igital Elechronics
’ Siqna: A Aunc ,that
tati on
Tepreients the Var
vo
any
phyal quanty
Sqnal ?s vaniaion of
Analog gnal:
can
DEVARAKONDA SURESH JAHNAVI
Upect to
wtth
ponamet
with
elecntead quantitylv e)) tirme.
deftne
deftne
any
any
valu
Qiscete ttme Stqnau : Can dettne
foY
oithin
diseyete
întesval
tine inteval
(nubser ot analog sqnal).
magnituade.
Siqital S9hali- Heve, we mepreent both time
to fed nmbey
Voe divide the magnttude 0
af
levels
and the stanals
Can
take
Value
equal to
these value hevels ony
Need of iqital Stqnal;
nAll Neal lide stqnals arre onolog
wed in Lornmunicari on process tD
Sqtal siqnal
minimige the
efet of oise (unwanted Srgnal)
qood when
Intoduction of digital qnal i
Drgital sgnal
noise s Smalu
muuibit
|Qigttal
syiem
fraley
cormpure s
calulaloY
watch
Ggttal nyiern
modulu
easte unít (Aoqic qtu)
ciauitatranstftoYA, es isto Ys, Caparitos)
Analog out
AAvantage of digtal Siqnal
Nose immuity
anaog:
|Ovolt 'o"OEF"
¬ncyptton
Hrciency is high fov ld dtitanu tran1mission
noo4 fevels
342
3-digit
numbe1
BoitChs
m no of
3-bit
Ibyte
the
O-5( a Sottehs)
Set of
uules wed tu
símpltty the givern kogic epression
wthout
It S
o-s(1 switth)
OV, 5V
Tnhodu ctton to Boolean Alqebia i
It is
bts
numbeY
$7
’S bit
not
changinq
UJed
ohen
m‘, aceunay 1.
HS funetonalíty
noof vantables ane leS5.
Qules:
i)
(not n) T
Complernent i A Complement
CNoT)
""AND: (both tlp gho wd htah
+0R
"’AND
’A.
0
[c+]]
+BJ A[B+c
tABC
ABc
area
qate) hadwane(l
minimigation:
‘, speud‘
Reducthon
of
Cost
’
’
Advantage
of
+ABY- 3)
lauo: Morqan1
+BC
Dei)
NOTAND,
0R
Ac
Jauwi
te
Asoiat
tve
law?Connutartre
A). (A+
(Vi)
()
+AB=
t3)
=
(6.c)
=
tc) A+b)"
(A
AcAB+
A+ -’
A(B+c)
tv)0shburtue
lawi
=
A +0
A
~
tlp leither
one
ahould
be
hgh)
oR:
i1)
Eq'
) Y(A+ B+c)ln+õ +e)(9t8tt)|- (ntB)
tot)(A+5)(A13)(A1E
AH+o).(+B+c)
(A+0).(ô +0)
(A+B). (+btc)
Redundanay
’
= AiBtAC (A')Be
heoemt
mee vantables
= ABlrtc)+ Ac(rHB)
Yepeatd tie
Cach Vontable ts
One vaniabe tS Cornpementol
TakeMea
the dlont
Corplumentel that
yaniabyoY= AB+AC
Y- Ae +Ac+oedundant teY
Vedund ant
F= (At) "(5+c)
yedundaut
11 al vantably ane complementd
non -comdamuuel
F AB + A
term
vedinada
than
tke
Jum o poduct (sop fom): (ued ohen the olp s 7
Kotal no04 combinationg
vani abl e
n= noo
X
3
m
m+
fym) standavd (o) Canontcal Sop Joom
(becaus e we d'nectty ottten fom
uth tábu).
|Minteyms +50p|
FA) Bc)
mom4 +m5tm6tm4
zm(a 4i576)
F= AbC+ 9Bc + nac +iC+ AB"C
=
ABC+ A[8+6)
7
hoinimal soP fomtec
yEach
Vantables
minteYn
noYm al
doeu
hot have
all the
complemunttd fom
but in Canonical /stand and sop fom each mîn te Ym
is having al the vaniables fn normal oY
Cornplementtd torm leq: f= hB+ AB+ÃB
Foto
here we hare
ay Simplids the
e pessibn fot
Y(9B)= Zm(o,2/3)
m2
motmg
= Bt A8+
Can aol
AB
n3
praduct of sum (pos) :
-
pos fom is
ohenthh olp is"o
wed
0 I 0 | | M2
4 M5
M6
Y= (a+6+c). (9+8+a)·(a tB+)» Stándand
cononical/.
3 marntema
pos foh
Y= (Are,c)-T(MO, MI, M3)
pos Sop
Ye (a+6+e)" (At+T)
Y- (atB) (A+B+)
Y=(A+&).(a+7)
Minimal pos tom
A
Mo 0O
M, 0 1
Y- a+8)·(
Y-B
Y- T(MI,M3)
Poduct
Standad pos tom
(Cn can onilal pos
Mtnimal turny
Tom each maR h
wi|) baN e al the
vafableu (tn nomd/
Compl menttd fom)
o minimal p0s
Vice veua
Y- TIMU,3)
Sop fom- More fND
qate
pol fom i-Moe DR
qate
Op 4 pos fom
Y
ample
Pob,c)
Zolmlo, ,,ms,m6,ma)
Testnumberf
Y(n 8.c) : TM(415)
Sop:
m
I
Y hC t
JJop tomo
-
Y= ABC+ Ab (T1c)+ A8(C+c)
Y ABc+ ABtAB
YAc+6 Pas:
Y=(A+84T)" (
Mînimal sop fomm
"(
Y-(te+8)·(F+6+c.)
wianonital
pas forr
Y- (o+)· (Bt')>Minimal foi tomy
Mintmal to Cononi ta torm Convesston
Mi
Ma
Y AB C
Step-I: houo many voniables :3
what ae they A0.c
Ate p-a:
Y- A(at)- (C+) +
Mi Av
Ye fAe+AB). Cct)+
tep3: see enanpe
BCA+
a F-(a+8tt) (õ+c)
cA
Y=98.c+ AB.+
t) A , C
A8Ct ABC+
Sarne
A+ 8CÔ:
|) fem -I
c
+8cA
- (BCpet B).(+C+8) anonteal pos
Q an a minimal
sop tom the numbea ot mine
in ogal npiean on t5C aTe
5
F=D utop eianple)
With 2 Vont abex
mantey
mainum
possibu mintm £
ade:
a" = mtn/ max ma
4 mor
po Mible
min B mad tm
are the e.
O foy nD,
wha is the total
piem10 n
no b4 Logital
ngital
Lno o vaitobu
16 Jogtcal enp
h noc varsiably
A
n4
6 5536
eupienton
toral noo! logital
Positve and Neqative oqtc:
tve Coqiu
~Ve loqic
5Hghe oitage
’Hiqher voltage
Comepond to
’Jaes voltaqe
Comupoolt to
Logie'o'
5V’Loqfc's'
Logic
ADgte
Coneponda to
Aogic o
6TYesponda to
dogic '1'
Aogc
dogic
-o6V
Posttye gtc v
Qual tom:
’
OR
qote
¬-ve ogic ORoR qae
We-ve
+ve loqie DR
AB
LLI1
L)
LLL
L
HL H
ve loic DNO qate-ye loqlc
AND qat
LH 44
-ye logicOR
DI
ve Logic ANO 9at =
dogic ANO
yeve ogie
qati
Jgic oR gau
Self Qual:
a tiies dual gre the
’for any sogtcal engression ,
ACAme
’
epeion.
tn sel4 dual epeAion
the
Jame
One
erpreanion
Qual
F- (A+B+) (A + tc) (Atete)
F
(A-g)+ (A8)+C:9
Bel?ual:
B+c) +(A +)
tÉme
dua
gTve4
(Aie))
(A+B+)
tAB F:AB
=
t) (At5)-
+5)
F-
-
At
A V=
A-o}
A-fareri}
0-fo}
U-{a,e,i,Duy
Complement:
)
+B+
AC
BA
Y
Y-(B+(ã.).
(+)
(A+t) (B+8).
neYa+B)·
fual Seli
,
then
4
y posS pot
aneare
many
at du eH se
an- how
ableyn-vant
Venn Oacq1om i
nw0 yoniablu (A,B)
Mintmi
B=0
the sop epeaion foY Ahadd ne gio
a)
G=
(A8+8cHcn)E/e
Bc
AC
Soitchinq
cheuit :
MSotte
vorniableA
+
N’ ombinattory
M=lo9
|OFFo
ION'
B |v(bub)
Seste
port alll
+
NAND:
OR:
8Ylyl)
+
dettetu7
Ex OR; Codd %
A
A B
o
ioqic
y
¬X NOR:
AlBtc)
A-(erc)TY
Y ACB+c)"D
ogie
logic o
Atalment. probeo!
a Loqic Ctait lth 3 flp
omtde
)
oY
tollouing
hu
the
ard C olp
A0R Y Bc4ñ+ABC+
() A and C ne
s
Thig)
ABC
() A and c ane falueac
(tv)
P BC on e -fale
A--C
Minimi ze the unction Y.
2) Y tor the
()
T
B’f
Y- AB+ ABc+A BC
t1) 4T
(B+ B(c +T))
PlpA
3) A dogic cxt have 83 ?lps
ohen the
AB 4c he outputiF is high
majonity ot tlpA anfe Logic |.
a) Minimige the func
b) 4mpleMent the Crt
49l: o
c|F
f=
A
A Be+n8C +ABcHBC
f
8(AC+ H)+ Ac
8c+n)+Ac)
f=
6c+ BA+ Ac
F
D
lx1 Ox2t |x16+0x8tI
+X4
0x2+1x29+
"brta".
eO)6
a7e (o)
Cald
342)1o(634 b
ditta
6ihony
/rad4
2
ease
1}
foNoqtens
,
- Brnany
(4
digira
(9342)10
no0f
(t892)0-’
q:
Ne
Ni>N
total
adi?
pastiory
ewetqh
bad
cn
dtvdid
b
3-tDd ereeiA
Codu LGay Unwetqhed
wetghtd
Binmy, Cdecimal,
4342=
t90+2t000+800
LS
codex
&yntem
4 ’Numbe
0l,2,3
4Hera
-l6decimal
-0,|,2
&9,A ,3,45/6,
- 12
O,, uodcimal5
9A
B
e, 6/ 2,3,4
5)6+819
4,2,, -0, DecimalIb
-0t2)3,4,56,1
(a-)
al ct
to O () Gaue
Name
lo) nadiz
quantiy
tued Valuat
t0
of Set
pieent
ne
Number
SyiSyttmem Nombn
defnea
a
B#0e
we change LSe (no
uch
ehange)
CHwe thange (Atmost eveaything otil change
b4 ba bb bo
Srnalest untt
|Nibble
0+ dlta
4b t
I8yte
ldoub
e9noy
ConveioM;- Becinalottal
Henadecimal
Recimal
octal
Recima
Binnyoctal
hena deß m
Biny
Bfnony
e1adctmalecimal
hena ducfmal.
Hezadctmal
Qecimal +o
to Binoy octal hena dactrnal : for ihteqeY port s- weiqhted dtvtaíon
for troactionad ponnt
to Bi e) Ci3),
we fohe d. mutipltCarion;
-(2 ),
LSB
6
3
MSB
eq2)
(25625)o ’ 100l-01),
2l25
2
LSB
6
stop
6625- l0)
9 to 0 (1),
60 ),
(31 s0)
O(2s.62 s)o
O625X-io00
3
I-6
oG25 X1G
Broy to Decimal:
I00000
to
Biqaly octal tlexade trnal
Decima
weiqhttd mutplrcaupD
JoiOIæxnt+bx2x'+ox2'+1 xX2+
- l6 +0+y
H0+l++4
4915
H to
i
162 16
= 1Bx6l0x16+4x16+ 4x16l
= 2tl6 +16 0tI3 + o2
29895
Octal to irny
etnery t ottal t
:
+legadectma to Binany & nny to hexadeetmal
+ to B:
(Cns"30)is
C00 1010 ||n0-001110,
ID00100l y00
8
Hea to
Dctal:.
octal?
to
Binony
hen a tD
Detal to h a
to he NQ:
Binay
betal to
(652)eC
(65
Cuo1o10 o),
Binoy hddttion:
1u bhraC1on:
tate boDo
In24+1x2oxS+Ix2+x2
Cany Yum
Jum
(-) Ox2 41*22
Cony
()|I0
+ 1x2
(3-1) x
,o
Binay Mutipltcatfon -
( )I x |
(a
()
Bingy ivtston:
101b>||0
2X2
1010
I10x1
lto (0001)+0
Ocral addtion
OCtal
T) 56 4
()
2
| 2
103
(t)
ost
10=X8+2
multiplcaton
X| 2
L
Octal
1404.
(6)
H=9
ubhgctioh
3 5
R13-||
265
334
56 4
&x143
(
&x2+1
6X16
&X143
|0 6 -
Hexadecimal fddTtiop:
| ) S6q
4S4
pA p
16 x149
Hern adecfrna subta #on
A
) q654
16x I48
(53 2 )
4 BF D
24
4 333
Hezoducimal Multpltcatton
3+16= tq-
I2
58
(K)
C
3E C F
4 68
24’ l6XI+
l6xi+4
2116x1+5
20H*
=2t-12
|5
Ts Complement-
n's5Conplement (adia complepent
14 Conmpumen Cdiminihud 1adin
Complumen)
ued to Stmpy luaactton operattor
e
omp of (1o
|DN5640
Ad
Deteamtne 104
formul a : nN A conplement
Complement
ADhry=10, N=5690
N qiven nu.
n= 4
n total nood digita
3) N t6845
10t-5690
4) N1101)
2) N= II01
a'A comp
de tkomihe sh (omp
105-|o1|
1D-4641
=t00000 -+689S
(32),-1ol
n4
o
=(10000o)- 110|
= 23105
o10000D
+1-nconpumant:
t31 0,
n Comp
10000-|01
H)' comp
t'a Comp
16 Comp
Dctalnc
x
(7-js
= (4096/0-[6 4-1
(z(0000564
2103
r-)'^conmp +í= q4 CompNO bono) Operatlon
ordded
bomow invelskd
AD)4 omp ot S6Y +
a103t1= 2104
o10
O1D60I10
+|
Ahotul o
o'
comp:
tep i: alt down the
qiven
umbe
all
Aepa:Atantng hom LSB copy
the 3e04 tll the
it 1
Jhps: Copy the
the inst 1
Atep4 Complemend au the
emaiing
Comp
or00too
:
Rata
o00
epeentarion
uing Srned Magnitude :
Data epseveNation
Magpitude
Complemet
stqned
both te -Ve
+We
4
ep
eentaioD +Ve
no
a
repetaod
orh Tange
fon vange
har ep 4-bit, 010D0
+6=
tationsepiesen
bit
4 bes nepratted(nemben
I000
8
ve
0101
eonga)to
+5-
t1)
nepstgrnedue
t9,
tohave
betng
be
can't
but oil,
Tor cDp
to -8
wil
-q weou
thiA
qet
nuoith
(-9
we
1hart001l of+4=e
to -5
3ea0
4 n
(bitn) n6
fe
+32
to-32
,iange
ot
w)
noA
becauae
îxt23
101o00
one Only
-23
oI f)+23
-4-101|
oI0|
(i)
rang
bitn
=| -I0
(4
++ to
n=4
’-
--6
o|0
ranqs
=+6
mplement:
9tv)
hre
0000J
t3/
-I6-
3| -
Comel
1?1)
n4
to ’-
+4
+{3
ttIS
-o=)thi
we
oves)
to
onp
?4
to -(3=
-I5
P
ange
=01|01l
n=5
+13
O10
-0l +6
stgneod
=+6
munt comple
(ft)
^epeent
btSign 1Dn-4
Magnitudei
( (0)
Coant
=-6
Magnitude-
gned Dbl
Binny ubiaction uing 1
omplement :
be kubhacüd to Ph 4
SI: Coneat numbes to
A-B At(-B
Cormple ment fovm
pefovm the addt tion.
*S3:)T4 the tnal comy ts , then add tt tb the
crn)
nound
Cend
Atep2,
Dbtafd tn
Obtaîned
44 the final Cors o so'then eut
() 04
A
comp tom
the
ngatte
(oto)- (i 100)
S
A+CB)
B ||00
0D +1000
A+-b)
finottocany
nesit
-
Rest
So ddd
Obtaind. J000
Binany Aub uing a'n Conypument:
S: Corveat no to be Aubhactd to t:
itn shcomp ovm
: petor m additjon
S): (1) fc
n then rerut
(t) Fc inO, then
e
t
O (10o)-(o 100)
I001
n tve
n=4
anqe i-tb
- Ve
torn)
Note: Neqlect fic tn at comp
Cie don't wntt fc In am)
negleg
Dves-to
&0,
we
tae fC
th en
not inange
X Conditton
ane
1
iA
the
toy
ovestioo
the Sqn bit 0+
Stn
bit o4
7 y z +7.4z
Co|0), -Cio w)a
no fic
o(No OVe stto
- 1(ove9tHow)
, n e t u ve în
gh comp tom
)
~
\4Je t<J hted
t
1
c.od~
1
Se~nrfal
Cede,
fa;
ft:il
' I
€icS -o
~:8i~
. 84:iJ
e~ •··
Oe-Jlectf'ie
•
C'a:lfA:
q--:,Co""f> ~o
fAse-st reacJ /
f '
l?-:1 c.o mp t>J-1
I
I
t,
..
l
'
j
t:.(
\'lecl m tU - ~411 Coclt
D
0000OOOl
1
2
0010
OOI I
01 00
·3
-t
t
'
I
'
I
to f I
t' f I 00 ·
S-
\ C, I o I
l 1 1t 0
' f ( '
'lo.·
r'·· ..
.
.
'
'
.
I.:
,
... ),_..-
'
1
8'?n00~ eocltcl ~ cimaJ ~ ) CA:)c:te.·~ Ct4-?. I toc!L)
b'J a -4- -btt- bYna"'1J nlJ,
➔ eo..ch d.tcin--aJ. di~U- I';\
'lepoeAeAft.d
(o-9)
-- P~Tti'Ona.J. wetQIAlu'Uf' run~
<0e.cimC\l.
~(1 ~•4 .,. J.. - 1
l?)c.()t~ 4 :>. 1
0
~000
t
000 I
0010
0011
0 I Ob
0101
2
2>
15"
('.,
iR
e,co
C(:)(UJ ,1o,
dttitf\o.l
dr~i '1-
0 II 0
0 ( I I
f O OD
I OO I
9
to
tJ
o o o t oa o
-f- 'f-.f-Y.,.
O O OI DOI O
clori t
ta'1 (?/.,
0
0 DO\
0 ¢, II
ooororo
oootoJOI
0001
I
1
1
f
.I
de.tirncJ
corWe..lj\Dn o}
~:f ~~Q-+~
f n-.JcJ. l d..
.
'
_,,_ (ooo 101111c_
0
otll
. ·
'
IU.
ec..v
~r,..-~SVH.QO ~ ~
~: U) \!_ 0 I O9) 2,W
_, (_ t
-
ir.c1ec"·
n ()C.~
f'
lo
to _g>:(n) ( 1<h),.
f;;:7
. ~ ,1
➔ @oo I o1 01 o11 O,su.-i
to clL c1 rnru. :-
4 )
ro
j)[bCD
Q__0 0 I OO
l19
-J
l-f 9 ) 10
(_
o 1oorool
Lt
~~il\ij
·
~
q
~nrl q.
BC~ tA ~, e..Hrrreru- .
fuo-n
I \I , -
000 I O I O I
8in~ .
~ 'fl'i it-N. rncutl ope1YatW')A,
a,e d.i-l-Jt~
1
•
I
'
l1ti) l__i) 10 +(q),
0
I
;"
1DOO
I
t I
IOI 0
+- 01 1 0
00010 000
r
1001
1
__ j '
l OO_DJ
L..- ..,
('\urn::- I c 9
----
t
f \ C. ~
+(:is)
~<?£1 > Cs~J
f
,
I /
0101 0 I J J . ' .
I .'
\·t) 0 010 011 0
I
cJ JI ' 1..iJ21
~ --------C 13 >Cf
10001
. 0 I I O ,'
00010 11'
II t I
~
Ui)ro✓
I
t
co..ry
!.
t10 oci~
·
G-1- fo1 ~ "B11
I
~
I
,
r~ -.
,
dd 2~,"
.c-
~
Q
roo{2.0 t 11
<
II OJ
~ ffl'A
,s-➔ , , , ,
1£__Corwt~
B ~ to_l3 cQ : .
'i'e""" , One.-<
O
1
OJJ1 flOI
(HIV
EH
-~
0 e'l'o.JiO{\f. U\t~·lno.1 ~ .
'/\ V\i4-l-
I
~~'j
--------
,.
- t
o · · ...
I\,
, 6001
OlO]
'
J.
, I J
ml
I I
0>1 \ . I I
. ~n\<tt-'
~j~ I
0JI
0 00
t OI O \
f 0 r OI
I
~. ~ ti~?
•. . '!+ we_ d.o -~ t't~ ~
~
.
ffiL(). ~ "tht n o~
.
y
\,Oe
~toy;
'}t.t-·
I
>1.
.
~c.rm.cu
ooo O
0001
~
O 0 ,0(? 1
· OOOI ·
ooro
ooro
OblJ
DOIi
oroo
oroo
0 J O I
I O I I
~,0
I I0
0 . fr I
r r ro
I It \
t, DO
t ro,
r , ro
t
r
I
I
i
.6
::c~
~:: 4
1
e,_a:
[?>=r) 10 ~ 14- :i. 1
_,_•
2>
oo I I
-=t01
Oe-crmaJ
-b-
r •·
·I
I '
i,J' o t oo t I o'o t r J Q_
1-
r,
I
\~
BcG
~cfmW
0
I
bOOo
· 0 00 I ·
1
oo ro
_
\I.
t!:1-t ttiti - 3
l
O000-t-O0 11 ::.- 00 IJ
ooo r t-oo" -. 0100
00
4
rI
oroo
+ 001 I; 0 IO I .
O DI I 't-- oo I I c. 0 I I b
D l OD + 001 I -=- 0 I I I
r-
0 IO i
0101' + ·0011 ::. 100J
6
-=r-
0
rI0
o rr I
0 l IO
.b
t
oao
+- Ooit
/
I '--..
I
l I
ll , oo , i o-o r •
loot
~
~
I ooo
T
+ ·0011
+ooq
0111
'
f . OO I
'
=
tor o
Io o f
I OD I
+
'lJ
o•
~ . ti,~. D~
f\.lnwe,T~ h.tt_d_
cod~ UJhtr.h
t\ elf- C.O
0011
10 1 1
00 I f =- l J 0
t l. -a c.ocif_
,oo o
ll
-==
1
+: oo I I -= r O I I
='=
000 10 o0 "~
1
\ 0 OD
"0100 -J n-1
O OI I
'l '.,/{"1_-_;
( ~) Le, S- 'i
e_,
[ 00 D
°'+J,t>
c~
f l) :)
J{i /
00) 0
-If--
rYflLtru l\.tf '1J
w~ w?-w,cuo
W'b t-W?--+w I +too ::.
t
Q-4-l-l
2--tl.( +'l- H
~q ✓
i+l.ft-':).tl -::..l~
-/=.1
✓ .tt.. °I
. ,t+!+I -H .~-9 ✓ .
.2,- ~- I - t =- i
-,
9
'1
~
,·& ce~A ... 2, rode • -~ddrtion :
--===-
---( 2) IO + ['5) I~
eco
l~) 10 ~ o o Jo
I
,~, oro,. ~~x-3
e'l.-2>
~ o t Ol
(5"} 10 --1 0101
'
I
1
-v-- ~¼ko
• l
1 •
0
~
(,
➔ ),o
i
l
l
~~-s
q
'IO'-:--;-,
t-X~(, '
l
.· ..
,.., .
10 D
.
(c"C-3 ·
lulg
J f ;'
. -001 1
.
.
~~
'
l~ 4J,o +0011
~ti, ~
1~
tf)A710 ~ 00~0 1 011 i --, OIOi : IOI 0
o
(~t1) 10 - j O ~ J_lO OJ ~ D\ 1 0 rI , o
I
I
I
. . .
~aioo) lD-t a o-1- & J ~ ,
s,,
::Fe-:::./
_,.
c..ue.
v.:,r/1
°'dd
6 ,._ TITO I i O_Jr o> GI
· I ,
i ;
2, ( 0011)
F( o-t co::O
l+J 01 1,0 1, oo
to rt- ·
, 6 .2 =- fc~ o -, we___l.Ol'I\ ,,Ub
, 1j ,I IO 0\ I D
i L•
t ' ~h2' I (D <D
i I
,,-,l I { 0 0 1I 0
':>tI ,
f
'
!
I
1
-oorl +0011
I lttll I qo1
-I . "
I
6--r~
~\
1
\
(ft+lechl 8lri~ cod..) /°1~1rc
· ·
d mfri,num
ftwo JUttul'rv~ va..l..t,u..,'(
Aw ~
n
'L:.)tn
_j 110. . l~ ConVQlh.o to
(l'l"lITT
t
'
.
l
l
(
eo-rre. cd D()
~
·.: .,.
~
,·
·.•f-,,\•·,
co~ · • .
. <" Gth
,
(xy°"'i
'
ood.~
tl)
'l'eA..tlCL
,,
\
'
l
.
~~~·
t."
_
1
I btt- - - - · · -,
.
.
1
"".£0'1---roc:k~~· ·• ,_ .· ; . \'·J
'
~
·.
e/,l
Jwr~~
,_ ...
. ;· .. ; • -l~ ._:., .
''
-.,.,
.J .
·. .:,' . '.
.
. ,· '
.
....
.
t
t ·
dr.:J-ft,r
. ,l. .
.
•
J
~
•
, l
-+3 3
~ '}
fl
unwet~ll<cl todt
~\Jnil:- c!~tantt. COdt.
'tu tel to
l
09
66
I
~
~
•
•··
. .•
.
. .
.
'
BrnC\'IA-/ .. ft ·~ ~ :
!._!!
~:- Convt:~t
0, 0 0
l t
~
O 0
i
J O 00
9
t OO I
lO
f
tl
IO I I
I \ I 0
':.
1 I 00
f
r:,
t 10 I
I O J I
0 10
~,
II O I
( I I
I
O I0
I
1.c..f
f I I 0
1I I I
f O 000
\5
lb
~
~J
it
C..tw Id
!P
Io oI
I 000
0 o 00
~n~ !
r~ lb ~ it i,(
thf
bit- OJn : .ftc¼,d •~ !b tv tht ~-x_l~
JUtll q
(i"'l <11j c.o l'L. , o tJD7 d th t.
· r ~ ttt .ep : ~ tn~
~
f1Jt'lt,«_x
~;(h/~~~II ~
i
''/":\r, .
. I
.
.
oo
.
I
I ·0
Re_w, d ~ t lo cu
f
I O I I
IOJf to
f'°" i
tt .',<-
(c,d, .
tt .
bt ,..,._ ttin ' tr cio not '
b~
tilt~ tott:J. ,,~
I
t
fl --bl t
l
i~
t
,H. hd
v-:> l
/l;'"°" r-:t
~- k>il-
t
\ l_
,~
I\ ~ bi l- r)he '-ltn
lrw o
odd. P\.0' o.J. I
t:J , o r ~ . ~ ve. n ru, -oJ I
01~~mcu JTqnaJ
p ~,,, ~ hit- '
f'v(O 0 ~
,
I
I O. lJ ~
:..--
,
~ 'ft.f\
t'\O
}'.:Q bla a.ti
,n, 00
·O+
r
l ,i
pa,r,
{}..- Q1l ~
OtOO -r
(J
.I JOO
e.v:'n·no 0+
-f-
b I ,...
I
(A t.fn~
rru>oo.ti p,t1T~ btt ~ I
p0\i1 ~ bt t -::. 0
01:1,n"'-
•tt.i<Ever,
1 : (9dd . ·
. "
~~
\
\t,nY'\ ~,
-t-l ::- 0101
·en1
·,.n.~n..J
O"l_i a
1,oo~0 ''•
/
1\
·
ttjP«
0 I O O ->
~
-~ t :
I
I
•
!;J:
'i. a.Mo \an
'
.
oj1ea_~itt-
AiqrioJ +1 "' o 1
tbu.t- ')ecJ!v;w:l
'l:0~ol I t\ 0
..
v$, f\! f\
{.t>t-~i 41 an
esef' t'c,.1,~~)
v,.o:i)
"
t
Ct'"tv 11'
~
l
\
, 1
\
gf
IOI '
L,10\0101 .
'
I •
even
t
0~
0
I
I'
06
D1-
o
I
Q
--:::>
no', Or '~
even pct~r
~
1
.'
I.
·I
1
)
l
'
0~ D~0=,I
0 I
JP. ~1\
--+-
''
.~
2,
; •.
· - ~c!d pa'l r ty
'
P,
p~ p:l-
(1
I
•
! '
JJ~ : :. (SJ,o
D
1"10
't
'
.,
:. . }. ~ ~. '
' l ' ~
I O 0d O I 1I . · .
4
'.
'
..
'
'
•
"
I
[
I
.
.
. 1
'
~
1
.
.
t •
I
'
{
;
•
T
~
I '
\
' \ \,
\
\
'
iI
~ibU.: ~bina.ttof)i of- t ~
0
'
trme. pe1it>cl -::,
th~ -tin'\.t
o.J- e.o..c h :rJp T
\! q.A~ rr e t..Oc.t~'-
i
l
T =-
'"T:: I cf 9
I .
-1'2-
,ooox-10
• f
1
t.
'
t -A NO: - ou.tp.tr re
•
~
Tip nNp
-
~
-lhe.
(l)l,
00
f
e ~ _p__:..
~ ,ll'u.uerl-
- ; - ~'( , -1\ ·~ ,C
ooo
,__
C
~ol(J~
0I \
4 <i:)?so.bk ~
~
0
'(
~
'--4 o
~I
o ~o
-ft
Y~ f\
ff
8- ~
I
o
o
I
~~c
l,,.Hu f
,>o"
I
0
1)
\
I
l1
I"
·
I
I
~
\
--> df~l,. wtt-h
Tt- , LOi "
;
~
;
ro
#J
t :
.
l
l_!i)
I
.
r'
y
1,..
~
i19, ~L ~ ~1 ~ . . . , ; -_ . ~ .
' ! ·,, ' A- ~ !~f) :'' / ,_·. :,,
8 --,.u , ~ ·,
t=CL: ·
0
! ,·· ,.;
S~~-
~-=D-YzO
~.
ol yi=- o
l
'.
, , I
1 1 - A ~f
•
,I
M.t- a... .
I t _.. ,
\ i
I;
I
I •
I
i
'
0
" ·.
I"
''<
0 A~
B "f
0
.
'4
~)
· ·. " I
~ e"'-.blR..
-
Cl.t
"1
i
I
-f\-
•
o.t~ cu l°(tJQblt .
\
··
o.~
ar tf oo..ti
O.CJ:
t". C L
II
-!r'XJ..01-
ru.u ' e'
fly, '.'. : .,
~t- l.O f II
I OI 0
I I0 0
I I I I
. f\ ==fZ]----1
!,
t
I.
re, bpt.n
Trp
0
0
loo
- UJ - ~ 'to
1
. , ~ ·t, L ln~rr, »-
0
001 0
blO D
I
-·
'
..J\ •P.> -=- B• :A
I
~
.
'
3 ~I
'.,l.
Cotnmltla.tive la..a.o~
-Jc
0 1
' I)
~ t"nab\e
htvh
Q'lt_ '.
.
J?J . - -
~
fnp.u--s.
rud_OCiGtl~¥t Jru.o :
-1\; (e,c) =-' (-A,~,c
• ..
'
---=:[)---'( ' A• ~
fl
-
hflj~ (.,)_ t.0h£>n
.
-
I, .
'
I
'I
°'l
I
I
i
~
I
I
:-0 '
.
1)
,,
,~,I~*-'I
,,-o -'f ~~;. ,
'
• 1' eno.b ti.
A-
I~
'
• •
<
<
J ',
,·
I'
•
~
.') -A-· t
s---c
•
~'
{ i! '
.
' ,...9
t '
f
.
~-
.P..·· f;
0
O
t
{
0
'<
0
0 .
0
I
'
f 0
t
-ft--
0C y
0
0
0
0
0
0
''
0
0
'
0
a
I
0
~
I 0
1
I
I
0
I
I
,
0
,'
,
-
I
'0 'I
' '
l
'
ft1f
'""T ,- L
J.,ol:j
C
C.
F 1'
\~
/-
.
I
'
..
I 1. ,
S+1
e,
_.
t•
'
'
I
♦
•
. I
I
\
.l ,
I (
,
i
I
.
: i
.
j
-
1.
, (__¥'-~
•l6+-)) ~ I
: (-A+~) • ( ~+t)
~ -A e+ ~+ -At-J>
. ~- l+-Yb+ 12>-+A-
-,
. : s-
f)
l -11 -H) +A
R,-f-A- '
,r
I.
- - ~··
N-AND ~ ~;-
-
- ·l I .· \
cao.1t ~
NOl2.-
,,,,_,,,.
-T~
0
dttt,..t:µ
o!p : - J
0
I
I
I
I
r
imtblt
fnve~tof
I
I
J 0
ero-bU-
•
-A rb ,'(
~ y
0
nwb~ -ll-No
t
,
I , -io Jp \
-
-------wy
'1 ·
clf6£1bl.-
0 " 11
0 0
i.
0 I/
I
! '
0
1
I I ti
I '. i I
I O
I
~rrL~i
-- ____
t
./tt1ou'n..nve .lru.o~ x
~
.
W;x ·
.
(rw;,',+<J ;; ;c' ,fl-:(ei~jJ,i
l
I
-----=-,
.
. ~ +-13 • C - *·B+C, .
Nt'oti o.:tW L
I.
i
I
!
'
-.-c::="
1 ..
-It- C -t-0 C
-"
f
--f\PJ
-
o
_ .
'" u
Com m.ut-a.trv~
+1 AC
:_eorn~r~e.
J..a.uJ : -
-
tf\+tb)
-;_ QA-1. ,,
(4' ~)' l ~ ~) '
\
r/p ·r.. Jamt_ o_.
·f'NV ~~
'J
r
( et-I!)
~
• 0,. -
•.
1c:.
· ,--, • B
-
-1~
8 .. n
---
·,I
.
. i ,. !, .
t · · l:t~.-,
·
,· · ·'l
:.:· ' '- ''.; :.,' ..
·~ ~:~,.,'tt; f-i1oa .
i. - .
0
i'
-
ta,~ ·
,· t'
I
~
•
+ "it {_&+c)"
~} C
I
j
?
J
'
-
-- -
·,
·.:'."
i .
. -?
'
.
-'
•
:
..,
'''
'
I
, I
I.
-
-
!
rtnJC'"lr ul CKt
'i'rru.th
Yr --1\@ lb
~ ~
.e +A · 0
l
<01 ) ( n t-8) · (li-t-,i;)
t"o.~
---
rf\ Q
i
'(
Oo
0
01
I 0
Il
I
,
t~ 00 ~
'
0
(~ 'lc)ete cto, J
Cont.olud
tn'it..,ik,i
O~~d~
b
0-::, o
I --d I
'
:~t>-Y~e
.. ,_.
o~'0
pope ,t~:
(fJ -A-@ , A ~ 0
(i:J A (0 ~ :. I
[iii) A ~ O :: Pt
Qt) -A(i) I :: ff
f)
~.f-
A ©fb
=C
1n,n
P.,(o C. '; It
o(t)
A(D tz, (B'C-::0
.
fl© A: 0
~© A
'l©C r 8
.
ii9
'
'
IT: -:.. --A
-lie ,f\t) ~ _.._ - -() ~ fi I O~n-fd
- c·
'
0 ',,~Wf .? _
.
..: \
1· o.f.-XOR, ,~ vcU~
G.~c"-c!rn
'I:. ?
'(, a
~ tt} I )
Y. '::
X
l '/~-;. i
Y, :; X©I
~ ). = X
} 'lever>
'-ll( :;. ){
'
Y-=. A©-A©4'<D~CDit©. 1\4}tfffiA®A
{Jy
· 1 · L-1
L
I
(i)
1· .
o,e o(D
1
I
t)
t
J
©
1 . \
©It
t
. C
ft
=LID
I
I
t
t
\
-z-) ::- tl©td)©
I
i.
=-1
'
l
i
i
r
~ (i) ~ {) "Z.
-z),w) ~
.;t l-+(~©Lf,
~
J
+: L-tl,_® ~, -z), ~J ~?
~ ---fu.rc.'
.:+-(~ {) lJ
'
~
\
'l61 ~® 'i ® lo/.
, 11 • ',,;
I
I
i
\
'
' '
...
l;
•
I ',
.
,
i '
' i
i
J ,;•,
,,-~•;'
I
I
r !
t
f'
..,. . ({ :. :: _,:', \f···· .,,·,} ,'
, ,
l. ,
<
I
I
..
.. ,._
·;~
" , ..~_:...:1..
. ,
'
,·
1.· ·
r·,
~t, ·:
.l
'
"
. .: I· ' .
.- I
tl'
1, .•
.
,t
\ .
1-.
: ==;p-v
'
1'
O 0
O 1
I D
D
0
r
--
, l ,,.
I
fY cicl.rriona.J ,
1~11\bOJ
~~ bk i d~aJ:u.•.
-\11 -
f)! ()p eY i~
f!-0ir ~ I
-A0 A- ::. 0
!1
f}G)
'j . .
,~
0
~
-A
/ I
'
l
-
,
I\ Q -1)0--A ;:)
f0 ~ -=- -fr
·
'e ll tecttYr'
- --f "
,
'-) ~ -f l ~ I
OJ-1:e. r f
•
I ';
.
@N_'D
i'::!!_ ;-
~ u!}jv eu aj
➔ -4\N lJ , 0 1( €
N~T
q.,ie
J
tSuHic,·tl\t"· 1o frttp l.tfl? t..~
clrfi hu S~ttt m ·
~ Ft NO o'Y ~o R
~f\Y t ~ t
-+ !r.-1 wt- can
sa.11 , iha. .t ant/ c kt '2Qn : b?.
~ coJ)
N fl ND ru NOT ~ .
L
~
y ;_
~
fi· £,
-
y ;_ .fl . ft
y == "
N-f'-N p
Q4
- --
_,-
'
Q~
th!!S e tf-f{-t.e._~
I
~!l"Pt.._~~
NO 12 :
!
j
I
t- -- ~ !
f
i+ ~tr,(.
:0
'\.U,I'\
N NO
~" e
~
~°'me
to
I
•
,
,
I
:
➔ Cb ~f'\ .tY n q
u
,
l
•
I
.,
I •
"
'TT
t
I
ri-ftf1 o
''
'-to
,
f
a.. o12. o/
¥
rlct<.
I '
y
V=--A+e
[4 )if\-NO 6ati J]
':
I
I
I
I
I
' I
I
•
I
"
t)
-EJ( Q~ :N-At'IO ~
--==
~
J!J
~l- 1
-JI ~
" -V
l
~
t
NOT
R-No -+- Lf r{A-NO ~olLj
f OR. ~0 NAN O CJ'¾
-tu t-a.l 9 N ftN D
v~+r•e,
:2--
I
-
•
Ceompletr.ef\l
= -fH fh-
t>fl OfQ. ia.liO n
f'fpl
_/
.,-Y~fl+(3
-fl
Q; N-ANo ~
-.
Cn.ot-- bt4t-
1~ nfTf'lt> SA-te]
\/.. ::.- .f\ ,[3
'Y ~ f\8 +AB / J
~ fio1 I ~ rvl\N D 1o.I:y
I~
.
~o
N -ft. N D 2A. 0 ~
,
~a:n.. .
No·Of: IHHiO~ .
i
N,01
\
ANP .
2..
OR_
.3
\;
!
!
I
NO~ · -
f,
'.
i
tKOR.:
I
/
I
•
I
Ii
I I
i
I
I
+
tKNOR _, S1
I \
fiV M!n ,ot-- a. , Ip «fttf P !
(O ~ '•'-d •7
---er~
1
,
-· .
--
: l
j
-·-=
VJ '
' I
\
l
Y.11
'I
-z::---:--'!
ld
!
j \
.I ' ! j
i
1'
I
I
• I
.
' I
''
l
!
I '
I ,
I
!
)
•
'I
1
•,
,
..
.· l
It
I(.
!. '
jI .
•I
l
. 1,
1
,1. ·
•I
f
.
:\}'r NJ2..(< ~ t1E.,I : -
'Ir:- ~
'{-:_. ~A-
'< ~A
-cD-)-'<,,_ "
4\
CCffoi.i ~
~
- N OJ'.!.
'\'1
~
A , C4't~J+°&l~-te,> .
~
,u
0'2. : __ ....,
I
{fr- l~~J) t e;. (-Mf>))
t
:
~ (-A--t{f\-tt)J} (s+r~)
~O'-i~ .~ ~,111 +(Me) ;
:. -Ad~,+~ •8 ~
~
Me,
Nd2. o.>. · X Ot :-
--.=.-
--~- -,, ~~:,f\l!,
', _
• '1-.-f'i 6-tA
-HM
-f\•e,H\ ·~
~y No,ol ~ ~,p
<aal"t.f ,-,~- to
NOSl'
• I
\
.
iJ\\.f»rtUl\t ~J'l' =- .l A+PJ) .(c~o): •
1~ not 'i~
t
I'
:
.
I
. t ~..·· '.. ' .
',
l ·.
!: , t :. .
I
~.
l
l'.
. ..
.·•
·•
t.
\ l
'
, .'
l
,
I
i t. I
~· .
,.
-
.'
..,_·_:. ..
.<t'. . '.: ;, . .-_ :·<,
'.:· .
:
,·, :
f
:
f" -::
-
fH {?) C
i
'
A~ ~
0
0
0
0
'lD
0
,
~
'-f
)
'
.
C
0
'
' '
I
'
1
I
a
0
0
' O
I
I
I
}!
I
0
I '
e-c +HBC., 0
0
I
0
\
0
I
D
,0
0
I
'I
' ·u .
N\U-4 t bt- · c
00 ·
f
''
f?> C
1
C
I
,.
~
.
l
+ -ABC+ ,4tBct- ' '· .
:: -AB(cfcJ t-.fi-ect-ftSC:i~c
r
~ -As -t- & . ~
'
1-t
l'
f
o1tt itrr
~ .
-. . .
ft~[+-f\(o C
...
'
ria.nse. ;:.
.
.
f
01
"
{b (_ ~
ouo.n
J,O
l\f>c
btr-
, ~fili/
·,
t-A e c
~ ~ 12>+-Lc-r~jf\-e,·t- ~ ~c
f\ Cb "t-00 t-fi l'bC :
~
=:.
1
• ,
A-(lb-rl?;)-t-APJl ,
::. A +ftloC
~
'
I
••
.
f
'
!
I• ' -
= --A+12>c
, \
I
I
:
,
,
'
1
''
i
--:i..'
I
-'
•
I
I.
' f
,
,.
l
[f' ~c JI
fMD I 1ca"1 ~
'\ I
;j.BI -F{B,B,C.)
==
I
. r
2rn(o,1 1 ~,4_,-=t-}
8 ttll;
..
F== 1+n +m+.m..
0
m
I
I
-f'\
~c
00
I
F ::: toe+
Pr
-tt
~c
i:
e+ Ac+
/
-I'~
~
lt~t} :- fiht
cpour o~f ~1A
i-J \ Cal.ltd
li!l,4-, %,16 -- ·· - · t,ft,
tq :
fmp),tan~ · 1
04
po I If 1-;,lt cruUf oJ.
Ja--<1~ t
fn . W.-m~p
0I
ttO
'r
1
,o
.
l
both
1~
1
tan COM.bf/le...
10
I '
..
I•
' i
~ : 4(- Mo.p VJith 4- Yolli ab~ ,'
'
'
-t l t\ I b, CI d)
I
l .
~I
f =- 1- +II t lll +'If.
F=- Cd t~bd +
abc -t e>tb cl
01
"
' i)
,
,,
• t
It
.l
--f
I
I,
r'
, ,
I ;
'
.
.•
'
,
..
•
-
f
!-
.
j
• '
I
;
f
i
\
'
I
0
~r+rr+m +n
t
lt
y<?di~i))
' l
t ",
I
I ,
f .
I .
'°()0l
~-i+-+-s_::::-...::::+.--:,r-:-1, . :rt1
I
I
\
ti
. \D
L
~~
•
,
'
l
•
I
'
'
\
I '
' i_J_~:::i=f::::::::_....[_~--t
• I I,
1..
mf''t
f ==- tu i, -+ ~ 1-+
·i , r
j•
I
'I
.
,
,.,
~
1(-ttt~e:-
'
,,
··,t• · ·
.
•
...,,...
'
t
- --- + -AC
•
f'-=- fil?J
,
~ -Rpp'-9 dt rno1~ns 1a.w
crJ =
s;
t f\-.PJ +ft c)
~)·
tf\e)
- (_A+e,J,t~+cJ
1
F~(-A+aj·fAt[)·~ po.s
•
01
It
I
.
i-= en+
, Aec:1l\sc
oI
,.
t
'
\
'
!
f'.A~8-ty,
C-A+B+s}.
1 F:{~+o_r
t
•
.,
'
,_
''
, ~- ·
'
- •
'
,
J
.
f
'
'··r .. /r
K-Mapwith 5-vo1abu
16
8C
Ackanginghangrg
chaning
3 2coly
f
C½ + 8p+ DeA + Rebce
don4o i t
hes
L o r ed
l io n 4
unnaif
npdokt
qnoup
Condye
Qutne-Mc Clus kay Mintniatton echnique ltatulat mutha)
foy Complex
9 v(A.B,c0) = m(0r3,+ &,9,11,is)
AB CD
0-00b0
1-000|
3-00I|
Group
min lerm
-100)
|-101)
Btn Pep
ABCO
O00
m3, m
I001
m4
mi5
m)
destqn
hatched
Goup
BtnRep
Compar e nth eh)h group
tale
pair
mirerm
oith
onevoniobl (bit change
0 00
0 00
eoup MP
Momm
m-mg-m,n00
'mg- me00
m-Mgtngh - 0-1 8
mmamgn0I
-0|
m3-M, |-o1
matnmirht
m1-mis|
|
mu-mt
Prime mplfcant table3
tunthesno
Jp-I mintrmy
4|
pime
matchd mplca
pai
13
inNoheo
e
g-m,-Mant
împlta
1sgiven minte
(X
ohe
nt
X
1,3,9,|
-
X
X
ep1- e) ertal
to Veaiby
A
piuimp lat
fTE+ÃE BC+pEBC
$Op o the
tuhtf A+8c i6
\8C
f-mli+, S69)
ne suehing plession orepohdirg to fre, C)
-2(04,5,41,12)is
AM:
C
ial
19
10
oy
(w,n,y,2)
1,3,4,6,41,12/4)’ otirdupendnt
how many
Vontase
a vaniate
0
4-bit eve
patty
b
-
Lohinno-of y3 in 'Seqianch ts odd
NPonity
b
qener atoY
k-mop for Po
bË eo-b Po
bibo
byb
bibo bybe bjbo bË bo
bsba
-o-o
au
bba
10
boa d
Gontguta
bab2
o--oo-o
Ca
n patitng' SrglePain.
-
Po= bgb, bibot bb b, bo t
ba by b,bot b¡b,b, be +
ba b¡ b,bo + bsb,b, bo +
bz ba by bo t babab bo
P, b.bo bz ba thabs) P.
+ b,0bo ( bsba tbba)
B,b, (bibo t bi bo) t
Po =by Obo(bba)+
b,Obo (bs ba)
bsb, (bi bo +bjbol+
bs bs (b, bot (bsbo)a
Po (b.b (bob)+
b,B,(b,botbibo) +
Po babs'(bi 9 bo) +
bz b, Cb,O b)+
Po = (6t bo)
TPo
(bba)
bo bOb20bB
bgb, lb6 be
Seven Seqment play deuodar : (0 o 4)
b ba bi boa b c d e fqlep
TO)oI
el. d
0 000
b
bo
lis
b
Heqmen
|ba
deod
bz
10
O
onr Cane
H
fof |4
a seven Egment
displayduoduy
NOw o
nucl
a
\bibo
bgba
101
|2
a= bg tbi+ bbo + bo b.
batbzt by +bo
d
b +b,bp tb¡ by t
ba bË tbb bo
e: bb t+b, bo
q= b+ b2b1 tabi tbi
b- b +bibo tb, +b, bo
CombinaTOnal Ns Soquanttal i
o Rs depende
OJp ts ONy duperdnt
pierent
pieent lp
lp
on
past olp
eq: ountey
+ prevfouA Olp
/prerolp
memony
4ve)
: nemoyl
HAIF ADDER;
to add siqnu bit no.
Soesn't take camy tom piev tum
Sum
canyuut
S= AOB
CofB
Cout
tul addu
Cout
Sum
-Comy
out
(Cour
Ctn
fot Sum
Chee
bo0vd Con
o Cout
Cout BCn t
ACio+AB
out
D
futt addu in
# (B+5Cto) +ÃBtn
A(etCi) +Bn
Hh
-AOBO Ctn
HA1
Cin
Cour -A+Cin(He9)
Cin
AD
Cin
4-bit parnallt ddu uing A :
3
5
So
fum may be
46Tt 07 b+
Sbit
Ao Bo
Isto
FA
Tc
74Hc283
fox 4-6t tull Adde
A
fnal sum
o1).
fo
bit FP!
Asa A fb
4bit f
Cour
Sy-9
Ba B6
Bo
tnalau m
Cin
HAIF
SUBT RHCTOR:
esen
0
-B
bomooaut
bo
dout
full AubnactoYS
bin
Bout
ol oWo
Choelk boand
tontlqunatton
1-6-0-0
rHA uing AAND
=AABBAD
ABO Bin
HA wtng NOR gate s
A
FA
F# uinq NAND au 3
S- ABO C;
Co AB +C+ (AOB)
AB
$= A BG
A+Cin (AOB)
Dazlo4a)
(0s405)
Jum s4o)
fA urg NOT gola
qak -
HS uing NANS qat
A
bovey
o,
= wa4b)
0,
(A+5)+5
Naso)
A+
AB
Hs uinq NDR
NAND gate ony
Full dubhacroi
02
Bin
8o
(AB0)B; 8r
A+5+(40+B
:)/
R-Bit
Multplier3
muutt plu a bth noh
Bo
ABo
X
Po Ao B0
P,=piBtAoB)
Ca Ci
Po =0
IAo
fJum=XO
AB0 X
xOY
ABtC
I A
B1
Cony dook head addu CeLn addo) mdiet th cany
Gupeio than CA duw to
pead
o--- glo o
S
S
dourt dapend
GatP (G,+PGo+P.AC)
P
=62tPa4, tP,60t
Co
popoqation
Cont
Pp P, PoC
qerinatoi
Co= GtPCn
Co= 6 t
PC)
Genat lon;
CG=G; + P: C
hed C2n fA we ed to
watt
oy
Co,CI
but
Co =60+PoC-0
tme of ll Saved
C)’
Po
P(Got
C, = G+
Oalt
A0 ho nud t0
dor cat to qehati
i- 3
P,Po C-)
C3- 6 tPal 6tBG, +PaA, 6o +Pa
PaP, P, Po C
PsP,6ot
Ps
+
Psla
t
P6a
+
6a
Ca
Pe
L
P
P, = A0Bi
Po
Ao
Bo
G
C
G
Co
P
min:0t0
Mar :4t9
rom o to
otO
(o-18)
fo000
Alde
1001
fo000 B,
9
1001
chy op9
weau
Ug
adirg
decinal
Which
* heye
we
don't
outdu comy
mev dum
Corutdu
Cay thun
19.
dum 0to
Decemal
Biray um B( kurm
ss s S c S S, S, So eothar
C
bt
D001
11||
Sanea
Jum
(Ws -(s+s)
(m) $t.s
zct+S(s+s)
12
13
14
15
16
y-bit addy
S
I00 0 0
I00 0
I006
Juf
1000
| 1001
19
ablu
(8c0Jun)
MuaiplererA i- (MUX)
Tntoductton to
CombinLional
into dom
that nelectx bingny
to. 0lp 1ine
E
diaecta
1ines
3lp
CKt
many
ne
Selueto
data
becauu
Reduu noiot
Ober
W
Ckt complezity e coAt
MUX
vantow
Ckt
wing
3 mplementarion
aselectd
untveASal Logte ckt
Noníabl
S, So = 0 0
th to of)
Selee ttd
then I3 wil)
sele ced
noof
Select LineA
noo}
Se
p'% )
81 MuX
16:1 MUX- 4
32: MUY- 5
E 3
Y
X
MUY
IoIo
II
E
Enable
= E(3 IotSI)
4XI MUX:
vlouput)
mlog,t
m-aAeetttd vanTabu
MUX
So
S, So
y
S,So Ia
SisoTa
8XI MUYS
D=8
8X1
MUY
mloa!
S
Si So
o
loqic qan alc to egn
MUX hee ((htghes MUX om ooes MOr]
axtMUY -
uinq
X NUX utng
Gmpumnt
4X
h4
MUX
9-Qx|
Sequentut
-
(Muk
Ax
I
thun
axIMUY neg to truplumen
xIMUY
onu we have
4x1
MUX
..8, So
10
I,
Y=I
MUX;
axI
uing
MäX
8x
avatlabL mux
muY
Ovailabu
n2
|S, S,SoY
t
I
sequre
I4
to jnpument
+
8x1 MU
(S)
Io
lo
T4
do
lo
SxI MUY uing 4XL MUX:- Lipectal ue)
h = 4
tx1 MUX
= 5 4xI MUX fo
the lp
it man
'0t the
ued
Ra not
can't
we can do
do
t
noimal Oat
enable.
Lo
I
+ t we ned y-I
thes
8, =0
S So
)4MuK OFF
Iy
O4XIMUr
8, 3o wil) ke
than Y=I
S, So
uxI ON Dlp v
O
then G=I
)4
S, So
MUX ON
fI| be)
then Y- I+
32 x) MUX uinq &xi MUx
Óoo-.-O-..
32
Sy Sa S, S, So
oo--oo..
S
y
)
S
IJ
thun N=10
Io
, 6)
for V= I6, to
y toy al
:|8X)
i
we
udY= Ic
y =| , that
enase =|
mplemertarton ot boolean func uing
Crnpumen
MUY?
F (ArB,eo) z m(i45,t,9,12,13)
uing
4Y| tMuX
So=b
A13
ut!
oJ7aEolIs
1
I-eit fA uing MUX 3
doY surn-B=|
Cou
46 Cen
Chur boand,
A=tB-0
A o ane
selelteol
for tomyautt
&um
C
C
Ct
MUY
Si
So
Loqical eupressibn hom
MUX:
sx
Y-
+ AB
Qemu : emultiplexua
Reve eie
operation b4 multt ple
to many
One to
eKt
tMany
n olp Iinea
n
o
data dytttbutu
9atath
eleet Iine
select tlPx
SoYo
1:2
Yo,
Y
I 4 0emutipleaes 3
|:4 Deu
S, So Yo Y,
Yi Y,Ya Y
.Y2
OX X
D
Yo E S,ST
hES, So I
Fuu uohactor ing
Bin
Bo
Standond op
RlA, 6,Bin)-Zmt.a,4A
ml,2,3)
E
BRin)
Bo (A,
Auy bo= YitatY4Y
emukt plez Celti
Ya Y3
Qemux
fng
931
Yo
1:2
ecodu -
Qemu
1:4
2:4 duodu uig
134 Qemu
[3: eod,
Yo=D
o
Dem
T
Ya0
:4 Aemud
tere Q14 peuody
etd vanialdy
H
o
Yo ,. Y, Y
RBit Gmpanato
’A digttal
ompanator
n-bit
a
Gornponato1
(omb CKt dutqneol to tonpne
npuh
Dlp
olp-1B
fo
A Ao
0)
C
A Bo
C
Ato
1
Ato
0001.
AAo B, Bo t
00
= Ao Bo B+A16)4
AoBot ho Bo
CA,5,tA81
06)
to to En CoderS 4daeodexs - (Mcdium sau
Mhay ane Condb Ckt
m" olp
tlp
Ic)
enode1 have n"
funuton of daodas s opp to encodua
p
ym logryp
OPNionity enodu:
it) Qecial to BCA
| t03) octal to Biray
zlduoda
ermusd
|iv) Ha to Bny
owet piioiy
T3 I,
I o
Y Yo
Jo
P«¬
then
X0oo
10
wedon't
Jo,IT
hare
du to Hp
Recimal
to B0
O encodos
-
0 to
0 to 9
Dectrnal
to
entodu
D-649
C=4
5+6+7
B=t3+6+7
C
A
nodj
Otal to Binay kLodly
Otoy
2
3
Binag
4 7 t6 t4
Ba
Hena cecirnal to tnany
Enco des
B Ba
hl6
fe
m: 4
Heg
2
B
6
enoy
A
bo= I+349+ 4H)H3+H
C
B
2+3H41
4t1644 t
49+10+1 H2+13H4+1T
Logte imement
DB0
Fuu oddu tir4
ady:
Cinqle Ic
Cost
paa
duedu
but conenttanal retho d qatea
re
Javed.
uhtast
O Mo
00
Cin
m
dacodu
Cot
m
m?
fa
O
Em(mT,ms m,m)
he cKt Ahon iolou
s(A)8) =S0,2)
not give antie
neplen
yexoe qadu oth
A
Y- AB-0+AD-0+
ilo,3)
îne
beto uw epieent tune
CKt
X. (n 1bC, 0) ay
z(39,9i0)
b)
(3,S AD,4)
AB C
m
001
C
I001 t |000
Zm(3, 8,9, 10)
o
A MUX
i
Y selita one ot the 'Je veaal flp
A) YotA The data tom aa
stngle
onn eah
dato
to
pe)tal data
y Corto crt
at same timo
XNOR
AMouldbe
aNmit
p o
t to a
Ot
many
Ddentlty th
Conrect
to touowng
ttatu m nt
Can act
a) x+Y
-4-6tt addu/
b) y-x
Y-bi
4-
uadou
d)y+}
Jup
z (4 bit o l p ) E
Vo
Yo t XD
a' op
adding
ah cop - Sub
houput
o Consides the
ven by
Y
tt auted Ife
dubtratos
V-x
Qch y a h
Olp of a/
CKt nhown belo.he
functon q= actbc
the
aCtbT
fine n
a) x xOR Y
B) YV+ ExY
c)
YEtX
d) onu.
A4T+AB+
X= A9BC + AD2C
lovcuan r
an
Q$1
MUX
alqe a enprenion
f(ADCZm (350, 1213,14)+d(02)
JDI:
000
10
t
S Si So
)
Comb
ekt
with
ohen
and
the
qre alu than
Dl2 sthe
the lp
hn the bfnay tp 4 4156 TT
Than the Plo
9
lean
the
u
olp
binany
d'iety
C= Z
(
MUX as univeASal ktc Cruit ;
NND
NOT
OR
fND
MUA
MUX
MUX
EXNOR
NoR
B
B
MOX
a)
MUX
AB
Seguentfal Cheuits i
’ me Sequunttal cHuita. the
the
ppelent tlp
present olp duperda on
past ole oY olp4
tn Sequrtial
0ut
an
CKt evething
Combinatun
Conbctt
eaupt
numoy
feudbak
be faptto ps
gs
Ckt
pat olp
to stoe
feudba
Memory
patolp
NANDEATE
’
NOR GAte
SP-latc h <
ihe bac Atorag ement s calluod
name
&uqgeststt
NOR GATE
lat Ches
the
uet
Cae )
3O, Q=D,
LATCH
gertQ=
=|
Gatis
bur
ger
ae ti
Cae (f)
buti - 17@-0
2 Pos
=0
Q1
BY
total
TV
to h¡ht
co
8inal
4 spud
tHs tutal
htgh S1qral
thre
o4Ratio
ttme
Kah
CKt matntan
=50
cyca uRuy
T
feading
t
6
not
d
Mo
edqe
L
eCIK
FF
SR
stgnaledqe
’not
.
tatg
cocre
a hat
-0 2 =0
oS-
0
uol.
NOt
lsle'
Caue)s4
ud Nor
beyove)
GALE
memoy
(al
O0
NONP
qatt
NDP
soY
leved (ohen evea 3iqrd hgb
higening Muthody s
edqeN
Stati
omb
chap/ tanaitton
labchlFf
memoy
CIk pe
c|k.
Llevel senuttvedge senumve.
OHienenu bho
Larch
Low to hla
tVe
high to louw
-ye
tirptopt
S
4n lath
Lbe don't
have corto
()Erable
Signal Ce)
out tn iptep
we haWe cIk
R
nable
)
Abve Ckt
oll act
a
?4 enad
latch
means Latch cant
be u ed au ff
but f£ can be uud cy
Aatch
tevel
hiqging:
erable
hecaue
En
Se latchv
when thure
edge tgertng
mam
SR Flrpilop:
lateh
SP Aatch with
NAND
not u .
Cx
wed
pevent
to
ccintty
CKt
whn
ofl chorge
thum changhg
Mend to
eveg
change
CIK
Rec1e= R+ TE
nei
C1K
R
edg biggeredalcto0
Ont
3 R
Mamet
ihvalid
0
Not
Chonactenuttc tatlu
#erctation tabui-!
R
SR
1
X
id.
ip ttopi e
e
to
need
each
othey
ve
becaue
a ilp ohich ane condemented
gtve
n 0ff
R. 0
8
thy qne
one lp
% tomplumerted o that îlp
an
CIK
|CIit
miam Q=0
elle 3 R
Chon tab:
Qn
D
1
tacttaton tobe?
Qnt
ivalid
JK
Iipilop
SRe
Ovescome
FF
that
hae
fvalid
probun
A
but we wfl)
OlK= o , c k
|1= Ik+ J+
CIR
omSRbtes
(NAND
y
fare ):
C
J-0, K=l, Q-0 -
1= Cik +3+y- Cik+K+
d= 0+!+Q4= 0+0+Q
A0, Gom
JR latth
au tn a
m
Canebr):
aMume ) -0
T+3tcic
1+T-+T
=0
=0: k.cIE
then, sl ,Y=O
renotibydo on
=
Chat table:.
ruth tatL:
1
eucttarton tabu:
do
Raa asound Cond o
iacing in TKfho opi
olP
-nachg
K:l
CondttCA to o vegome
actng: -
not pNotltal
so'not uud
< piopagation dulay of Ff
(m tuttad of
(in)
edqe toigg
lovel tgg
Mata 4laye
Mastes slave o4 Tk pttops
togy
muana
Ir ahould togu
Tacing u unconbolatu
which e
edge arggening
tre edqe
edge
Mastro ilpllop
Coollabu
qgei
Matka ilave
gYTng
igTSa
2slave 4ilptlop
1
Jtate
Hoved
Blarsi4
oont
’ l a e ON
cIK=
044initalu
stave?sON
0
now
eIK
Mattes shye
save
Aptto Ps 3
s,4 same a 6N
CiC
MOt
Do
slave
X
T-ipttops
do TfF
char tabu
Lttoqgle
T
Rmor
KQ
encitatton talou
h
QnHT
Odd i
deteetoY
X-OR
Fitpftop Convession?
) unttty avatlable
3) Mal
3) Mar
Teg
f:f
ea
characterest tate fo
aNatlabu fE
for
taho
encttarton
to aVatlabe PA
boouan enpression
the
JK
to
ckt
lpfop coves tio
1) availablu ff= JK
dor J
l) citatton taby |i)
ot
(ty chanactetate tasu
wrie TR theu
SP to
ptlop
i )ect ation table of SR
ovailole
TV
SR
T
chan tabl o
SR
T
O X
TV
(V)
R
SK
ke
()fyttatton tabu of sRi
(fv) Gooeon expeALDN
IXo lolx
O x
XD
(
CAL
SR toT:
(t) attation tob to Spi- v) foT
ano
r i) Chan tor T
X
P
foy 2 -
TK to Se Fo
SR
aChn sRi
Ontt
0 X
K:-R
X-X
X0
K
XX
TK to T fF:
Ovailou
S:
Ye
TK
OX
1X
X0
T=1
to
SP -
(i)f :
avoibda ea
Chor Sp
(N)-fo
t0T:
avaiobu
Ey,
Tab
:
o
i) Chon T- eT O
Ont
en T
o-x-0->X
C
S
CI
D
T.
(it)
¬u Tá£b
(iv) fox:
har
- E7]
T= pOBo
T
to
Sp
foY
-
Ho
0-0
T= QnR+ Sn
CI
Piesegt and cleon înputni
auynchronou tlpA.
nhey me dítect tlpa or oves71dirg
be Synchsonou lp
lp'a oT
ane
preereluarQn
duar
0
what e vea
6n
be
becouu @n =l
hot
ucd
the
fe
nora
ynehnounus ?lp
,presetlo)
CIK
clean(o)
PrutO
Stare table : A tablu telua uu the Telarlon bw
ard op.
Atatu
nt
rlent atau
stau tabbi
ps
S
ka an
yondoly
ke
Jeg CKr
sOrarm
4stoti
no ot ttpttops
LAtat'
Jk fP
we
can
NS
So
oxE)
si=I
IX
Qestqn poudue Jo
Cked oguuntial CCA -
) A sate dtaq+am ot timtng d(agam
descoroles
ohich.
that s
be
1) Obtain the
)
Ct
behaviout of the
the
deitgrud.
staue tabi
nhe
States Can
be
eduud by
Neductton mthod
) D0 Atalu airtqhmen (tf uq)
)
gtven,
Qetemine the
no.ot
Vi) Qectdu the Ype
vit) eatve the
ot
statt
uttea ymbo
tlpttops e9
Hltop to be
tabe
eLcltaton
ho
Atatr
tabu.
wtt ebtaio the eapiexnioo tor ctt Olp $Plpttop p
tr) mplment the
tploolp)
)State.
(t)
tablu
.Ps
NS
1=0
QA
D
d /olo
o
olp
Kmilan
to biroy
brCd
a
alody gven M re
thu
POtnt
otp
eciatton
Ps
tabe
B
NS
4rtp tlop
6n
(:)
A
Mealy
’heve
Machine
ane
ynohot
modalh
toi 7epseurtingy
developecd
teq Ckh
o/p u the ur
tatiMachin.144tati
lp
(0 Mooe CKt/ MOOTe
t) Maaly crt / Maly
the op ?!t! qenealal
(ony op
Machre
SBau
Moole
:
deuod
the oay
ddune ot ttp)
Ps
NS
Cob loqie
lombloge
olp
CIk.
frdsperdunt
-TA
-Y (olp)
PerfP
nehtdiqn
mooe
dagam
Mel
ta
Y-agt®aty
p omb logYc
Mealy
Stat1 machine i- Mhe olo A the
Presen Atat
Det Atare
Cornt logc|
doctd
oell
ot
Pee
olp
4 eornb logte
orth wth
Anaksis od
fune
ent
Sequuntial Chuét (uith 9 fF)
GA
yole
(1) ttepI: fnd our the tlp e olp 'eqn
Ole
tep 2: SBatu table
Pst
NS
00t0
0
H=0D +0:0=|
& dilpttops 60 4 4taby
Blep 3: Atate diaqiam
ep 13
o/
olo lo
a fnays
clockudlsoguurtta cKt
Cwtth Jk fP)
D
Plp egna
KA = Qa'
Atat tabu
ps
--o-o
Rtan diaqram
&) =00
00
clocieud Seqeinttal
tralynta of cdocnd
()
() TA
TA
7
Te
ytau dtoag Tam
nealy
NS
4
2 To Te
Q--o--o
C
10
PatteYn 01 Sequnu
She am
he
clK Ps
high
of
Netecto1i
bft
and
hu
port'ula1 parern equuree ty
detetttd.
hiqh
htgh
thun
?lp, ohun the
ben
becomy
dteetcd the olo
oenu
aqain beLpme Low
ovealap
dtele cIK
oletecto1
bme Tandoro
e.
atepl' Aata diaqam: (Mualy Mat hine)
GJ Ovealappng
() No ÔeAlappiig
Jo= Teet (powes up)
S|=0
(so
Te?\ate
oo
mtqnm nt
($2
Rengn a
Jequene detectoY
to dutect
3 07 moYe
Coming
bihh
CouecttVe
throngh
do
non 07y
o
frat
So=00
S
1
S 11
S|0
Sa=l|
11
8 tate tabk ;
Ps
cor nt;- DA
fov 4
A
3}ate
utannt
Neductton
olo
Bat taLe
NS
Ps
a
olo
b
d+
D
a
yeltmirati
olp 0+
NS
prelent Atai are
3
Same
thun
ehtinate
Can
one Atate
o afes eliminatig 9
mare
olp
NS
ps
a
a
d
fd
now, no
ps
£
NS a
olo
olo
olo
olec
%
Vo
ASm chasti
ttgoithmtc Atata Machine:
olo
Aue box
det ion b0
Cord bol
Vo
olo
4
at
Chant
ASM
bi
M00IQa achin
olp deperda on ps
g0
11
A’olp:)
-C-olp-0
ftynchronow
Synchro no
’feu ckA
dutgn
e
eony
-’ hese
but thuy oe oleiqn but
ckta ane
thy
di4t to
not prestn
d
ttmu delay element tu
memory elanintn CFF] a mumoiy element (iate
’ne statun ot mumony
’ fhe otatuy of mameny
alarnent a ate cted ondyvonl change
a
any
tirn
at the aottve edge
CIk
noduetton
t0
Te
a divid1 by
2Tc
u h a o u s
e
CK
3
4
(hee
TA
P no ot.PF
Je=i)
Ve edge
Treg wi
coujt
joromoDtb8.
tb8- i
we have
3
o
l6’0 to )5
nype o4 Counktvt
eippu Aynchonoy
CounteM
<y nehono
zourte
CaunteA
UPountn(ot-24-) Noun aouney
Upldaw
Aynchoung hppl
ynchnenou
Counte
)fF ne
D4
aunitd fn Auch) nhex uU no
that the olp
Fe dtyea the
Cou n
ConnecHon
blo
au cloced imutano
beore COmp|?catid
2) ff ae not clred
Stmult ane Duly &
&
mp
nD04
tor
AtateA
3)sped iu alow au cit
no o4 Atatu
$) speud
high a cit
given at same 1me
propog attd though
Atagea
3-bit tsynchmonouy Up countes:
Ja
MB
Couitts olp
poge betore
alc
Coun
0tay
To
-l6
sthe
te
bit 4-
up
Courtu annchnonouA
1
Fe
6h
6
count
manimum
0
414)
33)
fE
3
2
tnttially|
Decimal
eo
CK
Aynehvonou4 oon
3- b7t
changing.ol
MSB
thultgingolp
L
ke
(MB
LSB
cwnouy
up coutr
ntttaty
nitta4
a
6T5
o
ghd
t
foy
111
C. fF
have
deifgre d the up
pracrte
but
up o
Cono
thee
cet
e
Jeparety
modu
doon node
M
Olpot PfF
both
doon couney
Counterg
conOl lp (M ts
modu
eithes
fipplu CouN
UP /Douon
4-t
3-bt
ed
ne combined
to
elet
PE.
each pait 0t
lotw
tonnur
to
LJt
M6
61
M -0-- upwunti
M=1--doon Dut
t0 c lol
1
Y
MQ+M
DD
o
JA
M
docontouut
Teet
to
hae
0e
mean
MON6
cluan
=0 PST
Ter
CLA
KA
ire
Je
Jo
et eA PST
JA
oPsT
Aogic
-1
we
courlu
OI-3
MON
-2 O10
5Count-
000-0
MO-6
Atatu
6
mad
Countu
number
a
39
bih
Counta hao8
modulu4
ae
caled
oM0-4
toup
Counting
MOQ
n’no
bf
Counu
ix
ounu
ldouon
callud
the Modubus
ot
4 Countt
stau diaqnam o4 a Cauntu 3
a-bit up ounu
ytor
n-bit
4taty
down
douon
Oecad BCO
Rippu Courtu;
Cmp point
clocky UC
fs
Q
:
higed
edge
is Clock> C
ifYe edge iggeY ;
-ve
edge trtgger; ia clocr-De
ve
t) Coucodi ot
MOD-M
Countu
o0-n
no ot Atan I0
MOD-MN
0000
Caulade
ity
t oD0-46
,
Atop
t
Can uAe
MO-l6
Sunchonoua Counlu
2
2
) Crettaton tal
k,
9) tat disqran ert eT
Hatn simplted egns ufng k'map
)Qrau the Jogtc dta qim
"8-bit Âynchdnau op Counlu i
X I
CUK.
fi) Atau dtaqam
tati
3-bft Aynchrououa up ounli
mon Dunt-3
) noo
So
Ff =3, t-FF
) ET oY T3)3"01
Ho
8 &taty MOn aunt
s
ecttanoo labu
Ckt Et
0X
--
X0
X
100
1,01
.|0
M=
b
00
M=1
M=0
t
un
0’p
M=
Synehronou
M
Counii
Ns
down
PS
Up bit
cAk.
Foy Te
M
Tee Mo
M
C
pencil
see
thon
|n
ng Csustu
8 gcountev ts qtyprral applrcation
tea
’fhe Ony change a the o+olpAhtftets
NO-Ot ff ud
ot lan ff
Do
CLR
OR T
2 3
CLK
00 o
Courte)
frig
natl
tuotteh
d
(otste
Johnkon A Counte s
Stat ea =
x no o} FF
,
CLL
X
Tntoduction to neqtkA3
SFFs ' bft memory ce)
’
we
to
have
we
o fnNTeau the Stovage capathy, tnoon o Pe6STee
hbup of Ffbs qoup 04 ff
fF £ Capabl
no0
"'n
of
t.
consts
t,
he n-bit neqislea
bound to
Shoing "h-bit" wold
the
TUsec
lod
Aynehranu: Clocie
tynouu! doad
Data bmatn
load 4
Lo al
classittcati on t
Lan be ertuaal
serfat
in
Pasalel-0ut UbitA at
time
sevial ouut
poraly.fn
(0e
eq'sleA 3
bit a
a ttn.
Sental torr)- ienparal
Code
torn- pecral odu
lauitteudton
|() Dependtnq on tp $op
a) Snid t neg
b) Atorage neg
pplicato n
Bldewna
unvedcl
MJB
fesial -in= 1| I |
STSO-Seatal Plp- seaial olp
Sesial-in
o
4
Se vial
C1
nitaly
0.
Otn
1
Jorlong ditanu
SH0
bett
more
ene onductos
ît
PIpo
for
need
pulae
STPoT4eloclpey
data
Borethe
Do
Clock
pwee to
DgJ
D=lnt
-0
0-0
ff
4
puld
e
(x
paralOut wil TM
th
at
Modi
B
odmode
Te,
o|61
Shitt=l
Yp. Ro.
ff3
ff-2
Jenau
Bidiaectional Abilt NeqisteT
mochcoND
(M=0
hitt leu)
Du
D
LL
Sev
but
Uhivessal hft
neqista
t v 4salSR
(SISO+pISO+
Bidisectonal + e oading
(atotngobia) thLttlt
PIpO tfrpo)
seyfal
Ao
Lo
4x1MUX
A2
4X)
mUX
DfAoiedVaFlwae
321o
A
MUX
foilp
Sefa
CAT
afetpulss4C)R
IMode contTo Reg op
cIK
No change
ahift-1ght
elected o
atably
khitt-lef
t
has
& tlp
thuy ane
on
both
P | the
ane
lpA an
FF omplements
the layt
the
a
be harso
havtng
K#Y
oheh
tsel4 otherwise t
below.
Some
re
koth tlpa
ff
going
d1ferert
State vohich of the
deeibed
to et etse
f
thuy ne o1the
to etain
i qoing
tolooing erpie sions in
n
chariacte nts tc epjel sion fo1 the
FF)
ol:
CIl->
6 0 Compliment
char a b
X
6t
for t:
yen
Ofp
NS)
îlp= x2 oCPS)
X
s
1
1|0
D4A1 de tetu
PLA- roramabu
kogtc -nay (PLQ)
Lt s a type o4 hed anchitectune
proiammable
OR
AN D gaeA
blloued
witb
ogic deve D
b
proqya nabl
Qatea
Steps
Yr=B +Ac T Mioimal 1opm
Akpa;
No -04 plp ButttS, = Nob va
:.Noot lp Buteà = 3
*No-ot proqrammt
ANO 6hate
No.O4 min tin
Cnot epeai)
Min to
C
ase (3)
ABAc, BC
Preqrammablu fray Zoqtc (ea):
ct !t mottty commonts 24ed
preammabu
type od PLO
frud OR gma
NÐ amoy
x(ABc) = }m(&3,5/) - AetfC
By solving
y(nB)Em lo, ,5)
l4bc) =Em (0,2/3,5) Aotñc+
ABC
K-Maps
CaBc)
btteyama
No-o onfaßu z3 =no:of lp buteA
no.
No-ot
ND qaty
unfoe mink1y
=3
BO
we have to
3 AND fon
ta!
each Cale
total = q AND