PART 15-Elec Buk(Final)

8/11/2019 PART 15-Elec Buk(Final)

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PART15DIGITAL ELECTRONICS

I. NUMBER SYSTEM

1. GENERALIZATIONS

a. There is no number system with a base of 1.b. The number of symbols in any number system is the radix or the basec. The highest symbol in any number system is equal to radix 1.d. The highest symbol plus 1 equals 0 with carry 1.

2. COMMON NUMBER SYSTEMS

a. Decimal System Said to be of the base 10 because it uses 10 digits and the coefficients are

multiplied by powers of 10 Highest digit is 9

. Bi!a"y System There are only two possible alues 0 and 1

!sed in digital systems

c. Octal System

"ith radix of # Highest digit is $

#. $e%a#ecimal System !ses 1% characters of numbers &0 9' and letters&( )'

*ften used in registers addressing

&. NUMBER BASE CON'ERSION

a. Base (") t* Decimal use the positional notation method as illustrated

Mac"* I!te+"ate# T"ai!i!+ a!# Re,ie- Ce!te" Elc/"0!i

+ry,ell

12122112212211


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1342 Digital Electronics

1 2 1 . 2 1-

-

1-

0-1---

0 . - %

0

1

0

/

% . - %

. Decimal t* a!y ase (") )or the integer part diide the integer part repeatedly by base &r' then use the

remainder to form the required base &r' number in an upordered manner )or the fractional part multiply the decimal part repeatedly by base &r' until you

find digits less significant and then use the integer part to form the base &r'fractional number. To illustrate2

0 . 3 # $ % b i n a r y

0 . 3 # $ % x - 1 . 4 $ %

0 . 4 $ % x - 0 . $ %

0 . $ % x - 1 . %

0 . % x - 1 . 0

c o e f f i c i e n t1

0

1

1

0 . 3 # $ % 0 . 1 0 1 1 -

c. Bi!a"y t* Octal group bits by three and conert each group to its equialent

0 1 0 1 1 0 . 1 1 1 0 1 1

- 3 $ 4.

#. Octal t* i!a"y each *ctal digit can be represented in its equialent 4 bits.

e. Bi!a"y t* $e%a#ecimal group bits by four and conert each group to its equialent hexadecimal

character. To illustrate2

0 0 0 1 0 1 1 0 . 1 1 1 0 1 1 0 0

1 3 5 ,.

5. $e%a#ecimal t* Bi!a"y

each hexadecimal character can be represented in its equialent / bits

+. Ot6e" C*!,e"si*! if there is no direct conersion as shown preiously ma6e a sequence

conersion or practically ma6es use of the calculator een for the conersionsgien preiously.

Elc/"0!i Mac"* I!te+"ate# T"ai!i!+ a!# Re,ie- Ce!te"


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Digital Electronics 13- &

7. COMPLEMENTS !sed in digital systems and computers for simplifying the subtraction

operations and for logical manipulations

Ty8es Bi!a"y Decimalr7s complement

&true complement'

-7s 107s

&r1'7s complement&radix1 complement'

17s 97s

8ote2

1. The 107s complement of a decimal number can be formed by leaing all the leastsignificant eroes unchanged subtracting the 1stnonero least significant digit from10 and subtracting all other significant digit from 9.5xample2

97s complement 107s complement

-%14 $/#3 $/#$

-. The -7s complement can be formed by leaing all least significant eroesunchanged and the 1stnon ero unchanged and then replacing 17s by 07s and 07s by17s in all other higher significant digits.5xample2

17s complement -7s complement

10100100 01011011 1011100



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II. BOOLEAN ALGEBRA( set of elements set of operators and number of unapproed axioms or

postulates

1. $ISTORY *5 BOOLEAN ALGEBRA

1#%/ Ge*"+e B**le :ntroduced a systematic treatment of logic and deeloped or this purpose an

algebraic system. 194# C.E. Ca!!*!

:ntroduced a -alued ;oolean (lgebra called Switching (lgebra in which he

demonstrated that the properties of bistable electrical switching circuits that canbe represented by this (lgebra.

2. BASIC T$EOREMS a!# PROPERTIES *5 BOOLEAN ALGEBRA

a. D9ality P"i!ci8le 5ery algebraic expression deducible from the postulates of ;oolean (lgebra

remains alid if the operators and identity elements are interchanged :f the dual of an algebraic expression is desired we simply interchange *< and

(8+ operators and replace 17s by 07s and 07s by 17s.

x = 0 x x1 x

x = x7 1 xx7 0

x = x x xx x

x = 1 1 x0 0&x7'7 x &inolution'x =y y = x &commutatie'x = &y = ' &x = y' = &associatie'x &y = ' xy =x &distributie'

. De M*"+a!:s T6e*"em

;( + ; ( ;;( ; (


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Digital Electronics 13- 3

>interms logical product of all the function ariables that may or may not be

complemented?roduct Terms

logical product of the function ariables but not necessarily all the ariables

that may or may not be complemented>axterms

sum of all the function ariables that may or may not be complemented

Sum terms sum of the function ariables but not necessarily all the ariables that may or

may not be complemented

Ca!*!ical =*"ms

Sum of >interms2 f &xy' xy = x y = x 9y

?roduct of >axterms2 f&xy' &x = y ='& 9yx ++ '

Sta!#a"# =*"ms Sum of ?roducts2 f &xy' xy = y 9 = x y

?roduct of Sums2 f &xy' &x=y'& 9yx ++ '

&. TRUT$ TABLE a!# >4MAP

a. T"9t6 Tale( table that describes a logic function by listing all possible combinations of the

inputs and indicating the logical output alue

. > ?Ma8 (>a"!a9+6 Ma8) :nented by @eitch

?atented by Aarnaugh

The essence of the map is by means of oerlapping subrectangles such that

the intersection represents a unique combination of logic ariables



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134@ Digital Electronics

x y9 00 011110

00

01

11

10

w

/ @ariable

:f the number of logic ariables is % or more Buine >clus6y method is preferred

Basic R9les i! G"*98i!+ Croup must be in the power of -

Croup must be in rectangular form

The group must be as large as possible and as few as possible

D*!:t Ca"e C*!#iti*!s ,ombination of input ariables that neer occur

(s a result we don7t care what the output function is to be for these combination

of the ariables because they are guaranteed neer to occur +on7t cares can be assumed to be either 0 or 1 and that depends if it can aids

to further simplification

$*- t* 9se >a"!a9+6 ma8 t* sim8li5y t6e l*+ic ci"c9its1. 5nter a 1 on the Amap for each fundamental product that corresponds to 1output in the truth table. 5nter 07s elsewhere-. 5ncircle the octets quads and pairs.


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Digital Electronics 13-

III. LOGIC GATES AND OPERATIONS

1. LOGIC GATES ;loc6 of hardware that produces a logic 1 or logic 0 output signal if input logic

requirements are satisfied !sed in digital and switching circuits

)ollows the rule of ;oolean (lgebra

a. AND Gate ( logic circuit where output is high only when all inputs are high represented by

a dot in ;oolean operation

. OR Gate Dogic circuit whose output is high as long as one of its inputs is high and

represented by plus sign in ;oolean operation

c. NOT (I!,e"si*!)



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( gate with only one input and one output&complement' and is represented by a

prime or a bar in logical operation

#. NAND Gate ,omplement of (8+

(bbreiation of 8ot(8+

e. NOR +ate ,omplement of the *< function and its name is an abbreiation of 8ot*a6es use of pchannel enhancement type >*S)5T

0.1 m" approximate power per gate

Slow and delicate

+. Ne+ati,e MOS (NMOS) >a6es use of nchannel enhancement type >*S)5T

0.1 m" approximate power per gate

)aster than ?>*S

6. C*m8leme!ta"y Metal O%i#e Semic*!#9ct*" (CMOS) >a6es use of both p and nchannel enhancement type >*S)5T

Dow power consumption with only 10 n" power per gate

+elicate and sensitie to static electricity

I'. LOGIC CIRCUITS

1. COMBINATIONAL L*+ic Ci"c9its

,onsists of logic gates whose outputs at any time are determined directly from

the present combination of inputs without regard to preious output.

a. $al5 A##e" ?erforms addition of - binary inputs with two binary outputs including the sum

and the carry

. =9ll A##e"( combinational circuit that performs the arithmetic addition of three input bits

&two binary inputs and the preious carry' producing an output that is the sumdigit and a new carry digit

c. Dec*#e"( combinational logic circuit that recognies the presence of a specific binary

number or word ,onerts binary information from n inputs to a maximum of -n unique output

lines



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Digital Electronics 13-1&

#. E!c*#e"( digital function that produces a reerse operation from that of a decoder

Cenerates a number or code in response to an input

e. M9lti8le%e" +ata selector switch

(n electronic switch that permits any one of the number of inputs to be chosen

and routed to the output >ain function is to control the routing of data from one place to another

5. Dem9lti8le%e"( combinational circuit that receies information on a single line and transmits

this information on 1 of -npossible output lines



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2. SEHUENTIAL L*+ic Ci"c9its

5mploys memory elements&binary cells' in addition to logic gates

Their outputs are function of the inputs and the state of the memory elements

Two types of sequential circuit includes synchronous and asynchronous

Sy!c6"*!*9s seF9e!tial ci"c9its are cloc6 controlled to achiee proper circuittiming

Asy!c6"*!*9s seF9e!tial ci"c9itshas no cloc6 input

a. =li8 ?=l*8s(re memory elements capable of storing a bit of information >emory elements present in sequential circuits

(lso called bistable multiibrator

(n external can trigger the output

:t has two outputs that are complement to each other

RS =li8 =l*8

D =li8 =l*8 + latch

5liminate the possibility of race condition

,an be cloc6ed or uncloc6ed



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Digital Electronics 13-13

> =li8 =l*8 :deal memory element when it comes to circuit that counts

(lso it eliminates the undefined state of the


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$*l# Time >inimum amount of time the input signals must be held constant after the cloc6

edge has struc6

Set498 time >inimum amount of time the inputs to a flip flop must be present before the

cloc6 edge arries

P"*8a+ati*! Delay time Time it ta6es for the output of a gate or flip flop to change after the inputs hae

changed

Le,el Cl*ci!+ Type of triggering in which the output of a )G) responds to the leel of the cloc6

signal

Latc6 Simplest type of )G) consisting of - cross coupled 8(8+ and 8*< latches

Maste" Sla,e T"i++e"i!+ Type of triggering using two cascaded latches

>aster for half cycle and slae for the other half

c. Re+iste"s Croup of memory elements that wor6 together as a unit

?rimary purpose is to store a word

B955e" Re+iste"s( register that temporarily stores a word during data processing

S6i5t Re+iste"( register that can shift the stored bits one position to the left or to the right

C*!t"*lle# S6i5t Re+iste" Has control inputs that determine what it does on the next cloc6 pulse

Se"ial L*a#i!+ >eans storing a word in the shift register by entering 1 bit per cloc6 pulse

Pa"allel L*a#i!+ Doading all bits of a word in parallel during one cloc6 pulse

#. C*9!te"s


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C*!t"*lle# C*9!te" ,ount pulses only when commanded to do so

Sy!c6"*!*9s C*9!te"s( counter in which the cloc6 dries each )G) to eliminate the ripple delay

Ri!+ C*9!te"( counter producing words with 1 high bit which shifts one position per cloc6

pulse

UPJDOKN C*9!te" ;idirectional counter can count up or down

P"esettale C*9!te"( counter that allows you to preset a number from which the count begins

e. Mem*"ies "here the programs and data are being stored before operations begin

Rea#JK"ite Mem*"y ?opularly 6nown as emory &'

!ses bipolar or >*S )G)7s for static &S' wherein data will be retained

without the need of refreshing !ses >*S)5TS and capacitors for dynamic &+' whose time interal

to underta6e a refresh operation is a bout - ms @olatile memoriesdata is lost when power is turned off

Rea# O!ly Mem*"y +ata is permanently stored by manufacturer and can be accessed wheneer it

is needed Hold fixed set of data in the circuit

?opularly 6nown as

8on olatile memoriesdata is not loss een the power is turned off

1. Programmable ROM (PROM) (llows data to be written into the deice by a programmer

?rogrammed by blowing fuse using a hardware called ? programmer

2. Erasable Programmable ROM (EPROM) that can be reprogrammed

+ata can be erased by ultraiolet light

3. Electrically Erasable Programmable ROM (EEPROM) 8on olatile li6e 5?



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,an be completely erased or hae certain bytes changed using electrical

pulses

B9le Mem*"y Sandwiches a thin film with magnetic material between two permanent bias

magnets Dogical 17s and 07s are represented by magnetic bubbles in the thin film

C6a"+e C*98le De,ice Solid state memory where 17s an d07s are being represented by the presence

and absence of a charge

N*! ?Semic*!#9ct*" Mem*"ies :ncludes the magnetic core magnetic dis6 magnetic drum and een the ,+

TEST YOURSEL= 15Re,ie- H9esti*!s1. ,onert #.%013 #

a. 10.-/b. #.-/c. #.%d. 1.-/

A!s-e" a. 10.-/

-. "hat is the $7s complement of 104%$Ia. 3$/-$b. %341$



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c. %34-$d. 3$/4$

A!s-e"c. %34-$S*l9ti*!

$7s A?D 3333104% =1 %34-

4. ;inary 111111 is equialent to2a. 3/b. 34c. 1-#d. 1-$

A!s-e" b. 34

/. :n a digital system the number leel is2a. -b. 1c. 4d. /

A!s-e"a. -

%. :n a progression of 0 1 10 11J.what comes next after 11Ia. 1-b. 1-0c. 110d. 100

A!s-e" d. 1008ote2 The succeeding term is binary 1 = preious term of the progression

3. ( logic gate is an electronic circuit which .a. wor6s on binary algebrab. ma6es logical decisionc. alternates between 1 and 0d. allow the flow of current in a single direction

A!s-e"b. ma6es logical decision

$. :f ( 0 ; 0 then (7;7 isa. 1b. 0c. 10d. either 1 or 0



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A!s-e"a. 1

#. :n ;oolean algebra ( =(=(=(=J=( is the same asa. %(b. n(c. (d. infinite

A!s-e" c. (

9. ( = ; K is the ;oolean function fora. (8+ gateb. 8(8+ gatec. 8*< gated. *< gate

A!s-e"d. *< gate

10. "hich of the following is an inerterIa. common base amplifierb. common emitter amplifierc. common collector amplifierd. common gate amplifier

A!s-e"c. common collector amplifier

11. "hich gate corresponds to the action of parallel switchesIa. *< gateb. 8*< gatec. 8(8+ gated. 8ot gate

A!s-e"a. *< gate

1-. The number of full adders in a /bit parallel adder will bea. -b. 4c. /d. %

A!s-e"b. 4

14. ( half adder includesa. a 8(8+ gate with *< gateb. a 8(8+ gate with L*< gatec. only (8+ gated. neither *< nor L*< nor (8+ gate



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A!s-e" b. a 8(8+ gate with L*< gate

1/. ( 8(8+ gate is called a uniersal logic element becausea. it is used by eerybodyb. any logic function can be realied by 8(8+ gates alonec. all the minimiation techniques are applicable for optimum 8(8+ gate realiationd. many digital computers use 8(8+ gates

A!s-e"b. any logic function can be realied by 8(8+ gates alone

1%. The expression (; = (;7 = (,7 = (7,7 will bea. 0b. (c. (;,

d. 1

A!s-e" d. 1

13. The bubble or small circle on the output of a 8(8+ gate and 8*< gate representsMa. additionb. subtractionc. productd. complementation

A!s-e"d. complementation

1$. ,urrent drawn when the number # is on the D5+ display is.a. 1/0 n(b. 1/0N(

c. %30 m(d. %.3 (

A!s-e" a. 1/0 n(

1#. ,urrent displayed for a fourdigit liquid crystal display that reads the number #### is of theorder of

a. %30 n(b. %30 N(c. %30 m(d. -.3 (

A!s-e"c. %30 m(

19. The fan out of a $/00 8(8+ gate isa. - TTDb. % TTD



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c. # TTDd. 10 TTD

A!s-e" a. - TTD

-0. "hat term is used to refer to the positional alue of a digitIa. weightb. radixc. decimald. multiplier

A!s-e"a. weight

-1. The maximum propagation alue in case of a $/00 8(8+ gates isa. 1 secondb. -0 millisecondc. less than -0 nanosecondd. less than -0 picosecond

A!s-e"c. less than -0 nanosecond

--. The refreshing rate of dynamic s is in the range ofa. - microsecondsb. - millisecondsc. %0 millisecondsd. %00 milliseconds

A!s-e"b. - milliseconds

-4. TTD circuit configuration resembles what type of gateIa. *< gate

b. 8*< gatec. (8+ gated. 8(8+ gate

A!s-e"d. 8(8+ gate

-/. 5mitter ,oupled Dogic &5,D' has a ery fast switching speed as compared to the rest of logicfamilies what is then its typical switching timeI

a. % secb. % millisecc. % microsecd. % nanosec

A!s-e" d. % nanosec

-%. Dogic circuits can be sequential or combinational what is the output of a sequential circuitIa. present input statesb. past input states



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Digital Electronics 13-2&

c. future input statesd. past and the present input states

A!s-e"d. past and the present input states

-3. )or a TTD gate the recommended and standard fan out is .a. %b. 10c. 1%d. -0

A!s-e"b.10

-$. ?hanastron is a .a. speed circuit

b. toggle circuitc. data circuitd. delay circuit

A!s-e" d. delay circuit

-#. To represent number // in binary what is the number of bits requiredIa. /b. %c. 3d. $

A!s-e" c. 3

-9. "hen a logic circuit reEects an unwanted signal this is termed as.

a. logic leelsb. noise marginc. power consumptiond. propagation delay

A!s-e" b. noise margin

40. :n a system with >*S deices the main bus loading factor is li6ely to be2a. resistieb. currentc. capacitied. inductie

A!s-e" c. capacitie

41. +ata selector is also called.a. encoderb. decoder



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c. multiplexerd. demultiplexer

A!s-e" c. multiplexer

4-. odule &!D>'a. >ultiplexerb. decoderc. +emultiplexerd. shift register

A!s-e" a. >ultiplexer

4%. :t is an undesirable condition which may exist in a system when - or more inputs changesimultaneously.

a. race conditionb. contestc. drie conditiond. noise immunity

A!s-e"a. race condition

43. "hat is the memory element used in cloc6ed sequential logic circuitIa. gatesb. )lipflopc. Static


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c. relay datad. ma6es decision

A!s-e" a. stores binary data

4#. is not a type of flip flopa.


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b. c. ?

d. 5?

A!s-e" d. 5?

//. :n register index addressing mode the effectie address is gien by2a. index register alueb. sum of the index register alue and operandc. the operandd. difference of the index register alue and the operand

A!s-e" b. sum of the index register alue and operand

/%. The :ntegration :nEection Dogic has higher density of integration than TTD because ita. does not require transistors with high current gainb. uses compact bipolar transistorc. does nor require isolation diffusiond. uses dynamic logic instead of static logic

A!s-e" b. uses compact bipolar transistor

/3. +ynamic uses capacitor as its data storage element while static uses.a. inductorb. registerc. flip flopd. magnet

A!s-e" c. flip flop

/$. (n electronic counter in which bistable units are cascaded to form a loop

a. ring counterb. twisted ring counterc. bistable counterd. !?G+*"8 counter

A!s-e"a. ring counter

/#. This type of memory sandwiches a thin film with magnetic material between two permanentbias magnets

a. bubble memoryb. soap memoryc. magnetic memory

d.

A!s-e" a. bubble memory

/9. ( memory circuit has 9 address inputs has how many storage locationsI



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a. -%%b. -%3c. %1-d. %11

A!s-e" c. %1-S*l9ti*!

O of address -n -9

%1-

%0. The density of data stored on magnetic tape is expressed asa. units per inchb. trac6s per inchc. pac6s per inchd. bytes per inch

A!s-e" d. bytes per inch


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