Posted: Sun Apr 18, 2004 7:52 am Post subject: Binary numbering.
A f t e r g o in g t h r o u g h on e o f t h e p r a c t i c e t e s t s on t h i s s i t e l a s t n i g h t I c a m e a c r o s s a q u e s t i on a b o u t h o w t o r e a d a b in a r y n u m b e r . I kn o w t h a t b in a r y n u m b e r in g i s b a s e d on m u l t i p l e s o f 2 . N on e o f t h e b o o k s o r w e b s i t e s c an s e e m t o e x p l a in i t in an e a s y t o un d e r s t an d f o r m a t . An y t i p s on r e a d in g b in a r y n u m b e r s ?
w e l l b in a r y i s b a s e 2 n u m b e r in g s y s t e m u s in g 1 ' s an d 0 ' s a s o p p o s e d t o t h e d e c i m a l s y s t e m t h a t u s e s b a s e 1 0 f r o m 0 t o 9 .
a q u i c k c on v e r s i on w o u l d l o o k l i k e
b in a r y d e c i m a l
1 = 1
1 0 = 2
1 1 = 3
1 0 0 = 4
1 0 1 = 5
1 1 0 = 6
1 1 1 = 7
1 0 0 0 = 8
n o w in c o m p u t e r s w e s e e h e x i d e c i m a l n o t a t i on m o s t o f t h e t i m e in t h e f o r m t h a t l o o k s l i k e X X X X : X X X X
n o w b e c a u s e h e x i d e c i m a l i s b a s e 1 6 w h i c h i s t h e s a m e a s 2 t o t h e 4 t h p o w e r e a c h n u m b e r in h e x w i l l r e p r e s en t 4 d i g i t s in b in a r y .
o k n o w y o u a l l a r e t h in k in g t h a t 1 0 0 0 i s 4 d i g i t s an d i t s on l y 8 r i g h t ? ?
w e l l y a b u t w h en i s a y 1 h e x d i g i t = 4 b in a r y d i g i t s , i m e an F U L L d i g i t s n o t e m p t y on e s .
s o w e n e e d t o s a y t h a t 1 1 1 1 = 1 5 = 1 h w i t h 1 h m e an in g on e in h e x i d e c i m a l .
t h e r e a s on i t s 1 5 an d n o t 1 6 i s b e c a u s e in b a s e 1 6 , o r b a s e 1 0 o r b a s e an y t h in g , w e s t a r t o u t a t z e r o . s o 1 5 I S t h e 1 6 t h d i g i t n o m a t t e r w h a t b a s e n u m b e r in g s y s t e m y o u a r e u s in g . o k ?
s o t h e f i r s t 1 6 d i g i t s a r e 0 - 9 , A B C D E
n o w , b in a r y i sn t u s e d a s m u c h in c o m p u t e r s an y m o r e b e c a u s e i t j u s t a in t p r a c t i c a l . . . an d i l l s h o w y o u w h y . . .
c o m p u t e r s w o r k w i t h f a i r l y l a r g e n u m b e r s w i t h n e w on e s w o r k in g w i t h n u m b e r s in t h e B i l l i on s o f b y t e s o r G i g a b y t e s .
w e l l w e w r i t e 1 B i l l i on
in d e c i m a l = 1 , 0 0 0 , 0 0 0 , 0 0 0
o r in h e x i d e c i m a l = 3 B 9 A C A 0 0
b u t in b in a r y i t w o u l d b e ( d e e p b r e a t h ! )
a s y o u c an s e e , b in a r y a in t t o o k in d t o p e o p l e w h o d on t l i k e t o w r i t e .
I O W , b in a r y i s w h a t c o m p u t e r s r un on , b u t h e x i d e c i m a l i s w h a t y o u n e e d t o c on c en t r a t e on l e a rn in g .
an d t h e r e a r e a l o t o f t r i c k s t o l e a rn in g t o u s e h e x i d e c i m a l . an d on e o f t h e m o s t e f f e c t i v e i s c a l l e d
W in d o w s C a l c u l a t o r - s c i en t i f i c m o d e . . .
G r e a t h e l p g u y s . I h o p e t o o b t a in n e t w o r k c e r t i f i c a t i on a f t e r A + s o n o w i s a g o o d t i m e t o l e a rn t h i s s t u f f . A s f o r t h e h e x a d e c i m a l I a m g o in g t o p r a c t i c e w i t h i t a s w e l l s in c e i t i s w h a t w e r e a l l y n e e d t o kn o w . T h an k s a b un c h .
i f y o u a r e r e a l l y in t e r e s t e d in l e a rn in g a b o u t c o m p u t e r s , y o u w i l l p r o b a b l y b e s u r p r i s e d a t t h e a m o un t o f i m f o r m a t i on y o u h a v e a l r e a d y l e a rn e d .
i t w on t s e e m l i k e m u c h t o y o u n o w b e c a u s e i t s e e m s l i k e t h e r e i s w a y m o r e i m f o y o u d on t kn o w . b u t y o u a r e n o t t h e b e s t j u d g e o f t h a t . t a l k t o s o m e on e w h o h a s kn e w y o u w e l l b e f o r e y o u t o o k u p c o m p u t e r s . i t h in k y o u w i l l i m p r e s s t h a t p e r s on w i t h a l l t h e n e w kn o w l e d g e y o u h a v e n o w .
i t s l i k e t a k in g on an y p r o j e c t t h a t i s w o r t h w h i l e . t h e f i r s t s t e p s c an b e v e r y d a un t in g . b u t t h a t i s h o w m o un t a in s a r e m a d e . . . on e p e b b l e a t a t i m e . an d b e s i d e s , y o u w i l l f in d t h a t n o m a t t e r h o w m u c h y o u kn o w , y o u s t i l l h a v e a l on g w a y t o g o . t h e r e i s n o r e s t in g on y o u r l a u r e l s h e r e . i t i s a c on s t an t b a t t l e t o k e e p u p w i t h t e c hn o l o g y . t h a t i s w h y on l in e f o r u m s a r e s o p o p u l a r . p e o p l e w o r k in g in I T kn o w t h e y d on t kn o w i t a l l , t h a t i s w h y t h e y u s e t h e f o r u m s b e c a u s e t h e y kn o w t h a t s o m e w h e r e o u t t h e r e , t h e r e i s s o m e on e w h o h a s e x p e r i en c e d t h e e x a c t s a m e p r o b l e m y o u h a v e . an d t h e y a r e w i l l in g t o s h a r e t h e i r s o l u t i on . a l l y a g o t t o d o i s a s k .
s o on on e d a y y o u w i l l s t a r t n o t i c in g t h a t y o u h a v e s o m e o f t h e an s w e r s p e o p l e a r e l o o k in g f o r . t h en i t w i l l b e y o u r t u rn t o g i v e b a c k t o t h e f o r u m w h a t y o u h a v e t a k en o u t .
in t e l i g en c e i m h o , i s w a y o v e r r a t e d . d e s i r e g e t s a l o t m o r e d on e 9 0 % o f t h e t i m e . i f y o u w an t i t , i t w i l l c o m e t o y o u i f y o u k e e p w o r k in g a t i t .
J u s t a q u e r y , b u t w h y d o y o u n e e d t o b e a b l e t o c on v e r t b e t w e en b in a r y A l p h an u m e r i c , O c t a l e t c .
I r e a l i s e i t i s i m p o r t an t t o un d e r s t an d t h e p r i c i p l e s . B u t in t h e e v e r y d a y w o r k in g w o u l d y o u n e e d t o d o t h i s .
W o u l d i t b e f o r t r o u b l e s h o o t in g ? ?
I l i k e t h e w in d o w s c a l c u l a t o r m e t h o d . . . W o r k s a t r e a t .
C an y o u u s e a s c i en t i f i c c a l c in t h e e x a m s ?
T h e r e i s n o n e e d f o r a c a l c u l a t o r o r f o r b in a r y c on v e r s i on on t h e t e s t .
t h e r e a l c on c e p t y o u n e e d t o un d e r s t an d i s t h a t 1 M e g a b y t e i s n o t t h e s a m e a s 1 m i l l i on b y t e s . t h i s d i s t in c t i on i s b l u r r e d b y h a r d d r i v e m an u f a c t u r e r s w h o in o r d e r t o b o o s t t h e a p p a r en t s i z e o f t h e i r h a r d d r i v e w i l l a d v e r t i s e f a l s e l y t h a t t h e y h a v e a 4 0 G i g a b y t e d r i v e w h en in f a c t t h e d r i v e i s 4 0 B i l l i on B y t e s o r
1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 in b in a r y . w e l l w h a t w e d o n o w .
w e l l a c t u a l l y i t s e a s y . r e m e m b e r t h e p r e v i o u s p o s t
1 G B = 2 ^ 3 0 r i g h t .
s o s t a r t f r o m t h e r i g h t an d r e m o v e 3 0 d i g i t s . t h e s e a r e c a l l e d t h e " l e a s t s i gn i f i c an t d i g i t s an d a r e w o r t h n o t h in g w h en t a l k in g g i g a b y t e s .
t h en w e en d u p w i t h
1 0 0 1 0 1
l e t s r e w r i t e i t w i t h d e c i m a l e q u i v a l en t s b e l o w
1 0 0 1 0 1
3 2 1 6 8 4 2 1
n o w a d d t h e 1 ' s b y w r i t in g d o wn t h e a p p r o p r i a t e d e c i m a l b e l o w t h e on e
3 2 + 0 + 0 + 4 + 0 + 1 = 3 7 .
s o 4 0 b i l l i on b y t e s i s r e a l l y 3 7 g i g a b y t e s . w e l l a c t u a l l y s l i g h t l y m o r e s in c e t h e r e w e r e a c o u p l e o f 1 ' s w e t o s s e d w h en t a k in g o u t t h e 3 0 L S D ' s ( l e a s t s i gn i f i c an t d i g i t s )
Un d e r s t an d in g b in a r y an d h e x i s g en e r a l l y i m p o r t an t i f y o u w o r k w i t h c o m p s . F o r t h e t e s t a l on e a s f a r a s b in a r y g o e s y o u m i g h t n e e d t o b e a b l e t o s e t S C S I I D s u s in g b in a r y . S i m p l y t h e j u m p e r s r e p r e s en t z e r o s ( j u m p e r o f f ) an d on e s ( j u m p e r in p l a c e ) . S o i f y o u g e t t h r e e j u m p e r s in p l a c e y o u g e t S C S I I D 7 o r in b in a r y r e p r e s en t a t i on 1 1 1 , an d s o on .
T h a t t i p a b o u t 4 0 b i l l i on b y t e s = 3 7 g i g a b y t e s i s a g o o d on e t o r e m e b e r .
I g u e s s a s f a r a s t h e S C S I a d d r e s s in g I d i dn ' t r e a l y t h in k a b o u t i t t h a t w a y y o u s o r t o f s e t t h e j u m p e r s w i t h o u t t h in k in g t o o h a r d . I r e a l i s e n o w w h a t I ' m a c t u a l l y d o in g i s c on v e r t in g d e c i m a l t o b in a r y .
a c t u a l l y b in a r y i s v e r y s i m p l e . i t s e e m s c o m p l i c a t e d on l y b e c a u s e y o u a r e un f a m i l i a r w i t h i t .
b u t an y c o un t in g s y s t e m t h a t u s e s on l y 2 d i g i t s c an t b e t h a t t o u g h !
i c an u s e m y h an d s an d s t i l l h a v e f in g e r s l e f t o v e r t o e a t w i t h ( g o t t a k e e p y o u r s t r en g t h u p ! )
o r t o p i c k m y n o s e w i t h ( i h a v e s in u s p r o b l e m s )
I h a v e a s i m p l e t u t o r i a l t h a t I c r e a t e d s o m e t i m e a g o t o h e l p p e o p l e f i g u r e o u t h o w t o s e t u p a s i m p l e h o m e n e t w o r k . T h e b in a r y c h a r t h a s b e en h e l p f u l t o s o m e o f m y s t u d en t s in un d e r s t an d in g b in a r y . M a y b e s o m e on e w i l l f in d i t o f v a l u e h e r e :
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