The Sezuana shit Rayng us a type of

unit

8. The Base Crates and Gombinated

irwts.
Lae
O,-9A BCDEF
(Baie 2) 0,1
Birany
-’. Deimal (Baue io)
Octal (Base 8) 0-7

Aeza decina (BauR l6)

Ib) D-5

Biray to ctima!
(347 )a to (?
7x8
4x8' 32
2 2
142

-1 x5: (231)10

0O2

t60
:68

934) to - 7
 (1625) to( 2.)
Deoinal to Biny ) (auy Nurnben )
2 ]1 ,3
()t to(9>a1 (231)1o b (2), 25-1

231 )
0.25 0.5
23, - 1
25
22 l3-47 Conmplement
Complement
Binany to octal Binany to Heza deind 1101011

fonyorcou (0o1D100 )
(U32 1), p) 16
Ddal to Headeimal io binany Conploment Subs trac t
(132); to (1e (6D4) t(). (10101b1)e - (100 |D|01)
(00.I o1 otbi1) 1's |00l0)ol:
0clal to hea olecimal:
(onoliolloo|) I

Henato ocla
to( ?)b

(E1)16 (altl
(0o10 10) {lo101bl
to deeinal: 2
O01010 lo

x2:0.5

,2
(-ol000060)
Ans: In:625
 ( CDEF)6 to (?, (187), b (2),
ol0 (I100101m01) 7x8°: 7
g2: 64
(CDEE b to(?),
(a16) to (2),
(ot It0)a
(146157)g
1 Codes:

7 8421 code
BCD (o a) 9424 Code

* roy ode
0. 1
Boote an Theorems:
Tdentity theonerm
13 Cormpleentany theunem A1ã -1 , A.A 0

COmudaive AtB:B+A ,A.B= B.A

14|
(AB).
Distributive lau AC B+c)- A8+AC, A +8C

Tdempotent
theonem

Inveluton theor em

AbSorbton lau A4 AB :A A (A18 ) A

A(G+ B): A8
Assoaive (auo Not NOR

A+ (8+c): (94B)+ A(BC) (AB) c

A A

B B+C A+(8+c) Ar B(A1B) tc

1
NAND

Y: 9.B
Y: Ae

Lenorgan's theovem:

A-B A. B

Ex - NOR
Logie Gates :
OR A

AND TL08
B
Y: A18

B
A y: AB1
5V
wivesal Ghates: NOT uung wOR.
NAND
NOR

NoT Ciate ung NAND (rake

OR NoA

OR Gale uing NAND iate : NoT NOR OR NOR

A+B

AND ing NoR

A.8 A-B = AB

AND Gtate wirg ate:

Y: A.B
NQND wng NOR
uing
NoR Gat NAND Grule A

-
B
 be
13
bc a m7
(6
oobc
de de de de
be de de de Vebe
de Vaiablede abc
b a im
M3 abc M3:
t4 5
b+c a Mi àbc Mi
2
bc a mp
map Vaaiable
K 4 Vaiables
feins max munterms
maule Called
6
fach
2 tc) (atb (a+5+) (a+btc)
a 0
bc em: May
map Vauable
K 3 maVaiable:
p c 2
mnden
calle Proclucls
w
Map auah Kan 8ame which unlem unotuicua Eah
ab be +a bc abct
ab
abli) () ab mintgurn.
(C+) ab :
(âth|
1) +64c) tb+c)
( (a ab abe abct
ababct 2) ahC ab )
enpruon: lean
blauing
Bo
the tRodue (Pos) Gum of
procdud SoP) produck( ofSum
 )
ab
Map: k-cung enprewon 1he Reclue
ab
cod cd 00 ab
cd
tdbd't-
be tb ac *)
qb
14 Qb
a
5 4 ab
bta
2
cd
Pair b
(o,l,6,7,99,
1312, 1), )f(o,b.c,d)=
Em Dar
Octet
2
Quod
Pair
4,3,0,*3 znl6, fab.c): Groupmg
) Map - k
 Sm (o,1,3,7,9,1o, l315) :
RS
(o,1,3, 7, 9,lo,13,15)
RS RS RS RS RS Pa R1S RiS

00 2 P+a 00 0)
2
6 :) RPa t PRS tPRS
t SP?SP
15
|2
1 10
Plo 8 Rsp + RS P

+4R)( P1R1s) (PAQ+s) (P+R1S)

( wnyz) : Sm ( o,2, 6,8 ,10, ,19,14)
W 92 J2

fC PaRS) : <mo,, 3,7,9,10,13,15 )

Pa Rts RIS RIS RS
4 6
00
P+Q RS 00 (O
12
wN 0

0
fa bc) Sm (ol,3,4, 6,1) (3
be b Pta 10

:) (P+Q4R) CP+R15) (P+@ +s) (P +RS)

wt
o x 19)(G+z )(oiz)
(n ),
 ab
fcabrt : Dmeo,2, 4461)
Mini mie the neun
abt abo + be +b
uing - mag
12
t

Sandan
t kblc+ ).
abCc+Á) + abc+ abc Quine dusteuy melnod Cfabalaion method),
ab + abdt abc + ad ?
fco,b.c, d): (o, 2)3, b,1,8, lo,12, 13)
Stepl
+ad( t .
ab (c+©)(d+d) t abd (C+) +abc(dtd) b cd SBep-g:
Cb t6) mo mo
abcd
abed + abed + abd
mg mg
Sowe k Map
m6
b

1
Mi2

0
Step 8:
ab \cd

Mo, m2
c + hdt ab
mo, m
áb

ab
m2 m6
Mio

Sm (o, 2, 4o6, 1,I, 13,15,

de 1,21,95,97,29,31
bc
de de ded o c Je de de de
be l6
bc
be
Mie, mi3 20 24
bc
12 be
23
bi

be + bea t ade
Mo,m8 ,m2 | Mo
P T- 03
me,m3,M6 mi
PT - 4

Prime 2
Impiconls
m3, mng

tri m3 , mb,m1
Sm(o,5, 6, 8,9,19,1l,16, 20,24,26, 26,27, 29,31) Eml1,4,8,10, ,20,22, 24, 25,26 ) + c (o, 19, l6, I )
de a L de
a bc

de dede de ded5 dë de de de
\de de de de be de de de ode, bc
3

bc 1
bc 5
6 21 23
be X
bc 93 22 I5 bc 29 29 31

be
bc 15 bc 20 24 3o bo
be
26

) b +Tde tabe tabele t a bce

 m(, 3.6,10, I,12, 14,1 17,19, 224, 29, 20) nit. 4
de de
be be Combinaional Logic cYcui ts:
de de de de de dede de,
be 1 2
bc Problen dor mulaton and decin of (ombinatione
bc 6
be
20 22 aYuits.
bc be
15 I4 2 Deig n proedure:
b 23 25 2 26 26 25
’ Obseve fhe problem debnition
(0

- detenhune the No of i/p Vauabe.

/p Vauable.
Em CI3, 6,t0l, 12,14, 15/n19, 20, 22,
24,29, 3o) -> Assaig n Cettes (or Sumbos to the
the reqw'ed
de
-) DYaw truth toble that debines
a
de
be
de de de de bc de de de de yelaHonship. ate.
bô
Cuing the deleruned
bc
&inpifie boolean anion
16 13
- Deteune the the
23 22
Draw the logie dingYarm .
Combinato nal ÜTut
bc be
T
20 29
wing tao losnave loye
be
bc ba
24 25 21 26 gales. NO . oi
haing
output.
ard
abd tobce deperco upon e preen t State
bee t cde 4abce outpuw
inpui .
gt doesn't Contains any menoney lensrt.
ode tonventes:
83 Be B. Bo

-o
1

1
 to

10

18 7

12 2

B, Bo
Be. ). B.
82
1a 1 B Bo

83
Ba
Binay to BC D: Binany panallel addert

8g 82 Bo D4 Dg De D, Do

Ie le. e, lEo
2)

10
3)

Bo

(ou)

Caty Cok a head adden:

(ang projagate

Cuny
 8CO adden:

So

Da

4
So

6
3

1
 ()

2 bil magitude Ompaulor :

Bo

1
bi tompoulor:
13

()
 BoB,
9,8 BBo 8,8 Br8o
A,Ao A8
dor
AZB
2

6
5/

19 15

Decoden:
8,Bo B,B6 8,6o 8,B
dor A>8 n Vo ine, ünes

6
2 :4 Deoden
) AiB1 +AoBBot
AAo
A,AoBo 3:8 Deoclen

8.Bo

8160 8,Bo B, Bo BBo

0
3:8 Deode

Aa A Ao

o0

Y2