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O6MAT41USN

Fourth Semester B.E. Degree Examination, June/July 2Ol4Engineering Mathematics - IV

-,: Time: 3 hrs. Max. Marksil,00

% Note: ir";:;;ir,'{::l#ffi:*:r:rfrr". ..,*},:= "

.g l'T* ;=.=,'t':1 \ -,.-EE ,.=,=i PART-A . -"\'*j-+ "t' ,,,, ,.,. * uft:= +oC,,; r a. lmplffifaylor's series method to find an approximate solution co to fourth decimal

{ phce, dyldx =2y+

3e*, y(0):0 atx:0.1and x:0.2. (07 Marks)()rE\JI dw Ix)

gI b. Using modifled Euler's method, solve * = ,or,r[ll *itt' y(20) : 5 at x :20'2 and 20'4=- dx -'"l.V )* i by taking h:0.2. |.* (07 Marks)aaE t't

-"1,.^^, -( rd* dy .)

ry* c. Using Adams - Bashfortbgnethod, find y when N = 0.8 given *=x-y', y(0):0,.E& --'--o rq dxGS olc^E r y(0.2) :0.02, y(0.4) : 0.0795,,, d y(0.6) : @ffi62. (06 Marks)o q ;:.=oEH!"::

!Lo3P A 2 a. Define analytic function. Derive Cape'h@iemann equations in polar form. (07 Marks)

.i9

Z E b. Findananalyticfunction(r):.r*S#,if'u,,,-v.-e*(cosy-siny) (07Marks)or-b6i S c. Discuss the transformation w +z *! @+ o;.:'

'':; (06 Marks)

&E f3,,'" z 'i.$'G6t!:EE € 3 a. State and prove cau, integral formula. 'l:'

;:,:r ::: (07 Marks)

.""'Ee9= ='-':['

*62-1 . _ r - _.-,-L)_ - _-b. Expand (z),:{3-7-7 in a Laurent's series in'tho*region(i) 2 <lzl<3,

8"; \u.,J\l3;'al.'zl-J'

f.: e 323+2tg c. Usiffi"Qauchy'sresiduetheoremevaluate, {, ,.,, ^,wherec:|a}.:'=4- (06Marks)E.Eq\.,etheoremevaluate,rffi,,wherec:|z|:4.^a E q-\*! o Pn"b

>t -ug" ; 4 d.i Obtain the series solution of*E d2y ,FE - i+x'v:0Fc dx'o-5: !

o { b. Show that y: x' Jn(x) is a solution of the differential equation xy" + (l - 2

-:61;E c. Express (x): xo + 3x3 -13 + 5x-2 in terms of Legendre's polynomials.

(o

oo.

I of2

5a.

b.

],,,';"""'

Find the coefficient of correlation and the lines of regression for the datalon and the llnes oI regresslonx I 2 J 4 5 6 7

v 9 8 10 T2 11 l3 t4

PART _ B

Derive normal equations for fitting a straight line y: a r bxand hence explain the method of fitting the curve y: a ebx .

O6MAT41

by the method of least squares(07 Marks)

, (07 Marks)

(07 Marks)

(07 Marks)

with a mean of 3

(ii) takes between(06 Marks)

., lt.",i

c. The length of a telephone co'a:,,. ... :

ion hps$ exponential distributionffi (J)'dnds in less than 3 minutes,

7a.

b.

Explain the following terms: 'i*r',j'Dxplam [ne ro[owlng rerrns: ',,*i-".,,o

(r) Null hypothesis (ii) .F*,yel of significbflbe. . (iii) Tlpe I and II effors. (07 Marks)::::':'

'i!,i,... ,.. ",

,"11

rl6.6f 100 students was 5l with a S.D. of

(Use 5% level of sigd,ti

a random sample from@opulation with average marks 50?(Use 5% level ot srqry#cance). (07 Marks)

c. A certain stimup.fl,Edministered to each of the 12 patients f$dlted in the following change inblood nre.sslg{u},2,8, -1,3,0,6, -2,.1: l, 0,^a.San it be cdffi"$ed that the stimulus will

/nz tr^--t--\increase ffi#laoa pressure? (t6.s5 for 11 d.f :2.201) ". , n (06 Marks)

,i^;,,,1-,. "'.. i'..,,,,, ...,.

8 a. A faidtoin is tossed thrice. The random variables x and y are defined as"follows:x : 0 or 1 according as head or tail occurs on the first toss. y : Number of heods. Determine

,..;$l}'the distribution of x and y (ii) the joint distribution of x and y (iii) the expectations of

.,-= r"-.h, y and xy (iv) Covariance and correlation of x and y. (07 Marks)

=,,,t-= b. Define stochastic matrix. Find the unique fixed probability vector for the matrix..)" (o 1 o') ..*€ al+..;::.

.,.,-.="'u ltte U2 U3l (oTMarks)11.._rI o 2t3 t/3)

c. A software engineer goes to his office everyday by motorbike or by car. He never goes bybike on two consecutive days, but if he goes by car on a day then he is equally likely to go

by car or by bike the next day. Find the t.p.m. of the Markov chain. If car is used on the firstday of the week, find the probability that after four days (i) bike is used (ii) cars is used.

+ {< :r :r * (06 Marks)

2 of2

I nc lon:

x 0 I 2 J 4 5 6

P(X) 0 k 2k 2k 3k k' 2k". ,,{k(+ k

minutes. Find the probability thate

USN MATDIP4Ol

Advanced Mathematics - ll :,::.

,,';*;'Max. Marks:.l00

Fourth Semester B.E. Degree Examination, June / July 2014

'; igne: 3 hrs.' ",," Note: Answer any FIWfull questions.

rlli'.l.-,'ooo!a(d

(€

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EP

s i,'b0".g o9

.=Ndtf,

o ::J

oC.c!)o>EstssYdoo)do60tr(d cd

26o4

!d

-brE .!J

=d48"=d

9EiiooD lEaE9Ole=>' qioooco0()=!t E)

=iD():u<!,

.',1liq.

- 6.1

()oz(!

oo.

1 a...' fine direction cosine and direction ratio of a line. Hence show that 12 + mi4 n2= l.

'^ 'l-l;,,,tir1

rr. show that angle between any two diasonals is cos-r[f) ru

t *' ffi:::]b. For lffirbe show that angle between anytwo diag

F/=- "

c. Define plaff',Derive equation ofplane in general form. . (07 Marks)'tt"-',ttrt

=--. ,; + 1'^ :'' '

2 a. Find equation of fidhe passing through A(-1, 1, 1), B€,1+U 1) and perpendicular to plane

x+2y+22-5:0 ',',,,,r5. .i, (06Marks)

b. Show that the lire * =

4 ;y :2- =':=3 is parallei to plane 2x + 2y - z: 6. Find distance2 3 l0::

* 5: 4=-'t3*,*6 *;t = +=':5 are coplanar. Findpoint of44-5*"k*,,7 1s

intersection. "{ -, (07 Marks)

t-;*'',,,'* ,,,,r

* .,,{'"t',.

3 a. Find sine and cosine of agelj between the vectoisd$ + 3j + k , 2i- j+ 2k. (06 Marks)b. Show that points (4, 5, -{); (0, -1, -1), (3, 9,4), G4,4,"4) are coplanar using vector method.

.,.,'',... .:'' '\j ' (07 Marks)f- -) -) + + -l l-+ ++l

c. Prove that [a+

b, b+ c, c+ a] = 2[a,b, c]. (07 Marks)l_"r

'. .: a'

d:'\,J*4 a. a paftf't moves along the curve x: t3+1, y=t2, z:2t + 5. Find

WI"uUity and acceleration at t : 1 in the direction i + j+ 3k

U;*ihO directional derivative of x2 + y' + 4xyz at (1, -2,2) in the directionllq \4ii

\'l'q-ir +

,ut *rdfl) = -a .c. Show,1---_ _-__(r ) ,,

5 a. For any scalar function Q show that curl(grad$) = 9.+

" /-\ /-\b. If F=grad$,i:x'+t?+22+xyz,find V'l n land Vxlf'l at(1, 1, 1).J) (/ \i

c. Find a, b, c so that F=(x*y+az)i+(x+cy+22)j+(x+2y-z)k is irrotational. Find

scalar function. (07 Marks)

I of2

rr

6 a. Find Laplace Transform if t' and hence find

b. Find L[e" cos3t + e-' sin 2t + tsin t] .

'[,')

MATDIP4Ol

(06 Marks)

(07 Marks)

.Ii:,i:,... 1 ,

(07Mafts)' ]::.

. :+..

-v}_.,q. ,(06 Marks)

.'iq#' (07 Marks)

(07 Marks)

(10 Marks)

0<t<ll<t<2.

t>2

*4. ': 1

LD vD rrro "Yffip- -fl&qb. Solve by Laplace transforma,fliry'#. ?#P 16, = 4e-" ,given y(0) = 0, y'(0) = -1.'ffih'h, &/

\,l|'rd

d B . -[e'(cos3t-cost)-l'%,ru, t-utl '-l7"r'[.g.5ind L[sint sin2t sin3t].

where ,,rr=

{j"'{}*

c. FindL-r{,Jffi}I US*Q IL fl;frJ*#'*'

2 of2

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f E HERE:dc)

10ES42

Fourth Semester B.E. Degree Examination, June/July 2Ol4Microcontrollers

,,..' Time:3 hrs. Max. Marks:100N ot e: A n swe r {y., {: ::#::y: : :::: ;, #i,

. ,:,.,;;rl. least TWO questions from each part.

, ,,.t..E fl'e* PART - A ; ;' ;

E 1 a.*ffi.at is microcontroller? List out the difference between CISC and RISC. :,3t (06 Marks)

€ b. El#ain the 8051 block diagram and its features. 'b%, '' (10 Marks)c-I c. griefir.+xDlain about stack and stack pointer operation. - a- . (04 Marks)

.&q€0() 1 d...- t '::.-

g 2 a. Define aadie5lg-:od.. Mention the various types of addreqgffi.$nodes with an example

E g wtth respect to,8051. =,,..!' '" (06 Marks)

H= b. Explain the following instructions with an example:

"* 5 (D DrV AB (i0 SWAP A (iii) RRC A (iv) XCHD A @Rp (08 Marks)

A 3 c. Write an ALP to perfoarn 16-bit x S-bit multiplication. . (06 Marks)g@.= e..l

E a 3 a. List out and explain differeiffisnembler directi$@trsed in an ALP. (06 Marks)E : 3 a. List out and explain differeffi*.qembler directi$@trsed in an ALP.

B g b. Briefly explainabout what ard{dsteps lnveli"btO create a prograrb. Briefly explain about what are 4g1!g?r invelVoto create a program in an ALP. (08 Marks)

c. Calculate the time delay {FFrl\g' -following subroutine program. Assume

cr E *€: ":;.\f - ..- :i-E:r- - r- - o^ --^--

: .g c. Calculate the time delay {fu;tne".:following subroutine program. Assume

EeE .E MOV TMOD, #01

MOV THO, #OFFHE b rvrv v r rrv' ,, ". . rj_,

E ; CPL P1,550;€ I ACALL DELAYE E SJMP HEREh AUl;!E3 ---- . 1,

YE ;-delaYusingtimer0 ;^;rE; DELAY: SETB TRO

: t AGAIN: " Jlr?B TFo, AGAIN ._.! "

), d cLR TFOE E RET (06 Marks)go'a lE 1 "lilr ;h.

HEE f 4 a. ' . xplain about stepper motor interface with diagram and also write a 'C' prtigr;lq_if a motor

il? ,. * takes 90 steps to make one complete revolution and show the calculation. (Botk$ffib"kwise &.E :ar \/E € ..,....\.

-' anticlockwise). "{12 larks)

E g b. Explain DAC interface with diagram and also write a 'C' program to generate sfiHtase

: *-*' waveform. (osMm@*ot--.:c{ n^nr D.. PART _ Bg 5 a. Define intemrpt and mention the difference between intemrpts and polling method.z (06 Marks)g b. Explain about timer/counter control logic diagram dnd also briefly explain various timers

3 mode operation. (08 Marks)5 c. List out the various types of intemrpts and also write the bit pattern of IE SFR withexplanation with respect to 8051.

I of2

(06 Marks)

rFi

10ES42

Briefly explain about DB-9 connector pins function. (06 Marks)

Write a 'C' program to send the messages "Normal speed" and "High speed" to the serial

*,,,, port. Assuming that SW is connected to pin P2.0, monitor its status and set the baud rate.&s

UF

**4S_ SW:1, 56Kbaudrate, AssumeXTAL:ll.0592MHz. .{,&{vlarks;*ffi-*V/rite the steps to receive and transfer data serially. d%. K06 Marks)

#\it;r--

flp*" sk$*f *, e- "-7 a. Lisffuhe features of MSP430 hM

* (06 Marks)' b. Brieflflffilain about MSP430 architecture with diagram.

^*s : "

(08 Marks)

6a.b.

' b. Brieflflffilain about MSP430 architecture with diagram. #=j (08 Marks)

c. Briefly .Sf#*r, about memory space distribution with respect to$ffi430. (06 Marks)' '#rs..,.. - q6 d ""'fl*... , H

= f,hn u &*+'

ffi-a. Internal RAM structr&#f 8051 r*;\

b. Special tunctionregistffip* {=+.:,

c. Bit addressable instructiorfv*p.* , ffi.u qd. Built in timers. -W -- ,".&* (20 Marks)

d,.-.==.= ""*

+a-\-\r

*Hn..,, .=

", e ;"..:. '"+ j,;. j:;..

_#-. &ffi-

!*t'-.- "Ii =i

\sh$

q"i,1-,,,.=

\*d'*t'=

ffi M#

d\e-# .'J4rsd

dd#41

2 of2

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10ES43

Fourth Semester B.E. Degree Examination, June/July 2014Gontrol Systems

Note: Answer any FIWfull questions, selectingatleast TWO questionsfrom euch part.

PART _ AI a. E>r!@i6with examples open loop and closed loop control systems. r,istfr*4efits and demerits

i

of botfth#*" **; (10 Marks)vr uvrsrkks,g

Draw the"

tu1!=

{.-,.."" i=Ik

{.

&

b.

c.

c)()odEo.=qd'oo)(!{)L

E9a;r,3s569Ertoo ll

EOO.=.\(t+69p()gdo

o>Esg9bd

-9cdOo!boc

-o}Esq,Ed-bB5r9=d. 8.tro.6coo-tL.-o=8()ta tEe*trot=>!bovco0o=

=GlLL .()

69:9. h'of-.i c.i

tD

ozdLoa

(10 Marks)

(10 Marks)

I &t),

-j;"

.'ry&,d'-'t

|,;. ii :::

Ir.r'

,!: ...,::

3 a. Draw the transient response characteristics of a control system to a unit step input and definethe following: i) Delay time; ii) Rise time; iii) Peak time; iv) Maximum overshoot;

v) Settling time. (06 Marks)

'l+jFie.Q.2(b)

Derive the expressions for peak time to for a second order systemfor step input. (04 Marks)

The response of a servo michanism ii c(t): 1 * 0.2e'60t - l.2e'10' when subjected to a unit

step input. Obtain an expression for closed loop transfer function. Determine the undamped

q"*;

Qt

1r

natural frequency and damping ratio.I of2

(04 Marks)

10ES43

d. The open loop transfer function of a unity feedback system is given by G(s) = f {S, * ,),

where K and T are positive constant. By what factor should the amplifier, gain'K' be

reduced so that the peak, overshoot of unit step response of the system is reduced from75Yoto 25o/o. (06 Marks)

r,,,,t,,,,*, a a. Explain Routh-Hurwitz criterion in stability of a control system. (0a Mark&\

@= b. The characteristics equation for certain feedback control systems are given @*[.Gt$ei:

*W%' Determine the system is stable or not and find the value of for a stable system *{e ='

'l}, s3 + 3ks2 + (k + 2)s + 4:0. , *b€Marts;o." The open loop T.F. of a unity feedback system is given by

" i#* . k(s + 3) .q._15

Findthe"value of 'K' of which the closed loop system is stable. i..,- (06 Marks)

d. What iifudisaavantages of RH criterion on stability of controlqptim? (04 Marks)*

*l papr-R - "1\*-t**., PART - B gru*q i/

5 a. For a unity t$edback system, the open-loop #ryp$. function is given by. \" ,#,

G(s) = S{f;,,, r;]il*

i) Sketch the root locus fu 0 < K < co. 1#;"

ii) At what value of 'K'tlfffistun becoqbffunstable.

v(s) s'+3s+4 - :".

;;.l..,aThetransferfunctionofacontrolsystemisgivenbyffi=ffiobtairite+#' model.

u\r'' D T !D T rt r 2 tr, *"*J'-,*

''1;."" b. State the properties of state transition matrix and derive them. (10 Markslffi

on the root locus or not using rl'rgpmtn8.*ritSp*conditioS.r* (05 Marks)

*w6 a. Construct the Bode ...,,pots for a unity ,foedback control system having

2000 ;.,,1r{1i'';l!t1

]......" .. .::

from the Bodffi'Sdetermine: ,,,,.- -..=,,

i) Gainqr&#over frequency. "t#':ii) Plmdffioss over frequency. q?-)

s* h'%\-P&

ivfuffiase margin. W *- ffi,*nt on stability. ..+e

= (14 Marks)b.d-'e-*#t the limitations of lead and lag compensations. 1.'=' f06 Marks)

{:""1..'l ^ ''. "'1v(s) s2 +3s+4 * l\

8 a. Explain the procedure for investigating the stability using Nyquist criterion. (08 Marks)b. Using Nyquist stability criterion, investigate the closed loop stability of a negative feedback

control system whose open loop transfer function is given by

G(s)H(s)- K(sI + l),

K, q >0.s' . ior.r.

iii) At this point of instability, ffienni* the frequency of oscillation of the system.(15 Marks)

b.ConsiderthesystemwithG(s)H(;}k#&-findwhethers:-0.75andS:-1+j4is

(12 Marks)

USN t0EC44

(06 Marks)

(08 Marks)

Fourth Semester B.E. Degree Examination, June/July 2Ol4Signals and Systems

Time: 3 hrs' Max' M"n'-'lr.o't L.T^4^. .tl----,.^- ----. ,Ert7D c-.lt --,^-zi^-^ --l--ti,{ ir.r Note: Answer any FIWfull questions, selecting

a"'F"{' -1

" atleast TWO questions fro* each part.{"'id-"s

.J,.*,tr4*, b*- PART - A **I\

'.1 .arks: l@',.',

:,. i "^'

'""'q 'r

r,,, L

P ' Dlrt.rr a. @d*ae PART - A d*6),fr&-.g I a. "dspfigline the even and odd part of the signal x(t) shown in Fig.Q.l(a). * *,:#O - /w-* ' ^-ei.E ,r(\)A s.E d{w r,,E!nA+1.H *:G.*= ,4. t' ,- ,e'#"fr '' ; 1. \./. -.1'E *t4r1. ,/ _t y t it'

d ;" ;;"' ""'9"...-Z-\or

E q ff ,,n' Fig.Q.l(a) .,,.01 i..,

$= b. The signal x,lt;.an&ry{0 are shown in Fig.Q.1(b). Sk€t&,me following signals:gE b. Ihe srgnal x1(t) aruPffiQ are shown m frg.Q.I(b). slrct(

E e i) x1(t) + x2(t) .."r'*lt ii) xr(t). xz(t) !:. ';

A+ : ;^. xB.'H o iv) xz(2t) +"d #\ , ; "g d -).,' 's,a' \" $

E ; v) x2(t)-x1(t) \ ,,\ * "

Ht /\\."r1a;i ,/ t \>h J-J=$t---'2 o /$Eiiir *"."-t

o t ,rr.o.l(b),*.*

X E c. Check whether eaqtrM the following signals is peridflic-.g not. If periodic determine its€ € fundamental penid&* "" iS € tundamental pe.nlo&

- kxlf E i) x(n) *.sist2r; \

EB :1 :S-tizr ,) "*"';' ,*

I : iii) ,x(h) = cosl =n' | (06 Marks)a.d

'.1''^\u''-""'[g",/6ts;E ;' u',

! E 2 a.. ,Pdrform the convolution of the following signals shown in Fig.Q.2(a) and alsos&6h the o/p

iE *u" signal y(t). P(0s Marks)

8E

-: c.i

()ozGI

oa.

A E -' signal y(t). dt08 Mar

E$ "*\ *

^hto d ..

E.E ; ^* ',\'6'= ; ** -[7 d ae "' ^- r.\ ^ I \ l"F$l*:- )c (\) 1 , =h, , ,r ;.5i -\ ;t i "

h

Fig.Q.2(a)Compute the convolution sum ofx(n):a'[u(n)-u(n-8)], lal<1 and h(n):u(n)-u(n-5). (08Marks)

Compute the convolution of two sequences x,(n) = {\, Z,l7 and xr(n) = {1,2, ?, q\ .

1 0f 3 (04 Marks)

-z--\or

3 a. Check the followings are stable, causal and memoryless:i) h(t; : e-tu(t + 100)

ii) h(t): e-4ltl

iil) h(n) = 2u(n) - 2u(n-2)iv) h(n):6(n) + sin(nn).

10EC44 ,

(08 Marks)

g*_ b. Find the total response of the system given by ^.,1+\ /

- W-"

qry .\*-. -\ z{.,/r\ av(t) / =l r"

*''' d'y(t)+3dy.(t)+2y(t)=2x(t) with y(0):_r, ot/=0 andinprrr' " l. dr

t J dt

t LJ\LI - z^\Lt wrlrr y\u,l - -r: -- /t="'"- S-3 *(t) : cos t u(t). - -(07

Marks)-9.=:'*h - ,. al -- L- L1 - l-t ,! ,1 :------,,,t--, --:-- rgn::in-na/-\

S-3 X(t., : COS I U([r. su. "(u I marKs,

..q-€- a tn oii[]l.ir*e equation corresponding to the block diagram shown in qig{::3i;).T r.- *\" :' (05 Marks)1@_ xtnt

U(^,_^_k

Y

t**" 'il#l\ril '5*'w* 1 .l/t':''rd"\ *r;

{,,,1f _ Fig.e.3(c) .,_=

t: i,*u{.., {,

4 a. If x(n)+-EexG) @y(n)<4Y(k), tffirovethatx(n).y(n)+E> x(k)@Wlk

_ {t* : (07 Marks){ . .. Yut--

DTFS co.ffi.i.nts*fltqr@l=d%r.+) Draw the magnitude and phaseq**.(, *\13 6)spectrum. _ ry%fl\ (06Marks)

c. Determine the time domain sigffiH$

Fig.Q.a(c). k;ito the following spectra shown in

+ x(t<)ftt,

t2

-s \2

+ x(t<)- ETT,

\a

-ts \,

Fig.Q.a(c)

PART _BLet F{x,(t)} = x,UO) and F{xr(t)} = xr(iO) then prove that

l'F{x,(t).x,(t)} = * Jx,(j}")xr(jO - X)dX .

zTt "

2 of3

%&

..- n\ q

'a,sE.a+:!.

.... *c. ':

*ffi'**

5a.

(07 Marks)

b. Find the Fourier transform of the signal x(t) shown in Fig.Q.5(b).

t0E.C44

(06 Marks)

- .::a o

fs:i;q-+!"

.,. '\rJa

::

"., ,, l.,(07 Marks)

Find the inverse Fourier transform of

-!r#!:..,t,6 a. DfffiQrg frequency response of the system described by the impulse rqspofrse

h(t) $&; ie-" uit1. a. ffi (07 Marks)n(r) :rc#!F; ze - u(rJ. ^ "'\,'b. Find th; r transform of the periodic impulse train --:-- "

f 6(tltro) and draw the spectrum.

.\::::...

6r"(t): I66i=kT") anddrawthespectrum. *q3\* (O8Marks)k=-o td;--. --{ #-

c. A signal x(t) : cos(l$4t) + 3cos(20nt) is ideally samplffirth sampling period Ts. Find the

u,;'1 **'

(05 Marks)Nyquistrate. { , r"r/l

7 a. Determine Z-transform of thB'following DTS.#'*lso find the ROC:i) x(n) : 0.8' u(-n- 1) *,

F'" ,. - 1 -

:"

ii) x(n) : -u(n-l) . (+)' (dqF, '* (08 Marks)

b. It x(n)<-z-+ X(z), with RoC *R,ltien proVe,tlat n.x(n)4+ -rX{") with ROC : R.'oz,,IP,,l-

'* t'=1#,"",* (06 Marks)

Determine the inverse Z-tfthSform of the functiori'-;:122 +)z +l :-

X(z) = -o^ ' oo ' ' ,r.,. '. (06 Marks)z' +32+2. ."':',-\#

8a.y(n)-Zv#:j,. +y(n-2):x(n)+3x(n-3). " *?*, (08Marks)

b. Solve_t@llowing difference equation using unilateral Z-transforrh{,+,.{rR I -'"r

X(nIf V(n - l) + ; V(n - 2) = x(n), for n 2 0 with initial conditions V@{) ; 4, y(-2) : l0

y(n) - 2y,S*.4,$\ + y(n - 2) : x(n) + 3x(n - 3).

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Fundamentals of HDL ,tr*.

Max. Markstb0@"t 3 hrs' Note: Answer FrvEfutt quesfions, selecting .='.:lrr'"'''::::"':::"

at least TWO [ourtinrfrom each part. .,'r,'--o-r----------J- ---- ------ r-- -

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_,." PART _ AI a. rrrrlnimtfre tlpes of HDL descriptions. e*plain how half adder caqld'modeled in VHDL

and veri&g in any one description method. _ ;,.=

h (10 Marks)

b. Discuss firb'ghift operators used in VHDL and verilog with examqh. " (04 Marks)

c. Write switckliypl,description of an inverter in verilog. . ,,l :""-' (03 Marks)

d. A : 110, B : I 'C : 011000, D : 111011, evaluate A and.'Ut B or C nor 2 and D.::::.:....:::... .r " (03 Marks)

2 a. Write a data flow desCrlption in VHDL for two-bit itiffilhitude comparator. Show simulationwaveforms. (08 Marks)

b. Write a verilog code to rejalize D-latch witfu *aetive high enable in data flow modelingmethod. Show simulation waveforms, ' (06 Marks)

(06 Marks)

3 a. Write a VHDL code to realize JK;ffrofloffith synchronous reset. (04 Marks)

(06 Marks)(08 Marks)

c. Write the VHDl/verilog description of 16 x 8 SRAM.

c. Write HDL code for 2 x 2 combinational array multiplier (VHDL or verilog).;;'f;'s.:

b. Write verilog description to re4!iia;,"' "". ,,tr=i) 3-bit counter using case.sadanent L'r,rt

ii) 4:1 multiplexer usingjf{tatement (06 Marks)

c. Explain Booth algorithm with an example and writb the.,."flow chart of Booth multiplicationalgorithm. Write VIIfh#br verilog code of 4 x 4 bit Booffialq3rithm. (10 Marks)

4 a. Write the VH-p,Ldbscription of a2:4 decoder using structural m.o"deling method. (05 Marks)

b. Write the e Mtion table of an SRAM memory cell and wrifuffi,structural description inVHDL qf#ilog. (10 Marks)

c. Write,ittrh structural description of a 4-bit asynchronous down c@ppr using generate,

:trynt in verilog. ifti .*i (05 Marks)"fl

r,,.\i PART - B5 , a;'I Write a VHDl/verilog code to convert unsigned binary to an integer using proceduMask.

(06 Marks). ,,,,

" -' 't , a{"',,,

,t.i'.li b. WriteaVHDl/verilogdescriptiontofindthefloatingsum y=lt-t)'(x)' ;0( x( l uJtngi=0

function.c. Write a VHDL code to write integers to a file.

a. Discuss about mixed type description and its advantages. Illustrate with an example.

b. Write short notes on VHDL package and discuss the syntax of declaration of a ru"rlllI"tut'(07 Marks)(07 Marks)

I of2

10EC45

7 a. Explain how a VHDL entity can be invoked from a verilog module with full adder as anexample. (10 Marks)

b. Write the mixed language description to invoke verilog module of JK flip-flop with clearfrom VHDL module. (10 Marks)

l\

* * u. Discuss mapping of signal assignment statement and variable assignment statement to gate-

' , ** level with suitable examples. (S Marhs;

lS..* Explain mapping of if-else statement with a suitable example. "-($5 Marks)

c. how the synthesis information extracted from the listing shown below: *,;**-.r'

% ffi'I:ii:?ffi,"*,,,, divide, none); .q3*

=,=%

-

i;=' ':':" '-*$9+ codes; "*\*.h =erlffiALUS2 is , .-"foffip: in std_logic_vector (3 downto 0); * \ *

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end ALUS2i *{- ,n .

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a. Draw tlre." Cuit of an instrumentation amplifier and explain hoird"tffie*voltage gain can bevaried? %,.DiseirsS the operation of precision full wave rectif,ier circuit using bipolai ob. op,HAmp.

,,. ;''*1, (10 Maiks)tr

' ,f'l'r . ..

jrIrrr,!JlPART _ B,5',.''4. Explain the operation of op-Amp sample and hold circuit with signal, control and;,nd#utp,,ut

(08 Msrlis), waveforms.b.Drawaneatsketchandexplaintheworkingofweinbridgeoscillatorcircuit.(06Markijc. Explain frequency doubler technique using op-Amp. (06 Marks)

6 a. Sketch the circuit of a second order low lass filter and explain its working. (07 Marks)b. An INV Schmitt trigger circuit is to have UTP : 0 V and LTP : 2.5 Y. Design a suitable

circuit using a bipolar op-Amp with + I 15 V supply. (06 Marks)c. Sketch the circuit of an op-Amp astable multivibrator and show the voltage waveforms at

various points and explain its operation. (07 Marks)

Linear lGs and Applications

Note: Answer FIVE full questions, selectingat least TWO questions fro* each parl

I a. '."Define the following parameters and mention its practical values for op-ArqpJhl.(i)'CIVIBR (ii) Slew-rate (iii) PSRR (iv) Output offset voltage. ' (08 Marks)

b. Explalia;;direct-coupled two I/P-Inverting summing amplifier wffi neat diagram and

c. A non-inv amplifier is to amplify a 100 m.V signal to.a1,lryel to 5 V. Using a 741op-Amp, desi'gp a suitable circuit. r,:. r (06 Marks)

2 a. Sketch the circuit of.a.,!1Sh Zin- capacitor -coupled voltag&follower and design its steps.

i". L, i.,_u. (06 Marks)b. A capacitor coupled non-inverting amplifier using 741''op-Amp has A, : 100 & Vo : 5 V.

The load resistance is 10 k$-.and the lower ctrfroff frequency is to be 100 Hz. Design a

suitable circuit. -; , { .r*' ' (08 Marks)c. Explain inverting A.C. Amplifier,wif,h.neat ifidgram and mention its design steps using only

single-supply op-Amp (06Marks).

3 a.- Explain phase tead and phase lag Ep."qup.ntution methods along with frequency response.

maximum peak value",of, inusoidal o/p voltagel ifrJ#e circuit operator with unity gain(iiil Calculate the maxiffim oeak value of the o/o voltase. ifcut-off frequency kHz. (iii) Calculate the maxi ppak value of the o/p volta_ge, if

the upper cut-o is 8 kHz.

I of2

2 of2