0% found this document useful (0 votes)
5 views19 pages

Number System

Uploaded by

Chetna Sohal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
0% found this document useful (0 votes)
5 views19 pages

Number System

Uploaded by

Chetna Sohal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 19

-

li Lm,heH ,~ ~lt'm.
@ &isk do.H ~
~ No±w.ol Nw-n-6 v-t
0~ ~e. N~e;<.,
~ P,Jme., Nun\,hV-G
~ Ce-w.Fe, Nwnbex,
~ CopkJm c NLU'Yl,t)m
~ T V\JU'J P1W'\1e, . / C+vt)
Q
~ RotcYtt\ol NWYlbm ~(_-V( '..)
~ loow n~l\.g
dezcYW>vL Q
~ Roll~ NlJJWlhe,lt \pt6
Re_ CLlJJ1n_9
~ ~}{,~ Nw'Ylbm
dmmQLCJ

~- (X ) [)tv-f sl6~ l<ulu


C: ( I) Z y) 8) I~, 3 2 /; 4, - - -
1

( '-) 3 J 9- . . I

( 3) 5) 25; l~S) b~5, ____ _

( Y) i i [ odd pOJ..e, s.wn - e.,vw p\OLe, &um]

( 5) ':/- / ii / 1:, LrnoRe.. F ob 3ruJs, ~ !<J.tJt


F ~ l~]
. N:; (odd pQU) - ( Wef) po»v)
----. ~0x, °' 'VI.() . t, be. p!WYYl e., (

li) rd i-1¼,1, fi0 ~9


I½ ½ < 153 < 1£9 •
( 11)2_
(1 '?))1- •
~
.-to, c,\,i,.J'<. d,"vis~bllf~ t~t -r' ~me. no-less
-l~OJv"\ ® j.e_
'
&l,3,5,t,11
~
<@ I

~ - dMs1bie. 6':I
~ . ~ V ·•
r;;-, , ,.~.1-
, ,v\, °' p.-i rne. ,
o •
2
1 = I

(}_)._ ~ ½ 11: == 12 I &l'- = ½1i 1


)2 :: \L) L)
32.= q 13'.)_:: Ir 9
½2:: I~ I~)_ ~ Iq G
52- ~~) 152- == ~~s-
1..
6 = 36 l b as 6
J_ :::.

2._ '

l:r- =J 8~
'.2
Ii ::: '3~ LI
/91-~3G j
'l-.
2-o :: ½oo
L
(rr) 1t 6~(:_, ~ pk,ct, = ( l, -\ ½1 1) q1 9 ) - (1
5-kp I ~ - p owe.-Y d1v1 ded / ½
Skp 2 ~- 'o('..m =0 , ( _r\) Li Y) = r \ 'i

~~ ::- \ ) \ _ jJ~n+l ~ r) ,
J{~ ::: '2._
, ( __d_·y-\~t1-::: rl J

Ji.e.{'() ::: 2) I d 0½1n 3 ~ cl


( <_,

I , ~'\/e.n .
I p
()WC:'.K, ·=- @ un~ t dJ(j't
½cdd pcw€.X, ~
@unit JJ¥1



& ~eh ;::_ rYUJ) vake. () ~ U-1s] ~
(]L) -vvu'X e.E ~ (. ,
'•
~
(; I ~ 120
0
c..
11 = 50 ½O
~
0

~I
0

0
-= f; i 1=
9l
0

.)
~
y o"320

3bl~ %0
--
sI = t20 <.
v [DI ::: jt;2.%tS00
v
~

(I)
/ n \l l I l 11 , i tr

j~ ( I ~ C\) "' I N·--> D_}


n
h0 0 ) .
r

1 ' '
1\ ¼., , '.') I ( ~~-")
1
/· tJ • = i rJ..c,(~-~ (R t\/\,\l)_,v<,~1 -
'~ - .,_1
'

. ~ Rclo£ev, 6/V\) L cm
-
CQ, 6)
-
y,_
~
bJ ~ a_ x 6
J-i %
, ~
-- \

~ ':,,h'\e_ £-mo.J.t -wo,Jz po.:l:le,u,, t:x:l..!.d 9lle., :- L}~~ "'.~


/ 1"' PL L7 S
c ~ 4 ( -3 I ½ 5 ) = CD cL'tce..t
J

( c-
.::!.. )
121' 3) =-(0 cL ~tVv
f}J2Y ,2S)
pvrn (~} 1: J 11-) ::-~ cL'U ut
c,~J ( r! 1 ½r.JJ ½I) -= {jJ thttvt
I LI J (_fJ I GI ') ~ (0
~V"'VI ( Il I
7
./-) 1 ~ f ) ~ {3)
O,V(~ ( f GJ C3 , 6 S ) '
eJJ P ~ ( 2 O ; 2 l J 2 9)
( 2 8, 2S ',} S-3)
- ---------------
,1

pnd~ij ---
~ ~ - ':!!!!_e.. t')if 0 .,:t Md' ~ ~~
~
1,ll-
Jl j)Cf't'l/2) : -
-

cQ.) He.~ ot ium O'( m a-re.. ~o_e,toY) , s 8'"(:t') 6(1 ~ -


= (H c_p. o fu nl.lf'Yl v.{~ ')
( Lc_m o fi J.__11.no mf ncd:Jrc)

( b) LC.(Y) ob ·fw-o O"'f mer-re_ t(\c.tCJYlh ~ Q~ven bQ t -


- CL CJYl M: nu.mmcdoo)
(Hc_i: o
5 ctD)ru)mfo<!dm-)
Ct-7 ~u1-e$ ~ JicJ- ~ _
"-) Eit t}ie, <lic.f "t X <1/fld, ~ 1,. Gi I the,,,, Hc.f- at,
er) -x, ( x+
0, l6 ~o es,.
(4) X J ('X -G") ~ ~o G-J ·

~
0
CW) (-:{+ G') t-x-(p to ~o ·

~ ~ Q J! ~-

,. (a.+b) (o_-b) = a?.- - b:L


I
'.L · ( Q+ b) ~ = (a_?-- 4- b'° +:Lo.b)
3 · (o.-b'))...
~•
.:= (a_:1--+b'- - J...CLb)
( o +-bt-c'/ - -= (a?·+ b~ + e,2.. + '.lo1 +- .lbL +1-(a..)
'
50 c0 :s +b 3) ===' (a_+ 6) (a:2.. - o.b +-bi )

6 • ( Cl'1 - b\l. J ~ (ei_ - b) (a:2..+~+-61- )


1-• ( a3+b 3+ c3 _ 3oJ, c. ) ~ (a+bt- c,) ( ll'--t-b'--+ e-- a,b- bc, -~)
;; ~ (o.+bt-c.) ([o - bJ <.L + [b-c...J2-+ [c.- 0]1..J
~. IAJhen q t bt G =0 1 thetvi J C\3 + b3+ c_,3 ~ 3a1 c.
CJ 0 (q+b)3 =- q3+- bs+acJJ(q+-b)
loo (o. - b) 3 == a 3- b 3 +- 3@ (<r.. - bj

f p-ri°rne '>'10 . (r - /DCJ) == _qr


0( :, Al
I\J OS -






,• @ No etf ~,eh VY1 p
=-
a e.d-.o.maJ
100

== Ioo - so
---- (J -€.6 :::-
o°o lt}te.,
i-0
1 • /4~ ~
I •



• 1 i
i.




• @ No. °b tu:Qle-o U1 tu°'T






- ~

(0 P~ bcueA [~ eN\ 6C\h ~ l aU 6eui Q__,1

- odd 6Me ~ l1/\('Yl t2.) ~n+ 1)- I 1


-----i)'
eJ.Je.>n
-
bMe. -
l i
'\I\ (YH2 ( 2-n+ I)]

11\ =- lt -:: ( u.,ei., )


"V\-= 3 -= cad
'11\ -=- 3 xsx1- 1 :- --1/\ ( 'V\ -\-'J) (LY\ +I\

i 8
!,,a 6 )('1 ~~
~~ \0'; ~@ -==
~2- ~
8

- I> ~epl <?-b Q.\S_Vl,'\k,L, ~4f~


~ U) wu i m(llY) 6.
I:'

~ \ ~tll e}U, e., 6. :::: ~ 6,.

L = \ + Y1D · D~ ae.vw.e. 6, = 1-

= I + 2-lLt') ~ 1 6!!:,
j ~ @--) -'VU) . o ~ men6 ·

@--, ~ -\ C)~~r I

M, D, \-i, t I -= \(V\2.D:2.-H:i..t:i...
®--0 .'\A() . 0&~ LU-l6 w)_
@_, ob~{ia:d
'½D .

®-) ~&1 ~
(w°'-r 6) ,

~b ®- liYlE)-~
~et_ k l ~
~s
Ir
COM

lh-, eA~ is ,~'cJQ i,e. cme. J,- ~


r-
l ~ l.(,M ~&w~ : I I I I lona mdtto di

(L,C. M 9"-Tome, = ToW ~ .

' - Ii N\e_
·~acuf ' I I

6d(J1 {!½tmt+)-. +ow w~


d_rur LUY) c~, b, i)

'.J
8~-~ to~~
- - )\ l A+ &tc.] = _2L1 u.nit ~ / ~

,: bAo.l time +,,r (A.+ SK) =~

( -6,\"1 INo-rK = ~('{!;'ciQ A Tirncj


\,,
-- CActd)
(o P-) - (AND) Co ho\ ~ ~-
if) m
~
•I
~kp I ; - .-vw.J±j'~ fu-ne, t-v-'i±l1 fom~ "4--v,
•e
~4? 2-:- (of~ M- M & g,-13,) t,vili 8'ive. ~ :
in ~Cl~ [ODW] •

~ & C!stW) [ So..rvie. CoV\c.npt) 6.d:- ODW ~+vd ~_) •


o DW ODW-= - v~ ( Q.rnp~) e
6u.nit A == Li hA/4 ri •
4u.nil B=- bMl ~ ~'-1 ~ / t.JJwJ:: •
- 3Lll'\lt c~ g hM tmp~ ' :
i w1i{ (At 8 'I-(.) =- 1..4 hAb/Uf)it •

(o\\Ct ~ :- tD determ1ne_!1£gJ, Jo.clots :


N~ fx~\ 11,c--wi-ok~u
- ---- °tr °' 8"" I 'VJJ •
:
OIM) t e)U'('L6 atr •
(I ) No ot fod.Ns 1 @ ~ i WJ , •

NOF = (Q+l)(btl')(C+I) •

(1L) PhJ)ckd: 0 ~ fc±o-fs a&@ •


POF ~
NOP
N
1 •
fack-s ofi @--. s~ ex(\IY'\ple •
( JIL) SUJY) o-b

e,x:-@1
-~ J
f'2 ::. 3X22.

Nor =- ci +, ) (;it , >=:(0
PoF ~ 12.3:::: l~~X!l. •
So~~ 1X3 1
0
:: [l0 -\l1.\r) (~ +3'):
= fX'-1 :@
so~

(!+-2-+4)( 1+-3)


_ ,
r
t
r/J_(A~Jm \,\J
(lJ
C'

'( Nok±J'l

l\o~+-1 1\191.(th
l"~~t 't'"- / l:-o,st
/

/
/
-"71,:✓~----~ EG.6t

ScuJ--i.,
tfM.t

(1)
(o)
,kt
L~ ~
WJuti =
=
9o CW - ~-v1
9o ACW-d1,ec_1'\
OCLd:h

oco

( IA1) & R CY J L hw½ = q:cvtb oJw°f orroslli, d1,ez,-,,,


e..x~- ~R
- NCS'b-tti - GD...6t ~ -Sou:hi -w~l
Ov ) f
YRo-r Li L ve,; .so.me. d.v,,e,,,1-1
• b- 7 pilieJ-0'\ u_i 9 .
... l l) ~n°,\J°ol cUiiec.~ ~~ V~ :. ~ M~'\l l¾~e.d ,
-~ (u) roJ d.w.e
fL\J~ :.
111 tMlhol due,c,~ Ct.¢~~ e
·:., (uf) ~~~ bo.6~ ho~ ? [ ~n ~-n ~ u oJwr rn~Wii
~ + y ·- (\)(UJ
~
- ~ df;u~" w •.11 •l dM - t t a'ltl.F 1WAt.d 1 :\
·· • Cloris butd 1ue. ( C.O""fMe. !litua.l, •1,\b,.~4.evl W-0.h t!I/\J
- • .Sllo.tl.ew t lubi'&""11,v.J. J n
' I ()

r
r
(

(
I,

t (

C
(

( I
I

<I
(

( )

(
A111 'l (\.y . l
SLWYl c-~ c-~e»Jat~iM,
r
- tohJ o-bsw aiicnA-6
-1-.~. " . -, A-r ~ tMV~ct]
L~ n CM le o~ W-f,.bQ/JJ)}JJ e, 8 w, l¼ ~-
r l 1)
0
s~ == ~ ( Q-\-i) ( Q -4 ~t t,QU-1)
d-- l ->i tw,l ieJj'Y)1
r
r.
l_U) W-l "' ~ , l l0-+l.)
(~) ())J~ IN) AP~ -~ ltX+-l)
~e1e., c,v_e, . -t, '\!\D · o-tt tVJIV½ ~ -
U) t ~ 0 A.ct
1
'V\
1
(DE, wiliVe., t(\ \) e_y\ ~-
0)5,~ve__ t\Je.\l\ ~ -
fY1 \ ckll e.,
{tvY)
OJv C. - t 'ly.,_ + (.~'I)i1-i
~
® Pwcl ~ :-
(?
-4
("X+~) A ._ 1{ 'r:.o/h -- B

G) wh€Yi eva . & eovv.,ewJlve_ ( eJJ en IOdd) no 1s ' 1


0 Vet,, Jtrot~
&. ,,Q}, {:- =olw., (f( kl Red :- ~ V\.!) (\/2 I

l~u:t 'Wl. ~ A +(-•H) V- ®: OJJ~ •


1
t"")
~ t rm. = A- (1A - 1) 0) . . . AAf) • 0~ ~

(
.. -

Ip

(-

tu ~
\ 1.J + (N\ X 1\J volue) j I~ -l 'll ',( ~ e.d v ~)j (
o.J~ . we.i,ql,\t oi '8 re>Uo-v\.6 V'\c,u,o.ot;, ~ cl ·S' ~ ' ~ 0.. I
'WW! ~" "' cm-M-0 AM ~ ~ i '>& '!hem ~ w<lr± ·. ,
Weit±- 1,0 ~ . ~ .at ti the. wet.rt " ~ PW,OV\ ~ I

- 4o + l ix ~-s )

:if B_oh~ Av~ t,


\

- iDWRum
to M 1 ,
)-h &Jl;;w·1 Av tYJ101::.,
7T -::: c - c'
- tohl ~
tDhl 1Ni cRili
= ) j;J '- o,&,,w.k Pu:~.;,½@] ( k,re. 9-L d i ~ J
( 't ) °-n = 6.+(fY1 - 1) d.
cc
lLt) $-1,t\::: J'.L (Jo.+(r1 -IJd)
~
,- t cc
l lJ4) ~ = ~U\+l)
&

', T ) ✓ U: rr d,.J.(, rJ.£<fcule¥, l C1 • pJ ( 9 w:J . . .)


(f) ~'Yl = ax""-1
cc
l~) S'ri == O(Jtlf)- 1)
Jt-1
g'V\ = 0.. ( I- J{'n)
I- J-c

5-m= /_Q )
\_\ -Jt.

cm) -1-\ OJ-JA\DY\Lv ~ ~/) ( H, p)

e AP ~ 1).he_J_ (H ,P) l 1- l.. l .. . .


2- '3 ~ 5

·l en ri-wW#'tj
( A·P) I l 3 y 5 .. , .
R-mI ~ . (Y)l ri -~ v\Je ~u (f\·P)
lA, fY) ~ ~ M~He M )
0

M-\h e.tYYiL.t ff)e M qe.omehl m~ ~-\O){h\Ovlt nieCW\


=-lD +b) =- ~ o.b ""'" & 0-.b
~ 0+-b
,.
r
* /2tih1e_ ~ 0-tf Q.6 ~ ~ -
r\
l' ) 1+ 1+3+ --- + 1-1 -= "V)('Yl+IJ
~
lLI) e-+ ~ +t + - - - +11'}_ '.:: "Vl L'Yt+-1-') 0-n +I)
(
:s :i 1- 'Lb
(~) \~+ 1-?i+ 3 t _ - - ·t-'11\ = 1" (n+1) (

~ (

(
--+ --- + \
C3X@ (

d!~el,i\t~ [ 1
,Le>cvr) - 1!cl- h)UY)
(

1 l1-isJ (

- '61
)q s-
CALENDA~
-,, odd d"q-'6 [ l'.)(tr" ~ fhQM, cowpl,t;, we,e.R,,]

_ ,. WJ °b odd d,,o lin nannal QW-1,, ~ 2> b S" d°f ~ ikiM_d"JI


- • 'V\D of odd ~ lvl :i l"°f ~e,w,, ~ 3b b d'q6 = 't~ .'.J-

'
\

'
'
'

( I

l I

I '
NC)\} -@
. t)w ·--G)
Ref'{) oAa -d~~
• yo o ~ o
o 300 ~ i oddd.Q
0 ~oo ~ 3 ®dd d~
o 1.00 ~ s- odd cl~
~ wliile. c,Jwlnh"a d_~ F Cl.. dot, lHM -.DD- 'I 'I' /'I J
r neJ_ ~ i~ ~ 1l is °' Ie.a__p GtO.Jv
- \ L'-. 1J5 'f g, (_rn o,J1,i > rnc,uXl)
( o-1tw,Wt,1c ~ o..di\ + (j) od:m,
lolwlcctt'- hL~cJ1Q ) •


C!I

\
lN· CeM.t- -1]
I Ida'.M + ~ fYW.roan.th
t!
e
(lo.sh~ J
1
I ::::.

'-1 ' odd

/ ti ""
drur
=~
+

(
p~

e

1 tl lJ1 '\ ll e '.- ( L' p~ ( S eo.p ~ c.ru_


I.
I
~:- ~n ' " ( N ' 'I ) "
t' en
"
I -\:I, CW' Oi'lS w<,L

1 II "
w'.ilJ
"
be_ I
" ( N ''/)
.
r()),· '



8


• +.-o~o±
• ®~)

• @ ~~ ¥ +Y'f'w;
• ~ 4©~
•e

You might also like