Kenwood DP-1100 B, Service Manual

Page: 17 / 159

•P-1100B II
II.
FUNDAMENTALS
2 - 4 S I N G L E E R A S U R E C O R R E C T I N G M E T H O D
Bill (a) as s h o w n in Fig. 2-2 i n d i c a t e s prices of f o u r kinds
of articles A , B, C a n d D a n d t h e t o t a l . In bill ( b ) , t h e price
of article B d i s a p p e a r s . T h i s calls a d i s a p p e a r a n c e or
e r a s u r e . W h e n t h e total a m o u n t is k n o w n , t h e price of ar­
ticle B c a n be f o u n d e v e n if o n e f i g u r e is m i s s e d . In t h e
c o d i n g t h e o r y , w e t h e r t h e total a m o u n t is c o r r e c t in bill
(a) is c h e c k e d . T h i s o p e r a t i o n is called " s y n d r o m e " .
Bill (a)
A ¥ 100
B ¥ 200
C ¥ 300
+ D ¥ 4 0 0
Total P ¥ 1,000
Syndrome (Checking)
S = A + B + C + D - P = 0
(2)
In bill ( b ) , t h e price of article B d i s a p p e a r s . (It is i n d i c a t e d
by B * . B * = 0 ) C o n d u c t i n g t h e s y n d r o m e d o e s n o t c r e a t
S = 0 b e c a u s e t h e r e is a n e r a s u r e . H o w e v e r , as t h e
n u m b e r of erasure is o n e , t h e a m o u n t of B* c a n be f o u n d
f r o m s y n d r o m e S
= - 2 0 0 .
A c c o r d i n g t o t h e single
diserasure c o r r e c t i n g m e t h o d , o p e r a t i o n of c o r r e c t i o n is
c o n d u c t e d o n t h e a s s u m p t i o n t h a t all o t h e r data ( A ' , C
a n d D') are c o r r e c t . If t h e r e is an error f o r a n o t h e r article,
m i s c o r r e c t i o n h a p p e n s .
Bill (b)
A' ¥ 100
B* ¥
?
C ¥
300
+ D' ¥ 400
Total P' ¥ 1,000
Syndrome (Checking)
S = A' + B' + C' + D ' - P = 0
B = B * - S = 200
Disppearance
(3) O p e r a t i n g t h e s y n d r o r m e o n bill ( c ) , zero d o e s n o t c o m e
o u t . T h e r e f o r e , it m a y be f o u n d t h a t s o m e t h i n g is w r o n g ,
b u t it c a n n o t be f o u n d w h i c h of A ' , B ' , C , D ' a n d P' is i n ­
c o r r e c t . In s u c h a c a s e , c o r r e c t i o n is infeasible.
Bill (c)
A' ¥
100
B' ¥
300
C ¥
300
+ D' ¥ 400
Total P' ¥ 1,000
S = A' + B' + C' + D ' - P ' = 0
(4) Bill (d) illustrates t h e e x a m p l e t h a t t h e l o c a t i o n t o be c o r ­
r e c t e d is k n o w n , a n d t h e c o r r e c t i o n c a n be d o n e by t h e
s a m e m e a n s as in bill ( b ) . T h e m e a n s t o indicate t h e l o c a ­
t i o n of error in s u c h a w a y is called a " p o i n t e r " .
In t h e e x a m p l e s of (1) t o ( 4 ) , " T o t a l P " is used f o r c h e c k
of error or erasure of data A , B, C a n d D. A w o r d used f o r
c h e c k a n d c o r r e c t i o n besides r e q u i r e d data is called a
" p a r i t y w o r d " or a " p a r i t y b i t " .
Bill (d)
A' ¥ 100
B* ¥ 300
C ¥ 300
+ D' ¥ 400
Total P' ¥ 1,000
S = A' + B' + C' + D ' - P ' = 100
B = B * - S = 200
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