B Fate
 
n-)
Aza, lo = Ani +a, 10 +: - ad, 10% ol, 10'+dg10°
 
dig Anat”
2S
3
536, = 5x1 * ae 107 7K 10) 6x10"
m i , > = 2
E27. 28 97 AA HERE eae! $ 7X0 FSR 4 BHI
>
. ‘ Sener:
Jndaey oe Age de = dn 2” + nes 2h dy 2 4 ar Ade?
Tone ye atx ox2 t Vee URE
=e 30424!
Mo
Decimal te Binary con venion
NT
1°
2 2\nt i, = eee
ales 7’
2)29_ -°
alia_-!
ara -e
2
7
2a -)
7 -!
Convek  olecirrel pum bx (52.625) 9 in biomes:
o\52 B29 = 1019 %o
alee -2 0-625 221-250 (0.625) <0. ovo
aha 7? 0.250 % 2 =O:S0° =
ele -) O.sp0 x Q = 100°
ota. 7° 9.000% 2 = 9/000
1 -)
pou_rorailel Pol DD tattel oan 2 MoyBin ors to decimal Conversion ne
 
4 af 2
fours ec PX Dy oD AVK2 41K 2! pix 2”
fb +04 At 21
= 23,
Ho. Wools
lo 1
Lox2° = o ae
Ly x2 = 2
2
1x2 = 4
ol
: z ae
Ho. tot, = 1X2 41 x2 FOxD axe FIR > FOR?
 
pine”
Soya OOS FORS 4940062
= 6. Bl2 10
Binarsy Aalolilion
A BR Sum Gry
oO oO oO o
eo 1 ' 2 ®
1° 1 °
\ ° !
Bia Sub faction
A B Differnce Borer
oo ° C1
ol 1 !
1 0 t ©Convene dh A:
v vt We clecirnel  nernbor (i2 , t binary
equa valent
 
V2, g% 100,
2 ©
2 -o
\
o.7 x2 ENA (0.19% 1ONPs
0.4x220-8
o.g x2 ahs (12-7), = Hee. fore
og x2 2? *
or*2 70%
@
2) Convert (56). & ih equtvalent cekd number
sise7
sg} 72.7
8 3.7
—
2D Gover (422 24), t ib equivalent ocksl number:
8)A22
ee
6-4
(e67),= 6069s
on
0.24% 8 FN 9%
0-92 x 8 = 136
9.36% & = 288
0.88 x8 = 1% (422-24) 92 46-1727 7)
0-44 *8 0.32 :
o4a2 *F asé
(0-24)92 (17 27023,
non
Ref Rocke: Moria Mare —Digelal, DerkAdd jou, ant ott,
lew Meer 14
+o 4
| oo!0
 
Ded (8
Subbact 01002 from 1010,
Jote 19
— 0108 4
hee ee
ole e
 
Ota Num bor Slr
As ié va 8 aight, ie base BS
0,1) 2 BV S&T
He xa decir Mura ber Sgiln
a base of 16 Raving, 16 alight
01,2 34 8% 4, &) 4, AB, YP-E? F
Dein Birney, BE Hewaclectr®
° e008 @00° °
1 ooo! ooo! 1
2 oo le 0 010 2
3 oot ootl 3
A 9 100 «9te° 4
5 eel ove) 5
6 oie o11e 6
7 ott! o\ll 7
3S | 00° j ooo g
q \oo! joo! 9
Jo ,o1o 000) 00°° uO
it to tl © 001 09°! ut
12 ,1oo ose! 90!0 12
13 Llot ooo! ool! 13
th 111e cool oe? 4
ye . = cu
cool oo! SsUaca®
Heron Resoures
-Htemar Resaurtte (Hs
Decimal Ce He rarcle cen
) Convert Ta08),0 ts
16 | Bee
 
16
 
2) Convo 426 Io te
number:
Ts
926
ye] S7 —E
3 -4
0-62 x 16 = td
0.92% 16 = 1A 7
0-72 * 1e= We S52
0-62 * es 8 3?
we S12
0.32%
®
(926-19;
3) Convene (191010), te
4) Cor vok (1100119), ts
ool loo =)NO
eee 6
 
ib
Feemedcons
oes
&
eguivelent Hexade cirres rar ber
2 (326),
i6 equivalent He xade cimel
= @4 Ee).
9 (0-62)0 2 GER Soe
14 le)
1 (8)
S
s
c (396.12 881
it oct! egeivabent
= 52,5
iio eal
° (csr, 42! cook)
= (44)
Wy5) Convot EBSA, ® ‘.
° a clacindl ard 72905 &
Ronodecirmad ;
EB4A, 8 ee
iB le. 256
\ e
L— jo x16 = }o eG Hh
Axle = 64 ZOFe uae
WU xeh = 2816 ye ae
7 163 84
yx GBA fon
60234 46 sT344
42495).
9
re) 4556 77 (ice
Bins, & Heradecie’ z )
6) Conv’ (j1e0tloo), t it Herode coral ey vival.
[190 110°
c @ a (cc), (wie 24219 >
) }Oo L191 oool,. tb (G Lexactecinal
elec Ale! ooo)
A D> 1 GP),
oth _& Bines
8) Conwak (755), te it binorgy equivalent
= Sy S ue
= (iv 19119), le i (. wet)
9
ve per4) Convert (648.20), te 18 ome
6 4 Ss . 2 °
pb % 4%
Joo Jol + ole ooo
lie
0/0 0°°),
(648-29 z(ieloe lel:
 
 
 
Hexadecimed te binary.
19) Convert (ps9, & '% bing, (sq the)
A B S
: + yi } z(jore jon 0/0},
jor foul ole)
iD) Convok bs Bo bine
= (o111e° 3
(a), = 6 10%), ei 4
ol \oo
12) Convo (g58-0 x ints if bins en ectunlent
B §s ao» A ® Gasirgs 8429
we ¥ + +
® toll ool \ 90° yoto = O0'n
Octal te Hera clecirna’
13) Convene G29)s wate 3B og caivedlont Hereaole evel
) Convek Te celal rmrmbex ints binary
7 3 Ss
oe
we ou 19!
ii) Bin pumbr & Converted wto egedrabeal
Venade vid
ooo) {tol lle)
ee ee a,
ion 14
} Page mnHexacle cine to — Oeteh Convenseon
inte octal ..
”) cowot (A524
4
A eS a > 8
+ ¥ +
Jole 0} 0) ole
B > ob
(wire 42) Cody
mois gis ote (Asay S12,
5s 1 2 2 e
Conve (ioe), into Hexaclecirnal Kiovgh ocd
(So ae ob
09) 8 eu ®
eens
at = Hew
| 6 3S
oo) 10 ov
geo = (073) 4
_ basic Loser gol 5
Univew oe
Fuclunve OF, Enc lusive
Ref Books Di del Deri A
Peet ee Mone. Bt edhe
pese re:- 22 ShB sp ze
pale’ - Nok, fi
Ex-NoR
=p Ye a .
ye weret
= Ag thsBookeon Laue
Corplerrentelion Lawe (NOT bawe-)
AcA
AMD Laws
 
®
Dyunocialive Mave
Da (B42 = (axe) +e
D.(B- © = 6.8)-¢
Dv bible favs
P-(B+O> = DBAS
De Moye. * Theorems © .
sae = he
pe = B+®
Redlizalien of brols — wsings Universe) Cals
Nano gele iver ae :. AAA
_ SS pies eae
 
Red. Rook : Disibl Done 2 wtih —
‘oH Devon 24 ealihon-M ae
esl owis Ma
ino — Page ne QTOck§ ts Binotyy
oe Nene
ol
2 (10° Ho Lolot),
7 q c(onnine),
nw
ho
= ojo or ole lol
 
 
 
 
i
2 3 2 § = (2325),
Convere 9 (lis), and Gos), & Rendle cima) rumbers .
16 Jus -
yl2ss
ere a =@3
! | & he le} ioe
°
léLo I4G7E
Convak $Revadecinrl rambo inte docimal Cumbers
9
oe ABBY b) 2FSH
(psa), = axie™ ABR 4 BXIG™
= lox 167 FB x16 4 KI”
pox 2sb + SXI6 UK
= (2419) jo
@ i 2 \ Sl
FO, TBI A LAIE 4 BKIG = axree FISXIE + SX1
= S12 +240 43
Hera cdacérmal — Binary, Convewson
= G5).
@ ADs), so
oolo
D s
Nor Oto)
(ipower = Wy out
elo!
T RB
aruda — Octal Conveton
(a, = (ree Olli), (g2),2 (oli 910),
co 0) 000 \\\ =
= o\ 1010
= ( one,
= (A).
Ss
= b785),clecerw
 
 
1 Converk fo numba
amb 52.625 sat
hin ag renrbor + S ints an equrvalenk
5 osu 2
2/3 O625% 221-25 —> |} > MSR
O2S0K2. 050 > 0
ieSe ae el hoor on
ide sia oes oo! 6
(53-6250 = Grotor-ter),
 
bd — 1 2Mse
2 98).
a5 (u OOONO,
inte bin
3. Comsotk Ake binary
yor\\\
\ Levee? aN
Ve 2 2
eo 2 y
ie2h = 8
oz? =?
yuo? 8
AL
Ae Convark Gat ASO.
 
en
8 [444 0-456 x8
sLss 0-6 Ge x8
j 75 ols 4 xs
o472%8
o-776 XB
2(6%,- 3513 5
5. Corvak Ba otal number 0) (237)3
(2578)s 5 axe + gx 4 7Xe
= 2x64 +3x8 47%)
= 128 4 2447
=059),6
number Got. 1d,
infe 16 decind sqeivelord
 
23648 —?>
moreno once
2 LAR al
= 3.77e 73 ®
= 6-208 —s
ant (j20), & keimab.
(ize), = 1X8" 2x8! soxs*
(x62 4+ 2X8 + OXI
64 +16+0
= &)eUnit - LL
Decimd Number § lim s-
[ Tle bore . podin of Fe clectmoh rum ber
0,1, 9 B45 OST.
TP Lincrsy
CS mame lt 0 ole, ;Octal Number Sysbor ©
The. Bare (Roctn) of Coll mucber degli
w 8.
Tle ola numbers on ©, 1,%B&4,5,6 7
S. ‘
Beep & an
ok pum bers.
wl Nem ber Sigs Tern >
hore (Rodin) of Laredo cine ramber
oobd number, Ves 4 Peer
Hene Lee
The
Ags Gm & 16
The Le rodecirrd pember eysler cons ulEQ@
of th renner 0/127 874s S&Tad DBO DEF
Bromp™ ~ pg. cé
Relotionseep hetveen Decind, Birrsy OAD ard
Hexacle inre® numbers :
Te poh tionhps folloviegy
Decienwd  Binwss Heradecirnad OoGA
° oo°e ° ©
\ ooo! i 1
2 bolo > 2
3 oot! a 3
4 olo° 4 4
s ole) cS 5
& ole 6 6
7 oll 7 7
g [ooo & lo
4 loo) 9 u
10 [ole wA 1D
Uf lol B 13
V2 | 10° Cc 4
riot »> SsdA Wie £ bu
F vt
hy vv)
rumber [LOU ‘bo cle cinad
Conv rt dhe binary
pambe -
gies Ne WoO
Con venling Decent we ely
Nee Sy pxeaixrih 13”
[xto 1X8 + Oo FL xD AN
4
aig \x2%
Nese lre
The decir epvivelert of Molly & 27%e"
Con verk Re Ro eoole cinanh punrabor Agcs. ®
Decimal number:
Sol:
led Ne ABC Sie
Con verlirag ts clocemal , ve et
Ne (10x16 Fy ae (ute 2) (yur eid + (x16?
= 1,096° 4 pele ie +S
Nt 43730"
There Foe the clo cémad eg civolent of
ABCS eg i 439730"
Convak te
nurmbor:
sl
 
AX}Thvedse he Liners, egeiabnt of F855 is
0
Thpo pool,
Comvek ‘Fe cleimal number SE te ot
number.
1) Convert SS To te och! number.
gl) Ss7
ag] 69 -%
e1j8 2
et
®
Te ocked equivalent of SST) > 4 10
Se.
Convak decinnd do Heracbeanal.
2225, & Ra noclovimed .
16 ]2225
16) 139-1 (Tle Ravncbecinnal
g- ives ] equi volek of
222515 & SB: @
Bina, Reptasenrt oion
Ts 1s Compbament of AMY birotsy
nurbrn obsfeined Hinges by charges
o te I ad | doo.
Binoy number :
liouw
u
1A complement ae
“7 geleo
Vel. Rook. Diggtal DestComplement Agphesertadion <-
2A
a os complement of a binouy
number Car he ob tlatned bs, orlehing, | to
ids ys Compe rrenk
ob Comp ferment = 4 comp heme +)
Binots, number ©
[youl
Ly
Vs connpherment +> 1) Ol => Elo
vA complement 4 of , oo10©
1 @)
colo)
fe
2s Corphemret = ool) y
Cocos s-
Binary Cooler --
Peep fe wre edn Jeane oF Byrbols,
eeeta fin, ard bet tree SP
a enrsellues .
Weigh @A Coole :- /
There cokes Powe Lx eal weigRe fon
EE
pep code: &4 eI , 242) etc.
Her va exg teh coclos:- , ‘
Tose cooles don’? Rave a Red weight
fon AAA ark binary
Soeamphe  Emcen-3, Gday cokes
pe ageleors,Seg cen led Cooles:-
Tn dR coding, ayslew , we Rove Consecechire
Codes whose lever equivalent  dleffer only
Cor Enecons - 3 Code.
A bphanuunnerie cooles +
Tlere Cocke Oe uted fe Asprrsent
Cooled leech» (BED
deak rurcbea dugg lan of Coole eohie®)
purmbes Oh disgG t Aapreset
Bin ory,
gcD> a
conGirs 1° oligs (o-%,
fe. egetvelent bi rots
lo clavin~ad pumbea.
pumben Ar Ze
oritinnbwrBoD fe Binary Conversion *-
Spi Convel te BcD number te chine)
sipr Convert dlecinal 8 binary.
Snape!
Bc@D:- Oolo [oo)- oll olol
dove + 29.75
Comesporlrgs
The Liner equivalent of 29.75
liy0) don de inbegen pore ard -11 fv ie
Di Lunckined prt:
lve fox ,
(o010 100) - Olt ojo!) Be@ = (Wohl),
 
Pradi lion =~
Dad (2% and (39),
olo! 119°
(4 Olle 110°
_—_——
jioe 108° — -
UME see
Dy Ot doi, pram im
ma eott
hy
 
LZ}lee j}o0o
 
Secs meet
joot Lolr
Sabtrockion =
Poskn (185), - @e
yess >) olee! prowl ter
ool} ool! oo}!
ooo) ov y1o0°
Binary te hres, code @
) The MSS of te ROS code will be exactly
yued te fe fue of Pa gwe binary
numbers-
2. Now fe Aecord bit ea will be
encburive ~ oO” Re fuk ard cone Lil of th
yon | bins numbers:
de oe Ar fe resell
sy eee : debferenk
i ®
will be 2 a f dRow
nos wil be
(op) 00%) Bins
ere. Bo, Ol
(ea
° ! ! o |!
wRorse Te equivalent
code  Of10s,G ray Corte ts
. Binary Conversions
 
 
1 The Maw of te Jrirvrryy bf 7 2
. or be.
egal ts aa, MSe of TRE geen Bars carte.
nur
2 Now if ke ecord — ysasy hil iso. dhe
Becord — binoys Bit will be Aane as fa paoviows
of de -fias€ bre.
° ) r \ Gray
A
y lols 1s] ,
of 0 0 ! Binessy
tek dRe gay pede be Ollol.
Binorss pen eae olool.
Difphanurn X& Coal
Fonbion \ comp codere sed onby on
wheter:
fe — prepoae ‘of - Cofler
They, onlss used os Onl cerbeting device
Bak noe computers are not ese orks &
numeric papresenttalion ARs cxteal in
mublipuspose eh c-,
The Afplancemerc code called cRoracl
Codes
Boo Clean Ae baa re (0
Bookean Theosem
 
|__-5 !
'
2 Combin
n opt Logie F m= OeebeeliPro Loan Operators
Ro digital octyariv. Aepslien
Parvrcalles,
porforrs — Mave Rew fear oSghres operaliors .
Sr onde be make cherign ordlyze cincwihe
its ne C SO%K, Bb roe dE cebu of tes
Cinceils clernerds fon ary ve inpets.
x Not
a AND
a OR
Not operator
Since  AMSs Boolean Vatioba car orbs, be ike
0 (on) dee iPikv oO it’s coreplement un) og
Vice VO:
of pliable
as ib input
Value 8 | vf ard ons
ok w te ondoal It imped I acd foal 2 08
olf inpals aw |
8
iP
The OR
os ibe inp ad pasolacet
of ph ow
; ) if inpuk | onPostulales of Boolkan Afge bia
ies Haotoms of 07 Booken abeeb,
towed Rosle portdalir , which Sn be
Ainoplits, Rookaan Sxparsiors.
yrs
040 =9
2) jo = O-L =O
ott = ltoe)
3) 0-0 =9
\atel
4) or) and T=0
Theokeral- [operations with ‘pf ard “)
a) 0-Az=0 b Wwesl-
Thooser 2:- (operations with ol ad >
2» Ach b orA=O
hore theosems OF gpoaped Io falas Cabegotion-
pnp baa: Law of jatosection :
a) AA 
 Law of Lelory benk Jj,
Coit a / idenhly, fas:
a) A-A=A Hoishoborey
Ly ALARA
Theorem 4: bow of comp hemenladion '
a) A-A =0
b) A+A =)
Tasamn &: Jaw of Lnvcluation re
A=A
Theorem 6* tow °
a AB = BA
b) AFB BA
4 Cumebalive:
Thoosam T° A mocielv® ee
Ly (AFB) tC = p+ (Bro
Thooram 8 DY ie fave
a) p.(B+° - 6 ® +69
Ey p+ (eed = o> -(A+0
Theo ay Pbasoaphve bow
a) (are =P
BR p+ AB = A
° p. (A+ & = PE
a) AB+B =Are
e perB= A+s
Thacker 10: De - Morpn4
Jow!* JB = Ate
A:
B
dfeoer >
low2: A+B =Trandpe Ai loon On Denllly (ores
a) A+0=8
b) ABO = A-B+A-C
©) (Ax@-¢ = (A4O (O40)
a) A+O=4
A-l=A
ne oy Aystes cue roe fia. hints
D  Voriables ec tor
Jtols © Loose
i) Posilive hoge
1) Neagle hege
Digg Signa 2
o (Low)
45 \
@ 1 (HR)
The duath dab Bees & poblive jerforrnaDin
bho poole input hinorsy Varia bh coith ocefect
Tle Lox Aysteen oxlpul can be olfrined
fron Fe Bookear Booge erprerions:
TB
eeamaaa a hlogge Coles >
~~ Lege ols ora Aba building, Sbocks of oli)
clacdaonia:
Tha ooc at ® ose electeonic carceeils tok con be
Roohean axpaessios in oki gi 6h
Pe inp ment
i olesiog «
bogie fool
ae : a ful
ae (er) inv ° a
4 at input Bogie tool
Robs “ne epponi ke
3
be vee
ira, Ler (OA)
AND te . :
ae x a Loaie cancels Rovirgs
AND aphe UB x
Ll, ard ore oelpucls. -
mone inp
ANE BA
B
Vs AB
 
 
 
=~ ooa9The odpuk of on FOR tel, Bee Rio if
7 oi) Be
didfersk of .
poh 04 Tuorn tock offoa Compeleme nt Subdaraclion \-
 
 
1) Debuine Te ws complement of te
Beraller number.
wD Add Akar to 4
WW Remove Re cary
This call ert - cdourd Carly.
Re nan pumber+
ard odd it to Fe resell «
be Subdrack (010, Laon (II, wri dBo I Complement
meted:
pitt
o 1 comphmeat > 01 01 @
8
CA —>|)o0100
Add Cry, —> 1
o1ol
_———-
Faorn Go
 
2. subdsack (ol, oo) Ukr dfo 1% Corpment
method.
}ooo
° 11od
_
as Complement Sub taaelion -
i) Delon die 2% corep Lerner of te
ee purl
(nda fu & Fe berger onny Sa bdisack dors feom dP. "
lament eee (HID), eens Ba 24
Comp!
hho) @ iw corp herent of [610
ds complet 01 @D oio)
7 Lot
@ - 5) ee
Ty, > | olo!l Blak 301101
 
ye discarded. Thss, Hla orsever (0109
The Cary,
2) Subtrack (1010), feo ((000), rings a's Complement
me (Wolo ole)
yo Complore of User), 4 Ore
@
‘4s Co! ine ge a oa ool
2 ‘ ERD 1G)
—~F o110
pooe eae
olle Ge)
on) Ee
tlle,BR Sieplity ‘We A
phil, Pollowinn, Bor Grn empress
Q) ABCD AY ABCD
= Aen AavB)
xmAcCD.1 sAcD NY)
Ven
 
pidlaihadce ,
RvB |
K) ABV ARE LABCDAE )
= ABC) + O4D4 &) :
= AR
D pavaery ae = AA BAAR
= NAAAB
AAG
 
 
  
DA vpn rege VS
ag (ey 2) 1
Byte
 
oy
 
ce ATS
Cet AG
LD aw+ Be «Abo Pero
cy ABeS
= AB + AE TANBRS
©
 
e =
AB +A +A
sae+ AC + Am ©
DB
se
we
$lo,2,¢,>)< Em 1,3, WIS) +4= (28) °
gtd (929)
cD
eS
00
|
\\
role Le] hes
= E04 E849 1%
ooo)
 
 
i
[2
 
x
of
oO
oO
 
 
 
 
 
 
Vo)
ew)
FAB, 6 >) = Em (91, % 58/4)
>
se
 
 
 
 
 
pp Cloaq_ol| nyo
oof] J
o)| ° °
W]o °
10 |
 
 
 
 
 
 
|
 
= (BED
ol ON to cD =
— [A FAB, (B+0)
fol 6
FOS 6d)
—>-——_ e.
F(6,8,¢,0)=B D+ BE+AE>Kaornaugh Map. [Ref Becks Dig! DetgnS ecten, Fam“
. eee
The dimple freakion of Be AwitRira, fenebiona wring
Rockean Laws ard Weorsma bee comes Compbex eilh
de inctease, i Te umber of  Voriah ies and rns.
The K- rep Facknig ue paovidles a Ayilmelic refed
fon Aiep GF ging and manipulaling 
Caron Foren & ke =
Fe (A +B+o> CAt it) (A+ B40 (A +61
®n
 
 
B
Tp) 4+ BCA + ACP
B+ ABC B+ AST ARC
aa Bx crrcast Az
= AB pornceres 4 AB
”
»
ae CoB 408 C2 Bea
Ae the
- gf A+) = BySop (Sum of Procacl] :-
Tle word tum of prootuct ore olerived from Th
Aum bedi nopeusentolion of OR ard pnw by +!
Co ae pas pectivel,s
Bachem £(A,8,0) = ABC +ABC+ ABE
£0, 8.0 BD HPBCET AGED
POSE Paccluct of Sean'\2
Pos Ba Coklkee lions of tum tows produck
fae Re:
A ploduck of Gums expsondon conlains He
produce of olifferent Be. @
eg £ (0,8, e(prere(A+B+ 0) (ATE+ a)
Evpns df Boofen furckion F(A,8.0O=0+Be lan a
ohirdad Aum oF prin Cos.
Lined 00" of prsdacl Brera
SlpY Gg de piasirgs VasiaL es @
TA given & ton £BBO =OtBO
oe vepaeweis nine
: . , Board C mind
a
WA A¥K® Ono .
SAS: Supard fe. Ware | poorder ie,
= A(grB)-(c+O + Bc (A+A)
F(A,B,2
= (ag+ 08): (c+®) + ABC +ABc.
= pet + ABT 4 pBe +ABE +4 Beth BCShp 4: a
nevi Ae peated prooluck armas
F(A, 8 ©) = ABC + ABE + pBe +ABe+ ABC
Tie SOP Alardosd dorms ,
[Fre = PBC ABi+ PBC 4 ABE +E |
Corvot fe gwen exphensien in hedbod Sop form.
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