Download pdf - Sol_HA12

8/12/2019 Sol_HA12

http://slidepdf.com/reader/full/solha12 1/17

Department of Electrical Engineering, IIT Kanpur ESc 201: Introduction to Electronics

4th November, 2013

Home Assignment – 12

1. In a certain chemical process control application, a particular relay must operate for

certain input conditions. There are three input variables A, B and C, where A is the MSBand C is the LSB. The requirements are as follows:

Relay must be ON for 010, 011 and 100. Relay must be OFF for 000, 001 and 110. The

remaining input condition will never occur.

(a) Obtain a minimum expression for the above relay function using K-map.(b) Realize the above expression using NAND gates only.

2. A 4-input NAND gate is defined by the function z y xw z y xw f ...),,,( . Design a 4-input

NAND gate using 2-input NAND gates only.

3. A combinational circuit has 3 outputs F 1, F 2 and F 3 as follows:

y x z y x F

y x z y x F

z x z y x F

...3

...2

...1

Design the circuit with decoder and external gates.

4. BCD (binary coded decimal) is a representation of decimal digits using four bits. The

decimal digit can have values within 0 to 9. The four bit binary number represents a

decimal number N , where 0

0

1

1

2

2

3

3 2222 bbbb N , and 0123 bbbb is binary number

having four bits. We want to use a seven-segment display as shown below to display the

decimal number corresponding to 4-bit BCD input. Each segment of display is an LEDwhich glows when logic is 1. Determine the Boolean expression representing logic for

each element of display. Minimize the expression using K-map.

a

e

c

f

g

b

d

5. The four bit binary number represents a decimal number A, where

0

0

1

1

2

2

3

3 2222 aaaa A , and 0123 aaaa is binary number having four bits. Design a

circuit using 16 to 1 MUX to check whether A is prime number or not. Recall that a

number A is prime number if it is a natural number greater than 1 that has no other

divisors except 1 and the number itself.

8/12/2019 Sol_HA12


Department of Electrical Engineering, IIT Kanpur ESc 201: Introduction to Electronics

6. Construct an 8-to-1 MUX using minimum number of 4-to-1 and 2-to-1 MUXs as

building blocks.

7. Design the circuit using an 8 x 1 Multiplexer to implement the logic function

)14,13,11,10,9,8,6,5,2(),,,( m DC B A f .

8. Implement half-adder using 2-input NOR gates only.

9. Implement full adder using two 4 x 1 Multiplexers.

8/12/2019 Sol_HA12


SoLs, P-r

'B t5 a.rrrrrrntn3

a.rh err -rhe *-\

b-or the $iven

bittt

u,b.',..-t

iA ofF i ,oe

e onditton6.

+he 1% iA ,I

3of the bol\ar^rfrq

1

arDd bir'ot

Lrtfth t,able

.

i6,) tbe nniiilunr'+rrd axVre@n

A

AB

I

AE

= A.3 +fra

( c.99 or ll \o

o

I

o o Cx

>( 3 0

8/12/2019 Sol_HA12


b)l-z

Aod:u-) adrn bE y€6{,rZ.no)Thc",r et ptel*\ion , *tn| NAdS

AA bDTtoCDA.

Y =T,B:-=:--

- , A'B''r'f- *,8 *,8

= E B -''*,E-+htA im ptiaar 6€ vreel, to ,gcag76c:e

t\-lL ) Ar B

i; ) -r- - / F.B , ft,d1 ," ,

'.,\ttt ) and tFf..,

Nor,rr tbe yealt*atioO [,1,i

ffi, tt

''r i.

i

I,i.. ,.

:

8/12/2019 Sol_HA12


5o* O

4 c *rrr B r7,) = h,-t,fl. ?

t lvert,

ao

NAND

r^re 'ha.ue tE' r ,="m.

Ta$errerate,

?-3

rOotin1 7 -iny-b

lJaJ. A)

dor'gn go*..

ilato ond

r4 - i.rpuf, N*ND

NoT 3&6,

4 C *rzr gr zr) * r.' -r ,.,, ., ,,

=.1,^).2i.U,2

ii) ao4

b{nol reatfz,atian

At.au3

u

l^).)r

The

'tl\)

)t

ar.'[, ,ar

6+1+i+T

5,r = Sz.,

8/12/2019 Sol_HA12


-t = T,T,7, + .}.&

fL = r,E.A, + tr.X

,Fa : f,5.:l*u'l

/vap.caenk eaclr Srunttion

Dc. g,z +

E.5.ib +

)c, U,V +

B-r conanica[ A,r""', 4f

5r.:. z, {- &.x.7 =fu(tzrDec.j,C1u+I)

*..U. z * tt.3,fr .Y^ (rlre)

+ \ = frn(o,s,t)

i>=Z.m(rr3ry)

FB = Evn ( t, 0,r)

Sor-^, @6iv trr

It - tlrS

Prodtric$ borrn

vll

=

€b

=

€'3=

=

o

o

a

0

I

I

I

t

o

o

I

I

a

0

I

0

I

I

I

I

a0

o

o

I

o

0

o

aI

I

8/12/2019 Sol_HA12


: :- +1i

NouJ the'' b."to0 de,jigrt be'cawrry',P-5

|, ..

1

FL

.B

Y

v

t

i.--t

.1

l

..1

8/12/2019 Sol_HA12


P*,

b

Sow, @

olI4

e'llc-

s

a<t

+b3 b2 ba bo a t> c- L

) 1- i_o o o o l-r

IJ L\t\jn i-i(L o 6 1- o

o o o. 1r II

3. f-i ooil-

Lo o t O ir1l- olL I

{il 1. T Lo o tr _l

-=lI -.

t-r--

IrL:

I

11t-_+*,"..,

i,l1-

o I,.

*;-T^i^ la.o

o

rL

o o a \J J.

7_ L:T

**,----

ti--**"

loi

r'---irI

{-iI*-- --1-"

1i1,

o t t- o t_t-t

413-t(J=l

I_J t---

o ril"1-'--.-

irit

o

4o t 1- L I

{*

i,i11- o o " iF-,

_"--i---

ri:i.L

-'.---+-*

1-11']I

o t- l-L. o o

xrloTl-o"I

1-lc) xi* )\

)(

x.

K

&

x

A F* x)- l,ll

Ilx x.

lxI

i

K )\ X- f- )(1-; L o1o

x x- x x1_ t oiJ-

I ^ I ^l :-;-"--.*--1.*]

xix x- \11- 1- o

'x:'\i KL i1- L L ,x ^.

\i '\

i

X = olonr+' C-,o.na

8/12/2019 Sol_HA12


E3

o = f* L o, 4,5,6,8,9) + d ( &q t/t' :l-z' 13' 14'1"s;r

b - fne, [ 6, z,Z, 5, G,7,8,9) + ol (Io,[{, 12, 13'1+' 1's)

n" ( o, L,2,A 14,1,8,9) + d ( -1o, lt, 12, t3' 14, ls)

fm ( 2, 3, $, S,6,8,3, + d ( 1o, j-trtz, l"g, a+. As)

f t* ( o,2,6,g) + ot( o,:ti.,3-2, j.3, t+,Ls)

frn ( o.t,3,4, S,6, 7,8,9) +d ( 1.o, L ,Lz., L?.-f+, ls)

f rc,( o,2,a1=i

6,8, g) + c (10, 11, L?t L , 4, 1s)

L=

d=.

{=

3=

b1-boa, b3 b:

o

o

tL

)

b:-

b, bo

oo o:1_g br

oO

o1_

1- 1_

{o

L-

o

rt

-t

lo

oo ol i-t Io

Iq o o o

e-T\ o

r----

u i) a +- --LA\-t

-+-

t_ t I

o = bs*E1 f,.+u=E1 +-

8/12/2019 Sol_HA12


, ,t

b = bs* bt+ brbo+ brbo

bs b,

o

b1uC:-

bx b1 -r* btbi 1-[r

ba bz

&e

L=

9c

ol: -

d= be# E= bc

oooa

-t

[o

u-L* bf.

b5

. oo'o3-

lLt too

61

11-

to

R L A _v1l o L b

4 "l "ld

Wdh/

b6

o o O4t 1",1* lo

o

1*

-1.

o o

LgFT\ o L

k *il .l d

L

8/12/2019 Sol_HA12


P-q

e:-

Q-: [>"b5* br. b.

{''-

$:b=+u1 +bo

Qr-o'

b3,b-

G6

ot

t'

fr

bg br-

o

o

bsb- tt*

oo

o1-

L4,

Lo

btbo

\ oo o{- Lt -to

1_

ttlt

lo

I o o oo o o 1_

A 4 4 4

3 o1 a

be h^\- oo of tt_ to

)6

)[

Ir

to

{r q \o

{t TL

[4 d a A}

u { jal

oo ol1* 1-1- Lo

$ o u E

o

no t

Il

tr GJ d. a

L

t :b, bt bo* bcE + bs* f,r- ba+T-E:

8/12/2019 Sol_HA12


,: A

X afrre,

rS

{f -""

'6'an' f\a''se'A- bi+ "rrrr'mrbe4' s o rr

o- 15. T6c- P'rimc- Yenot'' {t's

ir- a' A' 5'7' f1':'tr3 t

-(alr{€., Ot\r- 2t -' -'

) so

o,=

L'- \2'3'5'?'tt-'t3)

S o F.= a, Gl.lan

e.[a e. l"- = o;

rit

''i

oA,

Lk"oIo

Loo

oto

,-66

Ao,S p.siro<',

=)

z3

t

I7&

Its1r'

Lzd.3

t+

8/12/2019 Sol_HA12


P-tr

fir.rlu.rnin3

rYe tbe

bprtot lin8

and I r s1 a^d 3o

uri, .\ata +he-

we carr ivnplcnnent

,l(tror.rrn 'beloul

Sou,.@

16 r a, .r - - - El o,^L +he tnorlfi

;e-teatiaa ["oeA th en cn g : t 11 Ux

tvat[ +^tble.

SL 5l 5o v

0

o

o

o

I

I

I

I

0

0

{

I

oo

I

I

0

I

0

t-

o,

o

I

Lo

rl L

x3

Iiff-

7g

r1

8: t hux uai^3 t,no 'q:l HoX and crle 2-il PtuX

ao

a,

z

a3

5o1

=q:t5

r6

11

5l

o0

Q:l0l

l'\uxllo

1l

o 2rl1 I4uX

oo q:rol N\uxz

lo

ll

5o

8/12/2019 Sol_HA12


i l l - :

n:li

P-tyor-r.,,@

LqI- A B'trD

*z-

A 13 c D tr

O F=A

O F=A

L

o1-

oo

o

o

o

o

oa

oo

oo

1,

I6

_1

o

o

1-

l-

o

b

L F=1-

L,.-.---*:_* F=A

1-

o1_

oo

1-

1^

:l

1.

oi a-J.

,,l' i r'o

oo

o

6 F=oo

oi Lt-i L

oiIi;ol

Ir

:L

1-F= {-

T

oi rLi L _

t(f-

o

L

Io

o

F =1-

F':o1-

L

L

L

1-

1-

1-

i<' +- Bit rur')tuerr'' so +c^-*"' to'r:to- \s'

^o,,n

o

?

I

IL

l03t\

4

t>rJ

\3

*t"6

l,t

?

It

,IO

\l:"

g'. rr3

FAU t\Iq

IsIc

L1

8/12/2019 Sol_HA12


+ 5=

irnple rnonf

A.B +- .*,7

tthi6 gAing

A. B +- c.e

P-rsor-x. @-Ihe trutr.r tab\e box hartr - oddrl i6,

frrF uX

FO*pt;&

& Sutnr5)

car.ft{

cc)

0

o

I

I

o

I

o

I

0

l,I

o

o

o

o

I

To

oool c = A,B

NoR g*%,

=(m=ffiC.

C=

tt,ia ?nrptirs

to

u)e hdxe to g cnerofe.,l\.) F and U'

.'\ :--:tr,l A+B and

3tt atro ye' U a,,ol

r.i%

-= fB +6-8

A +-6

^+B\c

# *

5=Fr6+ArB

= T.B+ A'E-

c=tr+E

=A.B

8/12/2019 Sol_HA12


Soru, @ rut'utt o,aden ha,: the bottowtnS t.rc,tth table

t"'rpr,rr OLrt f'ul:

7t KI L rrl Surn

cs)6a-{r -ottE

C Co*t)

o

o

o

o

I

I

I

I

o

o

I

I

0

o

I

I

o

I I

o

I

0

I

o

I

o

I

I

0

I

0o

I

,o

o

I

o

I

I

l,t)e Ube turo Lt r I

au-rn c 5) a.,d othen

A tbo let'A uae

ab the irr pat line

nlUX 6 ,act-t i hd oane i-. p) e m cnf the-

irn pt4mentA tbe cffia.|-orrt ( Co-F )

"d ) 4 in aA 6e,l g q 1 io^n 1 trrcA o-,ol l'

t.o the "rnutttplexeY.

SalLtCalc." * C

-$= ?t

Cor,tf * )l

5=iCoul = \

5=:t

Cout = I

8/12/2019 Sol_HA12


:rri:l:r':::: l:r::

,.,.1I-.:,.

,rord tt" aur-m - fiux t'dk [iKe)' ElF,

zdt

2

a?r

x

'x-

T

-