o()()

0Cd

C)

GIo)

E9oo-O.:aJ4,dui;\n;ilcoo.: -L.=N63txa{)otr-c 0,

ti L.oB*.a

.A ct

bdGloOEo0tr(Ecg

o>H)c5(g-

-? q.r

6ll

48.g o.oj

b'E}U<a lE(g=Li c)

6.:>r ttoooca0o=a.u=o)uLr

\J<-: c-i

o)

ozcB

o

USN

2a.

b.

c.

3a.

b.

c.tt'

,, t, _-

.

4a.

b.

c.

Derive an expression for output SNR of the quantizer and show that (SNR)o = 6u - 7.2 indecibels if a sinusoidal signal is quantized. (08 Marks)Explain the need for non-uniform quahtization. Also explain p-law and A-law companding.

,,. (07 Marks)A signal Mr(t) is band limit-ed- 3.6kHz and three other signals Mz(t), M:(r) and Ma(t) areband limited to l.2kHz. These signals are to be transmittedby means of TDM.i) Set up a scheme for realizing this multiplexing requirement, with each sampled signal

at its Nyquist rateii) What must be the speed of the commutator in samples/sec?iii) Determine the minimum bandwidth of the channel.

lOEC/TE61

2015

(05 Marks)

For the given binary sequence 101000110101, draw the digital format waveformcorrespbnding to i) ON-OFF signaling; ii) RZ bipolar signaling; iii) Manchester code;iv) NRZ polar signaling; v) NRZbipolar signaling. (05 Marks)What is the differences between PCM and DPCM? Briefly explain the operation of DPCMsystem with neat block diagram along with relevant .*pmriorrr. (08 Marks)Derive an expression for power spectral density of bipolar NRZ format and plot the samewith respect to frequency. (07 Marks)

Explain the following terms with related equations and diagram with respect to basebanddata transmission: i) ISI ii) Raised cosine spectrum. (10 Marks)Draw and explain modified duo binary techniques. Specify how the error propagation iseliminated. (07 Marks)A multilevel digital communication system transmits one of the sixteen possible levels overthe channel every 0.8 ps.

i) What is the minimum number of bits corresponding to each level?ii) What is baud rate?

iii) What is bit rate?

tla6 $"m F-LC

Sixth

Time: 3 hrs. Max. Marks:10O

Note: Answer any FIVE full questions, selectingatleast TWO questions from each part.

PART - AState sampling theorem. Write the equations for the spectrum of finite energy g(t) sampledat L/ZW sec. and g(0, if W is the highest frequency content of g(t). Sketch g(f) and sampledsignal g,(0. (08 Marks)

b. The signal g(t) = 10 cos (20nt) cos (200nt) is sampled at the rate of 250 samples per second.i) Determine the spectrum of the resulting sampled signal;ii) Specify the cutoff frequency of the ideal reconstruction filter so as to recover g(t)

from its sampled version. :j;, _iiii) What is Nyquist rate for g(t). i . ' (04 Marks)c. Explain how practical sampling is different from ideal sampling. Derive an expression for

the flat top sampled signal. (08 Marks)

1af )(03 Marks)

10ECruE61

PART-B5 a. Draw the block diagram for QPSK transmitter and receiver. From the basic principles prove

(10 Marks)

b. Explain in detail along with the block diagram a coherent FSK tansmitter and receiver. ,,, ,1.,,,,

(06 Marks)c. The data transferred in PSK is with data rate of lMbps. It is desired to have P. S t0 a with

PSD at 10-12 N/FIz. Determine average carrier power required at the receiver input' if thedetector is coherent. erfc(3.5) = 0.002. (04 Marks)

a. With a conceptu alized model of digital communication system, explair Gram-Schmidtortho gon alization proc edure. (10 Marks)

b. Three signals sr(t), sz(t) and s3(t) are as shown in Fig.Q.6(b) below..Apply Gram-Schmidtprocedure to obtain an orthonormal basis for signals. Express the signals sr(t), sz(t) and s3(t)in terms of orthonormal basis function. Also give the signal constellation diagram.

(10 Marks)

that BER for QPSK is )"rtrt,ffi)

.fl r't f-olJf-l -t;I--I+",,'' Fig.Q.6(b)

7 a. Explain tb. Consider

,(,) = iol

he properties of matched filter. (10 Marks)a signal s(t) defined.by,

;0St<T _j.;,.':,, _-_.r-_,__. J-L,.,i#proposed to approximate the matched filter for this signal by a

;;, ::r

lowpassRCfi1tera#iliobythetransferfunctionH(f)=+,wheref^=^Lis, :' .,' I + j(f lf ")'

-o 2nRC

the cutoff frequency of RC filter.i) Determine optimum value of fo for which the RC fitter becomes the best

approximation for matched filter.ii) Dbtermine the peak o/p signal to noise ratio assuming noise is AWG of zero mean and

,, ..,. power density NJ2..* ii'i) Determine by how many decibels the transmitted energy be increased so that the

_'* performance becomes same as that of perfectly matched filter. (10 Marks)

a. Explain the properties of maximum length sequence for a sequence generated from3-voltage shift register with linear feedback. Verify these properties for the PN sequence01011100101110 and also determine the period of the given PN sequence. (08 Marks)

b. Explain the principle of direct sequence spread spectrum system. (05 Marks)c. Explain with neat block diagram the working of frequency hop transmitter and receiver.

(07 Marks)

8****

2 of 2

USN

Time: 3 hrs.

Sixth S'emester

Write the memory matr, i'1-the TPA in lbrief.Explain the based, indexe,J, i:as: ,r",,i.

suitable diagrams and examples.

I

lOEC/TE,62

Max. Marks:100

PART _ A

personal conlpuier and explain each of the areas in(10 i\larks)

;C .:,r1 ,*1tti ,e addressing modes of 8086 with(10 N{arks)

[],,11. Degree ..{lxanoinatiCIn, June/Ju[y 2015Micropff'scessors

Note: Answer any FIV'il full questions" selectingotleast TWO qutt:;tiotis /rom esclt parl

b.

a.

.:(J

()!

a

()

c.)i<

,i ,'6)xco-

dv

co"t6

.= c.l(ss!'r b{ri()C)i-co

aa2

A-crx

bd

uotr6d

-6(E<

:)5vaa

o-X

o .-t;6L"qii ::

7) L,=

Lr (J

O.=

bootrbIJo=- ::tr>a-

\J<J cjC)

oz(gi,

b. Write the f'lowchart and assembly language prograrn se{rrnenl to sort numbersin descending order usi:ir; l;r"rbbie sort. 11s:: I as ir:de>..

Write an assembly lanq',.rage program sr.:nient to cerfonldigit l0's cornplement nunrbers, whc,.,3 upl, Ltpz andvariable mentory locations.

(DX) <- up | + upZ - up3 on twoup3 are unpacked two byte data

(10 [Iarks)in an array A

(10 Ntarks)

a. Write an assernbly language program segment to lrioveoverlapping areas and explain with diagi erns of overiapping.

b. Compare procedure ilt,J macro.c. Write an a.stsembly lanq't.y.:1 pt'i[iit,,'-!t :r' :r",lcilt io 1ro{a'.1.a+.a

VAI{4 to VhR3 using lv{Oi/E \4.zrCtlr.. (argunre: r.s).

a block of data betu'een two(10 Vtarks)(04 Plarks)

trom VAR2 to VAR1 antl also(Gti NIanks)

rows ano [, - bitpress, de-bounce

(10 NIarks)

microcomputer.(10 VIarks)

a. Draw the' intet:'t-t0t vs,:f'''- ':bi: an,i r',"ie t1,: Itc{-lr,tellce of operatio:rs that are p:rformedwhen an interrupi is rec., i': zecl. (10 xlarks)

b. Write the assembly langr"rage progr?r1t .:r.r-llrreri::; to set t:re trap flag and to reset the trap flag.(06 Marks)

c. Write the circuit for opticnlly detectin:. the presence of e new printed circuit -board as itcoll'les or,rt of the rnachine and keep fi irouflt cl' finished boards, so that we can count any

' board lost in the machine u,,hen a bca,'' nflsscs hetu,err I ED and phototransistor it sl.rouldsignal the I-{MI input oi'llCt,6. illg,lzfyl ; ) ope ri}ticn oicircuit. (04 iltarks)

.]ART -_ B

a. Interface a 4 x 4 rnatrix keyboard to 8{;86 through 4 - bit output port {,rrinput fbr columns. Draw tire flou,cirart ald expiatn tne procedure for keyand encodialg of the key pressed.

b. With a neat diagram interface the rnrritrplexe<J 4 - d;.sit LED display toExpiain the principle of'oor:ratioo.

i ot2

fbr computing theDE,\/ respoctively

lOEC/TB,62

(10 Marks)sample rnean and

r,vhere :

a. I)rarv the block diagr;rrn of 8{}E7 ancl r:r.prlatit.

b. Write the 80ti7 assenil:ly language rlf'l.gram seqtlerc,)stanclarcl deviation and store thern ar i',i; AN and Sl'iJ __

..;:l(xi - tvtrEAN)r

Standard deviation lSTD - liE\') _- X

lrY'X,,,-, n

j

samplr: (MEAI{) = r-.:- , x; , X2, - -.\,

Write the typical minirnum mocr Slrtr'i11

interconnections and explain.Write the ALP segment to initialize, rcad

E,xplain the features oi LISB.

NI _1

contiguration of 8086 with necessary devices and

.nd write the parallel port printer *irt ou,(H#l'ut)(06 Marks)(04 Marks)

)(x

7a.

b.

c.

a. Discuss the fla.g regis.r':r, debug and tcsib. Explain the salient fearurr:s ot'80486.c. f)rarv the block diagran: of Pentjr,iill rr:";,

registers of l0iil6.

rl0SSC,t' atiCi r.i, i;;;rin the

(06 Marks)(06 Marks)

ftinction of each block.(08 Marks)

:i< :i< * ;|< {<

").

of 2

USN 10EC63

Sixth Semester B.E. Degree hlxamination, June/July 2015M ic roe leetnermics Circ uits

:j] ,,ii,

. ;r,' "r'

Max. Mark$:100Time: 3 hrs.

Note: Answer any FIVE qwestions, selectingTHR.EE from Part-A and "tWO from Part-B.

PA.R.? _ Aa. Derive the io - Vos relationship of a MOSFET for triode and saturation region. (12Marks)b. For a MOSFET process technology with WIL = 8 pnv0.8 pm,.tox = Snm, €r = 3.9 pn - 450

cm'lv.s and v, = b.z v.i) Find Co* and K'- .

ii) Calculate the values of V65 and VDS,nin needed to operate the transistor in thesaturation region r.vrrh a dc cumeri; ii, = iCO FrA.

iii) For the device to operate as a 1Cu0 s? iesistor find the value of V65 required for verysmall Vos. (08 Marks)

a. Derive the expression for input resistance. outp,:t resistance, voltage gain and overall gain ofa grounded source arnpiifier with a ne-:,l ii rgram. (0g Marks)

b. Design the biasing circuit shorvn rn Fiy- () 2(b) 'ro estatrlish a clrain current io = 0.5mA.Vprt

oaL)9r

a

oOt<

atoX

v9(g \JE(r)ao llc00.=N6.+xaoEooi_cooB.Aoil

cr, =

UUdoaoc(g cd

!5}H(tr-

E(6

-br5so. F_

(,) ":., '-)()=

5oC/)iXc.i+LO

6.=>r (*ao"trboo=

=9Xrr

lJ<-i ciC)

oz

t'i1

!-#--.--l!I

"].{) *Fpi .ei''f

I*:::-

*{u,_l+,ol-r

+As-L";

,,,1 Fig.e.2(b)MOSpgT has vt = lV, kl(W lL) -tr rnfi lv2anCVrr: = 15V. Assume one-third Von across

Rp and R5 and neglect ctrannel ierrgiii r...;dulzi'iion ?. = 0. Determine percentage change invalue of io when MOSFET' is i'epi ate,:.n,i llr a;,",-,t,ter having vt = 1 .5V. (12 Marks)

a. Explain the operation of a MOSFET cuffent steering ci'-cuits with necessary expressions.(10 Marks)

before and after scaling in(10 Marks)

at voitage gain expression(10 Marks)

Gn, of the MOS cascade(10 Marks)

b. What is MOSFET scaling? Comprar: h^OSFET par:.metersconstant tield scaling and constant volt:rri ;caling.

a. Explain CMOS implernentation cf CSAu = gn.1 rs1/2

b. Derive ail expressiorr fo'r the shc*", ;i;amplifier.

aiapiifier and arrive

.uit i;'anscc,nductance

10EC63

Explain operation of MOS tiiffere,riiai pa-ir with common-mode input voltage V"n, anddetermine the highest ailC lowest -,';lue cf ''1.o cver which the differential pair operatesproperly.

b. For a MOS differentia.l t:e.ii: in i?i: Q,5l'b).

Explain the operation and anai,vsis cf single op-ampcommon rnode gain A.*.How op-amp cir@S can be useC as sigi:ai integratortime constants?

(08 Marks)

saturation?to operate properly what is

(12 Marks)

(08 Marks)(08 Marks)(04 Marks)

difference amplifier to determine it(10 Marks)

and differentiator and determine the(10 Marks)

(08 Marks)(08 Marks)(04 Marks)

_..1_sS

'ig.{}.5rb) '

Von-Vss = 1.5V, it'"1'li,'lL).-.i'i;;r\ 1",/2" 121 :: Q..JV, I=0.4mA, Ro -2.5 KQneglectchannel length modulation.i) Find Vov and V-cs ic:: eacri ii:-ilr',.si:r-'.ii) What is the highesi value of V* fi;r rQ; and Qz to remain iniii) If the current source i require. a :.'iir.il11u* vcltage of 0.4V

the lowest value allowed fcr Y, anci Vu"?

i.gELtra. Discuss v,,ith neat diagrarc the fou:li:i'ir: -'eedtra;,k tcpoicgies.b. Explain the pioperties of i;gzil,i.r'e i<:: ,l:,-ri:k.

c. What is the general strucfr;re of tne fe ":diack amplifier?

b.

a. Describeffi circuit structure anC sta'Lic cperation of CMOS invertor.b. With exhrnple explain PUN ani Fllld CMOS logic gate circuits.c. Realize two input NOR. ga';e anii twc input I{AND gate using CMOS gate.

***8*

2cf2

10EC64USN

Time: 3 hrs.

Sixth Semester B.E. Degree Examination, June/July 2015Antennas and Propagation

o).9()dadtr81a.oH.g b.

U) ,i

9o5 c.!w-g'-J4,GI qJ

=tnrn ll

c00:E& ) .,(R$ a q.

ET36 b.

o} rv.

En

(,X

bUE€ 3 a.v\JsE b.€b nBH v'lu=

EGt

-a" B'EsE= 4 a.

3* b.5(d

-C) i6 c.6()'v, lEE;l- n ) .ij'

t E u.;..,>: s .eAn Y g. lnr.... -.*.

trO0+n.!, 1

t : ): t:: 1!::; ,',:r .- .. !'u

- -#"-'i!

E ttl . ;i' -a+ t' r

E g*-q\*/? D.

H""#e* *"

=x,!tr^(r< v.:oid)

V 6a.shtr \r.O.^FU.

Note: Answer any FIW full questions, selecting .'d ;'*t *

atleast TWO quesfions from each part. * {r._.*

e

'to"ttt

' t t'''

PART-A .,*i.,Define: i) Radiation intensity ii) Power density. Derive the-relation between these twoparameters. i' (06 Marks)Show that the maximum effective aperature of a short dipo$................- mrcnna is 0. I 1 g ?"2 . (06 Marks)Determine the directivity of a system, if the radiation intuniff isD U. sin-O . sin2 0 ; for 0 < e (n, 0 < $ <n.,,.,ii,. i*

ir) Un, sin2 0 sin3 0 ; for 0 < e < Tcl2,0 < O < 2n.'u". o,'.li*,' -

State and prove power theorem. How powep-ffi,ptbm is applied to find power radiated by an

-tfr ,. ..'-"

Max. Marks I00

(08 Marks)

(06 Marks)(08 Marks)

(06 Marks)

(06 Marks)(06 Marks)

(08 Marks)

(06 Marks)(06 Marks)

(06 Marks)two modes of

(08 Marks)and a4 to 1

(06 Marks)

(06 Marks)(06 Marks)

(08 Marks)

A linear antenna affay consists of,"ft'tu;isotropic sources. The distance between adjacentsources is )"12. The power applied to'+he anay is with equal amplitude and a phase difference

- d.. Obtain the field pattern and,,,,,,, FNBW and HPBW.

. ,r''t,'

Derive an expression fortadiation resistance of a short electric dipole.Show that the radiationtesistance of )vl2 antenna is 73 ohms.With the help of nea{, diagrams, explain following antennas:i) Long-wire ante ii) Folded dipole antenna.

": "

,11'

Derive thqig$essions for field strengths Eq and Hs incase of a small loop. (0S Marks)The radjtis

,6f a circular loop antenna is 0.021,. How many turns of the antenna will give a

radi resistance of 35f)?E#ffi Babinet's principle with illustrations.

.I'" PART - BExnlain rlifftr'ent trrnes of rectansular horn antennas Whv flarino nf walls nf waveorride ins^4^v^v.^u eJ lrvs v-i ivv!6iiD;i6i iiv-iii $i:!'v'iiiili.>. f Y.!,.!,j i:-i:i:6 'J: ii+i:J --.i ri-i--,A+:-+L ---

isotropic antenna in terms of it's' radiation iitensity?Derive an expression for'array factor'..of ahanay ofn-isotropic sources.

case of horn antennas is necessary?Describe a helical antenna with the help of a neat diagram. Explain itsoperation with relevant equations.Find number of elements in a log-periodic dipole anay with TdBi gainbandwidth. The scale constant K : I .2 for apex angle of 15o.

Explain the construction and working of lens antenna.With neat diagram, explain embedded antenna.Explain following antenna types with neat sketches:i) Ultra wide band antenna ii) Plasma antenna.

108C64

7 a. Derive an expression for space wave field intensity and show that it varies sinusoidally.(08 Marks)

b. Explain duct propagation with diagram. (06 Marks)c. A free-space LOS (Line-of-Sight) microwave link operatingat l0 GHz consists of a transmit

and a receive antenna each having a gan of 25dB. The distance between the two antenn-4"ffidq

30km and the power radiated by the transmit antenna is 10W. Calculate the path lops,"ffi?fblink and the received power.

,_ ,r5f*.u.,8 a. Explain the mechanism of ionospheric propagation. Also derive an expgris$bn for the

refractive index of an ionospheric layer. +r,,,,,,*

'+ (0g Marks)b. Discuss the effect of the earth's naagnetic field on ionospheric propagatieg':' * (06 Marks)c. Calculate the angle of incidence and the maximum single-hop disianCe for a sky wave

iri i.'r '' (06 Marks)reflected from the E-layer with height 'h' : 100 km.

:lit''"'+ lili! rii

t{€rf ** t;.1

i,r #it:r-tr,,: "'

2 of 2

USN

2015

Max. Mad<s;,l00

1oEC65

(O9 Marks)(04 Marks)

loading of a page.(07 Marks)

(10 Marks)(05 Marks)(05 Marks)

Sixth Semester B.E. DegreeOperating

1a.b.c.

c).9()(B!

6

a(!

C)(s0)tr

8R

J-

d\J

= tat

io tt

ioo.E ol(g$

6 ?.0

(.) tr.d 0..)

Ee

aX

oc)(€O

o0g

vo}Es=t(c;? or

agtrc.o;aeC)Xg().h tE

6Fli 6)

=to.->' q-^^oc' o0

()==g)=cloaoi:oi6.)

oZ

ti

9.

Time: 3 hrs.

2a.b.c.

3a.b.

c.

4a.b.

c.

Note: Answer any FIW full questions, selectingatleast TWO questions from each part-

,, ' ,

.

,''" ,,,. l-

;it:: ! ,tl.' '';::

Discuss the common tasks performed by an operating system (Ol (05 Marks)

Explain the resource preemption, resource allocation strategips of an OS. (07 Marks)

What is a distributed syitem? Discuss the key concepts, techniques and benefits ofdistributed os' ::- i'jo (08 Marks)

Explain the functions of an OS. (04 Marks)

Explain the kernel based operating systemwitha structure of time sharing system. (08Marks)

exptain the following: i) System generatig[; ii) Configuration tools; iii) Dynamic

configuration of supervisor. (08 Marks)

Discuss the primary concernsireaso-hg$r process termination. (05 Marks)

List the events occur during the b$-ofation of OS. With a dragram discuss the event handling

actions of kernel. ,,j.. (08 Marks)

With a diagram, explain 'fu relationship between threads and processes. Discuss the

advantages of threads, ,"' = (07 Marks)

j "::jj'

Explain the lazy b allocator and slab allocator (08 Marks)

With a diagram,t4lain the merging of free memory areas using boundary tag. (08 Marks)

Compare -heflr'een contiguous and non-contiguous memory allocation. (04 Marks)

,. .'1.'i, PART - B

a. W{th a dragram explain the following:1) Practical page replacement policy.ii) Page replacement policy using clock algorithms.

b. Explain with a diagram, the copy_on_write for shared pages.

c. With a dragram, explain the virtual memory manager's actions in demand

a. Explain the following write a diagram:i) Linked allocationii) File allocation tableiir) Indexed allocation.

b. Explain the operations performed on files.c. Discuss with a diagram the directory trees of a file system.

I of 2

7a.b.

With a neat diagram, explain the event handling and scheduling.Determine the mean turn around time and mean weighted turn aroundscheduling for the following table:

10EC6s

(08 Marks)for LCN and STG

(08 Marks)

(04 Marks)

(07 Marks)(08 Marks)(05 Marks)

Processes Arrival time (sec.) Execution time (sec.) Dead line time (sec.)

Pr 0 03 04Pz 2 03 t4P: 3 02 06P+ 5 05 11

Ps 8 03 L2

c.Discussthetwofundamenta1techniquesofscheduling.

attt',. '

a. Explainthefollowing: , ,,, , ,'-".'i) Inter process message control block.ii) Exceptional conditions on message passing.

b. Explain the message queues and sockets for inter prose.ss communication in unix.c. Explain a mail box with its features and advantages.

':

* >l< :k'":F {<

2 of 2

USN

a

10EC666

Sixth Semester B.E. Degree Examination, June/July 2015Digital System Design Using Verilog

Time: 3 hrs. Max. Marks: lO0

Note: Answer any FIVE full questions, selectingatleast TWO questions from each part. :. .

o ltage,.r'*:;* tr.rrro td vo ttages and nois#gins ?

Develop a verilog model for a 7-segment decoder. Include an ddi;i;;;l input, Jf#,u[i*overrirdes the BCD input and caus.t utt segments not to be lit. . -' ' (08 Marks)Explain a simple digital system design methodology. ,., (08 Marks)

b.

c.

a.

b.c.

How rnany address bits does it require?Expt& the procedure to manufacture I.C.Explain the internal organization of a CPLD.

(04 Marks)(08 Marks)(08 Marks)

among four unsigned 6-bit(04 lVlarks)(08 Marks)

4-bit gray code to a 4 bit(08 Marks)

(04 Marks)(08 Marks)(08 Marks)

(04 Marks)(08 Marks)(08 Marks)

(04 Marks)(08 Marks)(08 Marks)

(04 Marks)(08 Marks)(08 Marks)

4)O

otra=a

0)

o

()xbo-

(d lJ

-o-^lltrco,= o{(g=f,

YC)oi-c()

a_^

zI

5U

u0i(trcd

2G

E6

6lro-XEir,JJal)grEatE

ii()?e>\ (+<

bo-tr400)=ir. 6)F>o-

cr<-'ojll)

z

a

2 a. hnplementthe following function f using sum-of-produ-ct form: f = (* *y.;) (-)

b. Explain the technique of using parity for error de-teetion.c. Explain the verification of combinational circ11@''

a. Develop a verilog model of a 4-to-1 multiplexer that selects

b. Design a 4-hit carry look ahead adder.c. Develop a verilog model of a code converter to convert the

unsigned binary integer.

a. Design a circuit for a modulo 10 counter. (04 Marks)b. What is a finite state machine? Explain circuit structure for a finite state machine. (0B,Marks)c. Explain the clocked synchronous timing methodology. (08 Marks)

:1 PART_B: ir: :1

If a memory'has 32,768 locations, each of 32 bits, what is the total capacity of the memory?

a. ''' What are the elements of an embedded computer?b. Explain arithmetic, logical, shift and memory instructions.c. Describe the interface between 8051 microcontrollerwith SRAM.

a. Explain the working of successive approximation ADC.b. Discuss the modeling tristate drivers in verilog.c. Explain serial interface standards with example

a. What is parallelism? Explain pipelined organization of an accelerator.b. Discuss sobel edge detector for edge:detection in video images.c. Explain prototypical design flow including hardware/software co design.

:|( :1. ,F X< rl.