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Unformatted text preview: 2 Unit‘l .IOIOIIIOIIIICIIIOC 1. Study Section   Digital 83 stems and Swirenr'ng Circuit: and answer the following study
questions. (a)_ WhaI' Is the basic difference between analog and digital systems?
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JJIGIIT'AL: meg dished; Si 5 (hi Why are digital systems capabie .of reader accuracy than analog systems?
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mm Dréaib'iﬁii Wake; mew (c) Explain Wmegiﬁrence between combinational and sequential switching circuits. CWQIMNTIONM Macon: W W; nuL'a up“ Pram infra?
SEﬁII'ENTIML QLRLMITLI W defends N {ha W I'M1d Pei} I'M (d) What common characteristig: do most switching devices used in digital systems have? swim denim hawe 2 sinker [WM%;0MLW (2) Why are binary numbers used In digital syslems'?
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2. Stud}.r Section 1 2. NuIIIbeI‘ EmmaIs and Conversion. Answer the following study questions;
as you go along:
(a) is the ﬁrst remainder obtained, in the division method for base conversion the. most or Ian signiﬁcant digit? 11.1; Imi damnm bi"? ("bi Work ihmugh all of the ex amples in the text as you encounter them and make sure th all
you understand ail {If thc'sleps. (C) An easy method for conversion bEIween binary and hexadecimal is illu‘snnted in
Equation {EIJ. Why should you snirt forming the groups nfi‘ourbils at the binary point
instead of the‘ left end of the number? jumMW%b$aDu;t4awwa (d) Why is it impoesibielo convert a de'cimnE number to bi nary on a digit—byrdigil basis an
can be done for hexadecimal? For mMmM—‘a ié' a» new» 6% 2(2“=Jé)=bwmttﬂ 4w:
Win one ModeeImeJ sugar For Mmei '«> [Die more; Pom 61,5.5. Number Systems and Conversion 3' (a) Cumplelc the following Conversion Labia. Binary Octal Decimal H exadacimal
(base a) (base In) ‘ (f) Work Problems 1.1, 1.2, 1.3,,and L4. Stuﬁy Section 1.3. Kimmy Arithmetic. (a) Make sure thatmu can £611th a]: of the examples. espacialiy Ihc propagation of
borrows in the subtraction pmocss. (b) To make sure: that you undmtand the borrowing process. work: D'Lll a. dctailed anal 51.595 inlnrms of powers nf 2forthefollowing exampic: ‘ 1 5' 'if _ 
1100 [‘Ixz’ +114 z‘+ 0x23+ m“ J =[1K2+'¥3+ In")? NWT“9:1. :ﬂ .. “:2" +oxa'1In29]  [Ixz‘+ oxi‘ + rszﬁ'ﬂ
1“ =[i 125.“; _)z‘+(gofo—p 2'+[ID+D)L=31
 rug? 1 o 32‘ + Jaw“ Work Pmblems 15. 1.6, and 1.170;). {(10le “P 0°“? '“91¥+"~19*° *leﬁ'mﬁﬂ
.. in + 0an + $29] ."z‘nudg.r Semen 1.4, Represenranon afNegqn we Numbers. g ”15+ I. KZ"+ 183+”sz (a) In digital systems. why are 1‘}. complement and 25 comp cment commonly usnd to
represent negative: numbm instead nfsignand magnitude? ”£1 '15 eugicr +1: Emu cimﬁi‘: +9 do 1L2. mmplmmi‘
in“ 2'; w“?‘”““ miihmealic (c) Sun: three different ways of forming the 2‘3 complement of an rtbil binmy number.
l N": ZEN, ic' sumac}: H {mm a“
2. Cow171mm} 56+ by w em! midi
a. commwan br'is “h: m tail! of me ﬁrsf 1* (d) If the word length is n = 4 bits (including Sign). what dmimai num'bar docs 10002
rcpmsent' ll'l sign and magnitude?— —0 H
In 2‘s cumplement?'3 —}> z." 8= [63 = '5!
in l s complement?
inCoaHfiemmi (not: a out; =r' loco}: ¥ {e} Given a npgative numbbl: represented in 2's complemaut. how do ydu ﬁnd its
mgn'md“? Find m 2'6. mmflmw oi +he number
['23 b0 Given a negative number represented in 1's complement, how do you ﬁnd its
magnitude? Fmi me, It comp lemma!“ oi 'H'E Number. mptomw b'+ E tan)
{f} If [he word length 15 6 bits (incl :15 sign). what dacimal number does 100000:
mmiﬁnrmsign and magaimde'? [11 2‘5 complement? _ 31 [11 1'5 complﬁment? 3! (3} What is Imam by an overflow? How can you tail that an avcrﬂow has occurred whcn
peafunmng 1's 01‘2’3 campiement addition? Pm OU'Q‘Eiow occurs when 49.; mm of m nbr'l’ addiﬁon
or :uhhndim opamﬁon ng‘uma (rm) bits ’
FUTM— Malian 2m "mbmﬂ‘"8 n mat ouB—vr. Waﬁdvg we 1+“ .  . . 
9.51“. ab or lieﬁahNe (Pnaﬁvzhi’osdrm
M _ Dgeﬂéﬁgﬁ‘ym out last bit ilionﬁdicate that an averflow has occurred? bio Number Systems and Conversion 5 {11) Work out some examples of 1‘s and To complement addition for various combinations
of positive and negative numbers; (i) What is the justiﬁcation for using the endaround carry in l's'complement addition? £31581: GAME.) {rsvisa) ”To d’{B—P05w~ocedlu
= z” J—A) r a 2”+c e~ FD—I sﬁw 1" ma odd I, to'ntd't ._
'[ ' 3 ts. done. Ina we endMound awai
n 5; Result of evd—mnt; "
¢E+B=t=¢t—Al+f="riB) = 2  C3“ ‘ (“+334 “‘6 ‘5 ziimrerJIk'iW’lri
6} The one thing that causes the most trouble with 2‘s compient numbers is the special ﬁat:3:
caseof the negative number which consistsof a' 1 followed by all D's (1000 . . . DOG).
If this number is n bits long, what number does it represent and why? (It is not new
tiye zero. «Far an r) bit 2‘3 eowtflwehi' ﬁQ, tonal—pt! i3 _ 25H. .
“M93“ +112. mmbet ls. woefulwe. 3...; W'H'ﬂg 3.: 2."2.'";2.Hi (k) WorkPIoblems 1.7 and 1.8. 6. Study Section 1.5. Binary Codes.
(3) Represent 187 in BC‘D cede, excess3 code, 673—11 code. and ZeutofS code. (act): 0001 looo Olll
“$531 otoo loll Iota
63442 GDOI loll tool aunt#5100101 [moo toolo _
(b) Verify thanhe 63wl—1 codeisa weighted cede. Notethat for modem ' a] digits, two different code combinations could have been used. For example,.either 0101 or 0110
could represent 4. In each case the'combinatioo with the smaller binary valuehas beau
used. (a) How is' the excess3 code obtained?
Add 3 (out!) he the Ed) cede. (d) How are the ASCII eodes for the decimal digits obtained? What is the relation betw'één
the ASCII codes for the'capital letters and lowercase letters? . ;. .
baseman dragrstsoHls At m 5.11m toto4 ekam 4a: brmg ref. emue
dillWM when . __
'{ej Work Problem 1.9. w = WW "'0‘” 10'“ 5 5‘37 7. If you are taking this course on a self—paced'basis, you will need to pass a readiness teat on
this unit before going on tothe nest unit. The purpose of the readiness test is to determine
if you havenseemed the material in this unitaudare ready togo onto the nextuuit. Before
you take the readiness tost: (3.) Check your answers to the problems against those provided at the end of this book. If
you missed $1ny the problems, make sure that you understand why your answer is
wrong and correct your solution. (b) Make sure that you can meet allof the objectives listedjetthe beginning of this unit. ...
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 Spring '08
 Brown

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