p ) W R N S ( 3 , 5 , 8 , 1 1 ) w a r t o c i l i c z b y { 1 , 4 , 6 , 4 } * { 2 , 3 , 7 , 4 } = { 2 , 2 , 2 , 5 } j e s t 2 + | { 0 , 0 , 0 , 3 } | = 9 6 2 ( 3 5 8 )
3 2 7 m o d Õ( 4 4 ) 3 2 7 m o d 2 0
Õ
Õ
Õ
4 . ( 3 p ) 4 1 3 2 7 m o d 4 4 = ( 4 1 m o d 4 4 ) m o d 4 4 = ( 3 ) m o d 4 4 = ( 3 ) 7 m o d 4 4 = 1 3
5 . ( 2 p ) W 8 - b i t o w y m d o d a w a n i u l i c z b 1 1 0 1 0 1 0 0 U 2 + 0 0 1 0 1 1 1 1 U 2 n a d m i a r n i e w y s t p i , a l o g i c z n e w a r t o c i
f u n k c j i g e n e r a c j i i p r o p a g a c j i p r z e n i e s i e n i a w y n o s z G 6 : 1 = 1 o r a z P 4 : 2 = 1 ( a l e H 4 : 2 = 0 ) .
6 . ( 5 p ) C i g 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 j e s t z m i e n n o p r z e c i n k o w z n o r m a l i z o w a n
r e p r e z e n t a c j l i c z b y x ( w y k Ba d n i k w k o d z i e + 1 2 7 ) . O b l i c z x 1 i z a p i s z g o w t y m s a m y m f o r m a c i e
z z a o k r g l e n i e m d o 3 . c y f r y u Ba m k a . W a r t o d z i e s i t n a o d w r o t n o c i w y n o s i o k o Bo 1 , | 4 | 0 | 6 | × 2 4 8 .
| 0 | | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | | 0 | 1 | 1 | 0 | 1 | 0 | 0 | & & | 0 | 0 |
7 . ( 4 p ) O b l i c z , s t o s u j c p r z e k o d o w a n i e B o o t h a - M c S o r l e y a ( 2 p ) o b l i c z w s y s t e m i e U 1 0
A U 2
1 0 0 0 1 1
X U 2
×
×
×
×
1 0 1 1 0 1 1 1 9 9 9 9 9 8 3 7
X S D 0 - 1 0 0 - 1 0 0 - 1
×
×
×
×
9 6 4 1
0 0 0 0 0 0 0
0 1 1 1 0 1 9 9 9 9 9 8 3 7
0 0 0 0
0 1 1 1 0 1 9 9 9 9 3 4 8
0
0 1 1 1 0 1 9 9 9 0 2 2
0 0 1 6 3
0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 5 8 5 1 7
8 . ( 4 p ) W y k o n a j z d o k Ba d n o c i d o 3 c y f r z n a c z c y c h d z i e l e n i e n i e o d t w a r z a j c e l i c z b d a n y c h w k o d z i e N B
1 0 , 1 0 1 1 - D
= -
= -
= -
=
k = - 2
X = 0 1 0 0 , 1 0 1 : 0 1 , 0 1 0 1 = + D
= +
= +
= +
- D 1 0 , 1 0 1 1
q 0 = 0
1 1 1 1 0 1 1
0 1 0 1 0 1
q 1 = 1
0 1 0 0 0 0 0
1 0 1 0 1 1
q 2 = 1
0 0 1 0 1 1
I l o r a z j e s t r ó w n y Q = . 0 , 1 1 . . . 2 Å"2 2
A R Y T M E T Y K A K O L O K W I U M 2 1 9 s t y c z n i a 2 0 0 7 © J a n u s z B i e r n a t
/ 3 3
5
I m i N a z w i s k o n r i n d e k s u p k t o c e n a
1 . ( 3 p ) D r z e w o C S A u y t e d o r e d u k c j i a r g u m e n t ó w w d o d a w a n i u 6 4 l i c z b 4 8 - b i t o w y c h w k o d z i e U 2 m a c o
n a j m n i e j 1 0 p o z i o m ó w . Z a w i e r a o n o 6 2 Å"
Å"4 8 + 2 = 2 9 7 8 s u m a t o r ó w ( T ( 3 , 2 ) = 4 ) , a m i n i m a l n y c z a s o b l i c z e n i a
Å"
Å"
s u m y w y n o s i T C S A + 2 îøl o g 2 n ùø + 3 = 1 0 Å" Å"6 = 5 5 . ( 6 4 = 1 1 0 0 0 0 0 0 U 2 , w i c 6 4 a r g 1 0 p o z i o m ó w )
Å"4 + 3 + 2 Å"
Å" Å"
Å" Å"
2 . ( 4 p ) U z u p e Bn i j s c h e m a t p o n i s z e g o s u m a t o r a C S A ( 9 x 2 b ) ( 3 p ) U z u p e Bn i j p o n i s z y g r a f p r e f i k s o w y .
Z a z n a c z w z e B w y t w a r z a j c y G 8 : 0
( 8 ) ( 0 )
3 . ( 3 p ) W R N S ( 4 , 7 , 9 , 1 1 ) w a r t o c i l i c z b y { 3 , 2 , 5 , 7 } * { 1 , 5 , 3 , 2 } = { 3 , 3 , 6 , 3 } j e s t 3 + | { 0 , 0 , 1 , 0 } | = 1 8 5 1 ( 9 2 1 )
4 1 6 m o d Õ( 4 9 ) 4 1 6 m o d 4 2
Õ
Õ
Õ
4 . ( 3 p ) O b l i c z : 4 7 4 1 6 m o d 4 9 = ( 4 7 m o d 4 9 ) m o d 4 9 = ( 2 ) m o d 4 9 = ( 2 ) 4 m o d 4 9 = 3 1
5 . ( 2 p ) W 8 - b i t o w y m d o d a w a n i u l i c z b 1 1 0 1 0 1 0 0 U 2 + 1 0 0 1 0 0 0 1 U 2 n a d m i a r n i e w y s t p i , a l o g i c z n e w a r t o c i
f u n k c j i g e n e r a c j i i p r o p a g a c j i p r z e n i e s i e n i a w y n o s z G 6 : 2 = 0 o r a z P 4 : 3 = 0 ( t a k e H 4 : 3 = 0 ) .
6 . ( 5 p ) C i g 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 j e s t z m i e n n o p r z e c i n k o w z n o r m a l i z o w a n
r e p r e z e n t a c j l i c z b y x ( w y k Ba d n i k w k o d z i e + 1 2 7 ) . O b l i c z x 1 i z a p i s z g o w t y m s a m y m f o r m a c i e
z z a o k r g l e n i e m d o 3 . c y f r y u Ba m k a . W a r t o d z i e s i t n a o d w r o t n o c i w y n o s i o k o Bo 1 , | 3 | 4 | 3 | × 2 1 1 0 .
| 0 | | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | | 0 | 1 | 0 | 1 | 1 | 0 | 0 | & & | 0 | 0 |
7 . ( 4 p ) O b l i c z , s t o s u j c p r z e k o d o w a n i e B o o t h a - M c S o r l e y a ( 2 p ) o b l i c z w s y s t e m i e U 1 0
A U 2
1 0 1 1 1 1
X U 2
×
×
×
×
1 0 1 1 0 0 1 0 9 9 9 9 9 8 5 3
X S D 0 - 1 0 - 1 0 1 - 1 0
×
×
×
×
7 5 1
0 0 0 0 0 0 0 !
0 1 0 0 0 1 9 9 9 9 9 8 5 3
1 1 1 1 1
1 0 1 1 1 1 9 9 9 9 2 6 5
0 0 0
0 1 0 0 0 1 9 9 8 9 7 1
0
0 1 0 0 0 1 0 0 1 4 7
0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 3 6 6 0 3
8 . ( 4 p ) W y k o n a j z d o k Ba d n o c i d o 3 c y f r z n a c z c y c h d z i e l e n i e n i e o d t w a r z a j c e l i c z b d a n y c h w k o d z i e N B
1 0 1 1 1 1 - D
= -
= -
= -
=
k = 2
X = 0 0 1 , 0 1 1 0 1 : 0 1 0 0 0 , 1 = + D
= +
= +
= +
1 0 1 1 1 , 1
q 0 = 0
1 1 1 0 1 0 0
0 1 0 0 0 1
q 1 = 1
0 0 0 1 0 1 1
1 0 1 1 1 1
q 2 = 0
1 1 1 0 1 0
I l o r a z j e s t r ó w n y Q = 0 , 1 0 . . . 2 Å"2 2
A R Y T M E T Y K A K O L O K W I U M 2 1 9 s t y c z n i a 2 0 0 7 © J a n u s z B i e r n a t
/ 3 3
6
I m i N a z w i s k o n r i n d e k s u p k t o c e n a
1 . ( 3 p ) R e d u k c j i l o c z y n ó w c z c i o w y c h w m n o e n i u 5 6 - b i t o w y m w k o d z i e N B m o n a w y k o n a w d r z e w i e
C S A o 9 p o z i o m a c h . Z a w i e r a o n o 5 6 Å"
Å"5 4 + 2 = 3 0 2 4 s u m a t o r ó w ( T ( 3 , 2 ) = 4 ) , a m i n i m a l n y c z a s o b l i c z e n i a
Å"
Å"
i l o c z y n u w y n o s i T C S A + 2 îøl o g 2 n ùø + 3 = 9 Å" Å"6 = 5 1 .
Å"4 + 3 + 2 Å"
Å" Å"
Å" Å"
2 . ( 4 p ) U z u p e Bn i j s c h e m a t p o n i s z e g o s u m a t o r a C S A ( 8 x 2 b ) ( 3 p ) U z u p e Bn i j p o n i s z y g r a f p r e f i k s o w y .
Z a z n a c z w z e B w y t w a r z a j c y G 8 : 0
( 9 ) ( 0 )
3 . ( 3 p ) W s y s t . R N S ( 4 , 5 , 7 , 9 ) w a r t o c i l i c z b y { 1 , 4 , 3 , 7 } * { 2 , 3 , 3 , 2 } = { 2 , 2 , 2 , 5 } j e s t 2 + | { 0 , 0 , 0 , 3 } | = 8 4 2
3 1 7 m o d Õ( 5 1 ) 3 1 7 m o d 3 2
Õ
Õ
Õ
4 . ( 3 p ) 4 9 3 1 7 m o d 5 1 = ( 4 9 m o d 5 1 ) m o d 5 1 = ( 2 ) m o d 5 1 = ( 2 ) 3 m o d 5 1 = 1 9
5 . ( 2 p ) W 8 - b i t o w y m d o d a w a n i u l i c z b 0 1 1 0 0 1 0 0 U 2 + 1 0 1 1 1 1 1 1 U 2 n a d m i a r n i e w y s t p i , a l o g i c z n e w a r t o c i
f u n k c j i g e n e r a c j i i p r o p a g a c j i p r z e n i e s i e n i a w y n o s z G 6 : 1 = 1 o r a z P 4 : 3 = 1 ( t a k e H 4 : 3 = 1 ) .
6 . ( 5 p ) C i g 0 0 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 j e s t z m i e n n o p r z e c i n k o w z n o r m a l i z o w a n
r e p r e z e n t a c j l i c z b y x ( w y k Ba d n i k w k o d z i e + 1 2 7 ) . O b l i c z x 1 i z a p i s z g o w t y m s a m y m f o r m a c i e
z z a o k r g l e n i e m d o 3 . c y f r y u Ba m k a . W a r t o d z i e s i t n a o d w r o t n o c i w y n o s i o k o Bo 1 , | 0 | 0 | 3 | × 2 8 2 .
| 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | | 0 | 0 | 0 | 0 | 1 | 1 | 0 | & & | 0 | 0 |
7 . ( 4 p ) O b l i c z , s t o s u j c p r z e k o d o w a n i e B o o t h a - M c S o r l e y a ( 2 p ) o b l i c z w s y s t e m i e U 1 0
A U 2
1 0 1 1 0 1
X U 2
×
×
×
×
1 0 1 1 1 0 0 1 9 9 9 9 9 7 3 7
X S D 0 - 1 0 0 - 1 0 0 1
×
×
×
×
6 1 4
1 1 1 1 1 1 1
1 0 1 1 0 1 9 9 9 9 8 9 4 8
0 0 0 0
0 1 0 0 1 1 9 9 9 9 7 3 7
9 9 8 4 2 2
0
0 1 0 0 1 1 0 0 2 6 3
0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 5 1 8
8 . ( 4 p ) W y k o n a j z d o k Ba d n o c i d o 3 c y f r z n a c z c y c h d z i e l e n i e n i e o d t w a r z a j c e l i c z b d a n y c h w k o d z i e N B
1 0 , 1 0 1 1 - D
= -
= -
= -
=
k = - 3
X = 0 0 1 1 1 , 1 0 1 : 0 1 , 0 1 0 1 = + D
= +
= +
= +
- D 1 0 , 1 0 1 1
q 0 = 0
1 1 0 1 0 0
0 1 0 1 0 1
q 1 = 1
0 0 1 0 0 1 1
1 0 1 0 1 1
q 2 = 0
1 1 1 1 1 0
I l o r a z j e s t r ó w n y Q = . 0 , 1 0 . . . 2 Å"2 3
A R Y T M E T Y K A K O L O K W I U M 2 1 9 s t y c z n i a 2 0 0 7 © J a n u s z B i e r n a t
/ 3 3
7
I m i N a z w i s k o n r i n d e k s u p k t o c e n a
W s z y s t k i e s e n s o w n e r o z w i z a n i a z a d a n i a 2 a i 2 b b y By a k c e p t o w a n e ( c h o n i e k o n i e c z n i e o c e n i o n e n a
m a k s y m a l n l i c z b p u n k t ó w ) .
P o n i e j p r z y k Ba d o w e a l t e r n a t y w n e r o z w i z a n i a z a d a n i a 2 .
Z a d . G 1 / 2
Z a d . G 2 / 2
Z a d . G 3 / 2
A R Y T M E T Y K A K O L O K W I U M 2 1 9 s t y c z n i a 2 0 0 7 © J a n u s z B i e r n a t
Wyszukiwarka
Podobne podstrony:
ARYTM KOL2 05 06 rozw errterminarz roku 06 07 latoterminarz roku 06 07 zimaIII lek zagadnienia 06 07 poprTI 01 06 07 T plplan zajec semestr 3 06 07kolokwium 2010 01 07 rozw06 07R 06 07więcej podobnych podstron