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CHAPTER Uy Eley
¢ zomple os
Delouw ne he Values oh A,Q CD “Thal
make The sum leun A424 0465 eqyush
te zew.
MRICIb 2D
ott + D+ Eee FY +
O20 -3) Tae
~pelaled -pafblem 2
— Deleunine the values = hand ®&
tet hed make tun Teun “A+2 equal
le zexp.
Cnample U-2
Enanple U-4 aed
= tap — Relaled pysdlemy
; Apply Dendig ons theoren. tothe
Reloled Plus len
Delewune the, volnes. o ) fond g 1 the)
make the Puoduct tekm AG eapuals
c lo UFR
‘top ec Pugblem -
Nenoki gan) Tease to The
ofl lon RE ue J
xX Ve wes |
YZ pes
— WKY. 3 —
: iy Pee eit
v
seller Pusblem
Hop” Dentin ons ‘thente bb the
apesiow ! AB(C4B) +e
\
AB(CaB) +e
| he. telean explana
Reade wn ARLAB wile Win ona
~ ttl, = aint... we. De Mow aun, feorem
Se or Vai etha, _Urles Torn Lawewse
thot od applicaale to develop an _
eapleion " re elusive. seats
~
Aga nn - Cae) BE)
(A+8) (RR)
(A +e) (at Byis hs.
AA +A +80 405
TS
pa a an
Polied pitiem Is
‘Goiling wilh an eimest on platen
_ unis aie + ie. Denon Mec
te dotleleP an expres iO. topo
- Henpuk negalinee 08. aele.
ee |
TaD ake 8
Bi qo
? a, G podlean Pe ag
J ep herSon Z ee
A 4A (RAC) 4 & BiB) —
yet he sc 4 BRIBC =
— nh Apne. pA, BBB
— Ams Ac +R +20
avi.
mpl ais (ABD ag nt cys
{on Nppy Diemornan theorey,
[is Ca Ban) + Aalen
Fa
a
&
*
.
8
| [A AC TARR + ROS + A8 Cd
2 &-&- 0
|
|
[ec SDs
|
|
so Cg Be
|
|
|
Agch is cS Ghog
|
ST Pa
cb (AR +A +68) -
bea Sh aes pee Seo
w i ate is SS
aaron BL +fec FABRE +ARC +R i
+ Age a: ill
©
—8¢ Ae) i AR (Etc
= A Mee 1
$C +t A 4+Abe OS™ ie
os Be + BCA +AC) ———} |
eed
“eee (hE
Oc ry ABHES..
ARC + ABC Acree
ABC+ Abc +fARco +hbc
ABT 4 AB (c+e) 40 AC
ABest)
(Bo 4 AB HC
a
cen ple se
edt wh heflean ale [p SOP _
osm. a —
a) Opt B.C 7 ER) _ -
—A® +R eee
») (8) Btw) A
AB+ AC+ASBADS BBrRC+en
_Reliled_paiote io tsp Be ae,
— Lowenk Jat (N48) (B+E +AB) te60P
ABE 3 AS 4 Ac. +08 +65 4 Berio
: fell fi = A ~QR=0
— ARe + AB +4C + Ab FRC 4B
ee ABTAG=AB
ABT 3 Ap +e +e +tOc
£4 ausp\e / \ aft.
UAW sent the
dod 30P
ues Aree AB +AGZB
pus a SAPLensich nb
Ac (D468) tHBC+E) tech
ARCS Wan 4 ABC + ABE +R Ach
AB c+ bBcA+ ABC(DYD) + KET (v8) (ABCD
oe RRD yo
cD. Nicd +f1Bcd+ RBch + ABC pillich. ABEL
‘Delaleal pub fea. a a
Convert Soe lal) x yeenie
_———____—-Stevdaid SOP yom... ___——
INKY (243) + Kyz (wed) +0 + WKY 7 (z42)
nity WHE. + WYz HWXYZ 40 fp
faaple U-iG = as ~ incinaing
p enue Di valve
em cop a an is i
ARexy an + aS L
etl gtiat Der
x yo4 x y2 4 xV24 X24 Kyz
— Xs Yze4
we UE eT Te Ls he
a _ i.
—~ ths _u_ow_srdard Cop expression
Noletunine fre. “oinas values jes ‘hie,
the plowing POS GION
ential tb ol
(4 Fazy RZ) ONE)
(A4 y42) ep)
ex a st veld. Por 7"
foo nba
ath U- a
low het Allowing SOP expreulin
Led 5, hy
tb Wn . Seapiessiy _
Ane ee eae
the <alolualion iy
ee +B a “is Aa +B. ous
The 40P and POS ane zap)
Ek rs
ié eb My
i Voie, zap f greg
Ce
ARC + ete ABC + ABC 4 ARC
Re i ——
— tiene me TREC)
te Catto top (O18) Oraa1)
} | \ \ | \
I- IF OF | |\SClo\lp
i \ | | ' \
i i | } i
|
Coun ones at _ Abc, ABE , ABe bec.
7 oo SOP wWha
Re AOL ABC +Aae +A8C
| as tall. q zeae Wey oo ;
aca Acs ROT ABC GG an
go Pas willbe -
Mos Ae
(B18
‘Ee voaple
or pibben
Nap “lant (oP expretsin
4 Aec+hhc+ ARE on
Kana ah mon.
Aac 1 hac +Aaée_.
Orr ade oO?
“at FLOP on B-ma -
Map “ie ALD +ABCD
a O10 io TOO” oe
og
Enample. uD ii, DBlolem))
Map Hise aapheislon At (Dancy
“ARB 6ak-map
— ep mb: Ach auies | :
whee “Olt... 14 Ou oo...
(Lio. |
a
| a
iN _
Ltr \ i
a ——.
ae
Ee U8 |
E tami | ee |
' oP Led! 0%, |
De e-map> lb sinpliy. =
XYZ FAVLER YZ ANB
XY +
---&= x XZAKE. ali NZ£Z
Q- em. (x2). a “YY (z4Z) _—
24ed A ! ae
Aa = yy Lt VX youd
i te A oa
ott oe Rey =
See
ae
Wek oe pics POL on | Gn _Ketrep
5) (N4Bic a) (Nie oa _
Che Bet)
10, fhe a
es DE Egle
(X*¥4 2)
~
puobl ens
Usin A Batlenn “aed Noe |
ot ry
©)
ery a AAI
when all the varalle,
(A, Ry¢ yP) cue & Os,
A t (23 C+ D
2) weak EAPLERSION thet “y i iw hen
One OF morse °} ‘lh vattable (AiRIC0,2)
ore Os
Xe fBEDE X. AWRECHDVE
3) Wule expression | v thot Guhen
we One Or, 7 Sear Uk varbalole_
(AB onc) are. 0.
x <a dot oe ee
a). Evalucle the palowing
ay OFOF01D BD o4O+04l
oy. L
Ey bed pia
i
+ Bind value, oh ‘vatiable § Uo t- noke
each pwnd}
‘Lun 4 ond Each (um
4tan0, <i i
» ABC = - ay hee
Le A [+141 =~
rn) AtRac ;
D4040=05 a oo a
OeBet ja
1 +t1+020 a
—4 ‘Tipiables
hy) AN WAC TAA 6 fee
Lule i] hf fy
Aho . pee
1) AIBCEALI ANG NPL Phe
Pole 4
Aif A
AO he . Mecyene
B) Rb Ne ARUD « MOPhe apy
: Vule I}
A ie. 4p,
Me Pp fpe fy W ce fs
fine { fy tf {fs shh fy
6, it, / fh a ji p,
/
rh Penge ( theorem
pht8 >) BS BR a
dl = ie.
a — iby « +)
9 (ks) (Cab)
iis =~—— —
A-B yf.
AB 4 ¢
dp pla Renaige’s Aen ——
0) AR (Cad) by(O+84CD} Anes
3
B
EG ae
- BEC 8) hse “Dien |
hae +d).
(Rec) (FG). OT) (eT)
(i eC) (E16 +G) (HE) CECH)
p) Wha 3 RoBlean 2 ApLexior 10
» tN,
: ‘
=. _ 7
AE SBT Sw eh ol es
_ - _ Td
= Sn legen
oe a a
Ia). he
ololol oo
ftp
PLU | An Ee
beélaom. alpen bnplty eh wk
pone
Bc Ath) +Aec
Bc. ptt
BC +GCN +B |
B (C+) +8cb
2 =) acs -
2 B+
G+ R+L+b
RR —
ee eee
al \tC 24
_ Vad
E
e - the fellausing oie. ui mpl at
0 ce ste) AEE ta)
c CE. es 46 +e
ee E ae
=O cece ce ea
BC _ CAN Nee) Gite +b)
them
bets ROO + (GiB) "
\Jake. commen Hom | S
DT (DB) Nee
bois. stytbe iN
E BC 4 + BCE Seri
&
b) “BED 4 (BD) + Reb -
BCD + BHC tte)
_ ae \rEsh
ecb + ach
=o aren =
—_ CC #+CeE TH Ss + RE
—__Cler)} 4 cpr) =
ued. “tal —Qop foun :
[CCAD CAND)
CAACR. St AD IBS se bBz0
i A(AB 40)
ARB FAC AAS
AB+ fc das -
tenet the jing ib SOP jou
wes Seleee
is
ba Sic. 2. + DEBt +DE DE
_ 2 SE NG = ye
a oat | Neer + De es
BO 4 DE 5 CLARE) BE
Jes BO PGE fewest.
ba lt
b). +c fab + CORE]
Ri C(BD+ cetbel
Ba Bc Cee aCRE
LCE is 8
0). Comet oP esfictox 6 edad
a SS
0) @& 4 DE(REHDE)
ma a DEBS + DEdE_ a
. DEDEDE
Bc + DERC RPE el
~ BC (BiB) 9 Dee 4 ECC) —
— BCDy Ach 4 BERT 4 Bec +bEC
C
pevelsp Fath tebe
the polowing
Abe 4+ AB
t
Q)
a) Ang +
—) oo ae
oe | |
| | S$ 08 | | | G = | |
SH | Aree 1 | | | | E}.) MO O
eee ant
ee Hays] 4] | | alga
Sa aa dedad tld |
13 ia tess TW ddada | |
TR Fede -gocdad dae re
[4 acho oodddddddalae |
ig geccaeseddgvaagse 1
3 Tf = cogcosagd Joo 8 Tr
ri Paaeefeee SO SIE S Se ELH
= | | fies —a=S= “ae Fess mann
= [ss |
|S | *
IS! Lal
WA lah ry
a. {<=
a Decl a tuth table [D1 POS ewpegin
(A +Bid) (+c) (A4B+0) | :
| ( Ae) RBC) orc) |
be iHere QV°9Cs>
OP: aes _ _
ech + + ARCH + Ach + Aect*
‘Aacdst- ARE + pecd
pos
(tec (A+ Brc4B), yaseB) 7
{At Bec) (A+ RECESS
_(Rt8/GB)_(hiBvcD)
aera) BY (A+R+C DS). We
y Use nko hep. © Fite a insane
yo each, | _
ff ac+ hic 4 Rc
e051
molCyp| ae
| prt | |
is fe
lo | (@) Abe
4 | | AG+ABc
Hee he.
ok ee
\ fae + ABC + Foc +Aac
p) Age + }
ya Ci My D0
W) Use K-map to aimplyy the “each
sapien tad than oP
nel TEN a Bt
—O) FBT + AB +ABcABe
ic. ac) + 2) ARN
ABC Hee TB ha
Bc.
NC Ia
a
us,
’
f 6 ©
enep melkod tb i 1 iPlomesi the
Mininun SOP pox lagic funclion ec
mn Tul dle ;
ACK 4 AOC 4 4 BiB. D+
ABCAd
. eee
ee ee
Jin Af a ee
ee ON eS :
Nt re
{ve’ pudblem¥G in whch last
_ & linet womburaligy
aie nik allowed
Oooh 7 COND +01 OtoUlsH009
(C) (A) (C+) & —
Fee 48)
~~ bec + ABC. |
ARC +ARBL
_ ara ABC fw.
wy) Use L-dpp cimpliay exch ex buextitn.
te lee eet |
Se et SS SC |
Pty |
|
fot |
|
a
lag J | | | | |
a | | | | liduiqtsOor | 7
| FO — 1 O10) | Os)
a) ;
i} ‘> | i ; .
Ss | OTL SEL 4
$\-<
6-0 0 8 8-6 40-0
| i | | | | | | Yo |_|
~ | |
x
zi i | | |
"BO O JO4-|7749} S Q— =
} ot |
i ae L 1 ' u a 1 1 ‘ 1 ' 1 a
cies CY.
O0CO
OCO |
O10} s
OUO sree ema arate 2,
mi saniewsitig
ul OO ee
hideous meets Abed
Mp APOO@O |
m, 1 _|oo00 k deat’ ;! cad
(ote a} pst leva)
“Lon
gake a toss
I or enprensi ons in pe
s J
_ a
Rech + hBCd 4. Wacky +hech+
fiechK +Aécb
Jom pech
—_ © OOO
\ OooO!
2 | colo)
OUO
LAO! i ee
_, LOU 14
{Noo »
~ ABCD 4
nu nleuns OL ae tn ‘meal
gy
ck Jovel minlewn
O Mo | LOO Beer Poe
\ m, Oc°a 4
100! OCOo-_
DL} ME | CIO | O- oO 1 mane, .
m. | Olio —
Ma Loo} C -00 hixm,
mo | 0m | Poa
m, |uoo fo
| pnd } Lene amin
Ze Ene MAXMe
Mm x. Me a
——— ane _ ange