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Topic
Introduction : Functional units of digital system and their
interconnections, buses, bus architecture, types of buses
and bus arbitration. Register, bus and memory transfer.
Processor Organization : general registers organization,
stack organization and addressing modes.
Arithmetic and Logic Unit : Look ahead carries adders.
Multiplication: Signed operand multiplication, Booths
algorithm and array multiplier. Division and logic operations.
Floating point arithmetic operation, Arithmetic & logic unit
design. IEEE Standard for Floating Point Numbers.
Control Unit : Instruction types, formats, instruction cycles
and sub cycles (fetch and execute etc), micro operations,
execution of a complete instruction. Program Control,
Reduced Instruction Set Computer, Pipelining. Hardwire and
micro programmed control: micro-program sequencing,
concept of horizontal and vertical microprogramming.
Memory : Basic concept and hierarchy, semiconductor
RAM memories, 2D & 2 1/2D memory organization. ROM
memories. Cache memories: concept and design issues &
performance, address mapping and replacement Auxiliary
memories: magnetic disk, magnetic tape and optical disks
Virtual memory: concept implementation.
Input / Output : Peripheral devices, 1/0 interface, I/O ports,
Interrupts; interrupt hardware, types of interrupts and
exceptions. Modes of Data Transfer: Programmed W/O,
interrupt initiated /O and Direct Memory Access., vo
channels and processors.
Serial Communication. : Synchronous & asynchronous
communication, standard communication interfaces.INTRODUCTION / PROCESSOR
ORGANIZATION
Computer architecture and Computer
set of rules and methods
that describe the functionality, organization, and *
implementation of computer systems. Some definitions of
architecture define it as describing the capabilities and
programming model of a computer but not a particular
implementation. In other definitions computer architecture
involves instruction set architecture design, micro
architecture design, logic design, and implementation.
‘Computer architecture is a specification detailing how a set
of software and hardware technology standards interact to
form a computer system or platform, In short, computer
architecture refers to how a computer system is designed
and what technologies it is compatible with. As with other
contexts and meanings of the word architecture, computer
architecture is likened to the art of determining the needs
of the user/system/technology, and creating a logical design
and standards based on those requirements.
Data nput Pamary
—+ pata Fiow
Tt Sentrriowwal
EGE ronnica
og of tools available for any operator
ganization will be the way the
ore ehose cataloged tools can be
i 3 of m ‘computers.
Discuss various categories of modern on
y classified by size and
s fc ie overlap :
Bee eal Computer +A smal, single-user computer
rocessor.
opTowerful, single-user computer. A
‘evn personal computer, but it has a
processor and, in general: @
wser computer capable of
‘of users simultaneously.
i ter:
‘owerful multi-user comput
2s nt many hundreds or thousands of
6)
@
Supercomputer
can perform hundi
cae i omputer is a
1 uter and Mainframe : Supercomp'
Supercom Poe one of the fastest computers currently
available. Supercomputers are very expensive and af |
employed for specialized applications that require imment
‘mounts of mathematical calculations (number crunching).
For example, weather foreeasting requires a
Supercomputer. Other uses of supercomputers scientific
Simulations, (animated) graphics, fluid dy
ealeulations, nuclear energy research, electronic design,
and analysis of geological data in_ petrochemic:
‘reds of millions of instructions per
prospecting). Pechaps the best known supercomputer]
‘manufacturer is Cray Research. : i <
Mainframe was a term originally referring to, hi
cabinet containing the central processor unit or “main
Couputer OncANATION AYO ARCHITECTURE
frame" of a room,
emergence of sm
1970s, the tradit
"mainframe computers’
‘mainframes. Nowadays a
expensive computer capable of supporting hundreds, or
éven thousands, of users simultaneously. The chief
difference between a supercomputer and a mainframe is
that a supercomputer channels all its power into executing
|. a few programs as fast as possible, whereas a mainframe
uses its power to execute many programs concurrently. In
some ways, mainframes are more powerful than
"supercomputers because they support more simultaneous
programs. But supercomputers can execute a single
program faster than a mainframe. The distinction between
small mainframes and minicomputers is vague, depending
really on how the manufacturer wants to market its
machines.
Minicomputer : It is a midsize computer. In the past
decade, the distinction between large minicomputers and
small mainframes has blurred, however, as has the
distinction between small minicomputers and
workstations. But in general, a minicomputer is a
multiprocessing system capable of supporting from up to
200 users simultaneously.
Workstation’ : Tt is a type of computer used for
engineering applications (CAD/CAM), desktop publishing,
software development, and other types of applications that
require a moderate amount of computing power and
relatively high quality graphics capabilities. Workstations
generally come with a large, high-resolution graphics
sereen, at large amount of RAM, built-in network support
and a graphical-user interface. Most workstations also
have a mass storage device such as a disk drive, but a
special type of workstation, called a diskless workstation,
comes without a disk drive. The most common operating
systems for workstations aré UNIX and Windows NT. Like
personal computers, most workstations are single-user
‘computers. However, workstations are typically linked
together to form a local-area network, although they can
also be used as stand-alone systems.[LGD ron ica
signed for an
rs range anywhere
“je to over five thousand pounds.
ccroprocessor technology that
van entire CPU on one chip.
onal -computers for word processing,
Fktop publishing, and for running
ee and database management applications. At
saa most popular use for personal computers is for
tec and recently for surfing the Internet.
computers first appeared in the late 1970s.
st and most popular personal computers was
duced in 1977 by Apple Computer.
‘Qs and early 1980s, new models and
competing operating systems seemed to appear daily.
‘Then, in 1951, IBM entered the fray with its first personal
Computer, known as the IBM PC. The IBM PC quickly
fecame the personal computer of choicé, and most other
personal computer manufacturers fell by the wayside
Pc. zs short for personal computer or IBM PC. One of the
few companies to survive IBM's onslaught was Apple
Computer, which remains « major player in the personal
compute: marketplace. Other companies adjusted to TBM's
Guminance oy building IBM clones, computers that were
~ almost the same as the IBM PG, but that cost
ess » [BM clones used the same microprocessors as
IBM PCs, they wore capable of running the same software.
Over the years, IBM has lost much of its influence in
rng the evalution of PCs. Therefore after the release
the first PC by IBM the term PC increasingly came to
jnean IBM or IBM-compatible personal computers, to the
exclusion of other types of personal computers, such as
Macintoshes, In recent years, the term PC has become
more end more difficult to pin down. In general, though, it
applies to any personal computer based on an Intel
microprocessor, or on an Intel-compatible microprocessor.
For nearly every other component, including the operatin
system, there are several options, all of which fall und ©
the rubric of PC
Today, the world of personal computers is basically
divided between Apple Macintoshes and PCs. The principal
intern
Jess, Beca
CouruteR Oxctnzaron ns Ancyarecrune ‘
Aa
characteristics of porsonal computers
However, although personal computers are designed. as
singlowrer astm is common to link them together
a network. In terms of power, there is gre
variety, At the high end, the distinction bethec herent
computers and workstations has fade, Highnd models of
the Macintosh and PC offer the same computing power and
graphics capability as low-end workstations by Sun
Microsystems, Hewlett-Packard, and DEC.
3. A digital computer has a common bi
i -ommon bus system for 16
registers of 32 bit each. The bus istructe
eens is constructed with
() How many selection inputs are there ii
multiplexer (MUX)? eer
(2) What size of MUXs are needed?
(8) How many MUXs are there in the bus?
Show the organization of the bus for the above.
st
80
aatcfeaaltient teat
Bus
(Figure)
Numerical Solution :
(1) 6 zegisters = 2!= 4 selection inputs
(2) 16 registers = 16 x 1 line multiplexers
(3) 32 bits / register = 32 multiplexers
Discuss the functions of Program counter,
Stack pointer and Flag register.
© What is the use of the following registers?GG osc,
@
a
@)
Program Cout
0 perform. An
puter processor
jer, an address is a
A register is
processor uses
‘Some engineers refer to a program co
n address register or an address ;
stack pointer is a small register
stores the address of the last program request in
‘A stack is a specialized buffer which stores
and the program
re atack (also called a pushdown stack) operates
in a last-in/first-out sense. When a new data item is
entered or "pushed" onto the top of a stack, the stack
pointer increments to the next physical memory
address, and the new item is copied to that address.
When a data item is "pulled" or "popped" from the top
of a stack, the item is copied from the address of the
stack pointer, and the stack pointer decrements to
the next available item at the top of the stack.
Instruction Register : An instruction register is an
clement in the central processing unit (CPU) of
computer or other device that holds the programming
COMPUTER ORGANZATON AND ARCHETECTURE
eee an
1s are given to the
nother part of the CPU
r, which serves a very
vad to the next
le information the instruction register
holding is executed,
(4) Accumulator : An accumulator is a register for
short-term, intermediate storage of arithmetic and
logic data in a computer's CPU (central processing
). The term "accumulator" is rarely used in
reference to contemporary CPUs, having been
replaced around the turn of the millennium by the
term “register.” In modern computers, any register
can function as an accumulator.
The most elementary use for an accumulator is
adding @ sequence of numbers. The numerical value
in the accumulator increases as each number is
added, exactly as it happens in a simple desktop
calculator (but much faster, of course). Once the sum
has been determined, it is written to the main
memory or to another register.
The term “accumulator” is used in a wide variety
of non-computing applications and activities, such as
electrical engineering (an energy storage device such
as a recharge able battery or ultra-capacitor
hydraulics (a mechanical energy storage device), in
stock trading (a contract or agreement), and even in
‘gambling (a parlay bet).
Function of Flag Register : The flags register is the
status register in Intel x86 microprocessors that contains
the current state of the processor.Coupuren Oncaniza’
OncANZATION Ao ARCHITECTURE
wa
Jain the block diagram of a
(2017-18)
Draw and ex d
computer with 5 functional units.
A computer can process data, pictures, sound and
cv can solve highly complicated problems
and accurately. A computer as shown in Figure
forms five major computer operations or
Jone irrespective of their size and make, ‘These are
Tr accepts data or instructions by way of input,
It stores data,
It can process data as required by the user,
It gives results in the form of output, and
It controls all operations inside a computer.
We discuss below each of these Computer operation :
(2) Input : This is the process of entering data and
programs in to the computer system. You should
[now that computer is an electronic machine like any
other machine which takes as inputs raw data and
performs some processing giving out processed data.
Therefore, the input unit takes data from us to the
computer in an organized manner for processing.
(2) Storage : The process of saving data and instructions
permanently is known as storage. Data has to be fed
yhe actual processing starts. It
into the system before tl
is because the processing speed of Central Processing
Unit (CPU) is 60 fast that the data has to be provided
to CPU with the same speed. Therefore the data is
first stored in the storage unit for faster access and
processing. This storage unit or the primary storage
Br ehe computer system is designed to do the above
functionality. It provides space for storing data and
instructions.
‘The storage unit per!
functions :
(a) All data and instructions are
and after processing.
(b) Intermediate results of processing are
here.
(3) Processing : The task of performing operations like
arithmetic and logical operations is called processing.
‘The Central Processing Unit (CPU) takes data and
instructions from the storage unit and makes all sorts
oy)
graphics.
forms the following major
tored here before
also stored
tructions given and
Tt is then sent back to the
(4) Output : This is the proce:
ante cess of producing results
fom for gotting useful inf
similarly the output produced mputer afte
processing must lao be kept eomewhons werd ar
computer before being iven to eauiayiaeas
lable form. Again the output is also stored inside
co ecampster or ther preening ieee
Control: The manner how iastrictions are executed
{and the above operations ate performed. Contoling
ll eperation like input, processing and output,
performed by control unit. Tt takes eare of step by
step processing ofall operations inside the comparer,
In order to carry out th
1 operations mentioned in above
computer allocates the task between its waroua fnew
its. The computer system is divide c
units for its operation. ie eee ceo
Logical Unit : After you enter data through the input
device iti lord in the primary storage vit, The actual
sing of the data and instruction are performed &
rion are performed
Arithmetic Lgieal Uni, The major operations performed
by the ALU are addition, subtraction, multiplication,
vision, logic and comparison. Data is transferred to ALU
from storage unit when required. After processing. the
output is returned back to storage uni
processing or getting stored. 7 ag
Control Unit (CU) : The
(CU) : The next component of computer is
the Control Unit, which at ike the suprvisor seing that
things are done in proper fashion. Control Unit is
responsible for coordinating various operations using time
signal, The control unit determines the sequence in which
computer programs and instructions are executed. Things
like processing of programs stored in the main memory,
interpretation of the instructions and issuing of signals for
other units of the computer to execute them. It also acts as,
‘a switch board operator when several users access theWhat are Registers?
purpose resistera used
Explain general
central processing
4 "i of
is Register? Explain different types
irs seer eorking. of there registers also
ao ne effect of number of registers and tl
igth of register.
7 by
processor memory of a CPY is served
of the key differences itiong various
rogister sots. Some
e whole,
ane “ay be classified under two basic
: i jistere
ca Je Register : These regist
“Framer vse, Reese The i
programmers to minimize the references to main
memory.
«
a
@)
ie Registers : The ger
for various functions desired by the
irpose register can contain
calculations of address of
code of an instruct
‘ated to floating point
ines, the
pers
ta reginters are used only for
iate results or data, These data
registers are not used for tho
ister may be a general
Purpose register, but some dedicated address register
are also used in several machines, Examples of
dedicated uddresa registers can be :
Segment Pointer : Used fo point out a segment of
memory.
Index Register
addressing scheme,
Stack Pointer : (When programmer visible stack
+ ‘These are used for index
+ The issue related to the
register set design is the number of general purpose
registers or data and address registers to be provided
in a micro-processor. The number of registers also
affects the instruction design as the number of
registers determines the number of bits needed in an
instruction to specify a register reference, In general,
it has been found that optimum number of registers
ina CPU is in the range 8 to 32. In case registers fall3 jisters are used. These
as of aractoristics. Reduced
= (RISC) exhibits this
co of having less
red for memory
‘execution of a program,
foe important characteristic
randire’
ter Length : Anotl
use.
‘maxim
coeke jong enough to hold the ma
neetble Pee ‘Similarly, the length of ee
possi should ough to hold the data types
a d to hold. In certain cases, we
ee vopistere may be used to hold data w
sonra aeuibensearinge
dition Code Registers : de
(9) Condit only be. partially avaiable to the
reeryammers, ‘These registers contail 3
Perce also known a8 ‘Those fags re
comes wine CPU hardware while performing
‘n addition operation may,
peration. For example, an_ addition operates Fe
codes are collected
ne or more registers. RISC machines have several
in one or more
set of conditional code bits. In the
instruction specifies the se
is to be used. Independent 0
‘enable the provisions of ‘having paral
instruction exocution unit,
register + 2
Stina several registers are used: These rested
tT used in data manipulations; ywever,, Hy
caniot OF come of these registors can be sed yt
rogrammer. Some of the control register for 0
Neumann machine can be the Program anor
Memory Address Register (MAR) and Data Regis! j
For control of various
ouputen ORGAWZAHON ao ARCHTECTURE tas
a——ramee aa
Almost all the CPUs have status register, a part o
sthich may be programmer visible. A register which es bo
formed by conditions codes Ned conditions code
register. Some of the commonly used flage or condition
codes in such a register may be
Sign Flag : This indicates whether the sign of previous
arithmetic operations was positive (0) or negative (1)
Zero Flag : This fag bit will be set if the result of last
arithmetic operations was zero.
Carry Flag : This is set, if a carry results from the
addition of the highest order bits or a borrow is taken on
subtraction of highest order bit.
Equal Flag : This bit fag will be sot if a logic comparison
operation finds out that both of its operands are equal
Interrupt : This flag is used for enabling or disabling
interrupts,
Flag Supervisor : This flag is used in certain computers
to determine whether the CPU is flag executing in
supervisor or user mode, In ease, the CPU is in supervisor
mode it will be allowed to execute certain privileged
instructions,
In most CPUs, on encountering a subroutine call or
interrupt handling routine, it is desired that the states
information such as conditional codes and other register
information be stored and restored on initiation and end of
these routines respectively. The register often known as
Program Status Word (PSW) contains conditions eode plus
other status information. There can be several other status
and control registers such as interrupt vector registers in
the machines using vectored interrupt, stack pointer if a
stack is used to implement subroutine calls, ete.
The status and control register design is also
dependent on the Operating Systems (OS) support, The
functional understanding of OS helps in tailoring the
register organization. In fact, some control information is
only specific use to the operating system.
‘One major decision to be taken for designing status
and control registers organization is : How to allocate
control information between rogisters and the memory.
Generally, first few hundred or. thousands words of
memory are allocated for storing control information. It is
the responsibility of the designer to determine how much_ GEM Forma
n rogisters and how much in.
eoff between the cost and the
Cowruten Onaaezntion 0 Aneecr
c tA19)
MOV ks, #
ADD R3, 6
DIV ii, Ra
rithme MOV X,R1
Te Write a program to evaluate the 4 ithmetic oy NON
statement . LOAD D
a A-B+C*(D*E-F) (2018-19) MULE
G4 HFK 7 SUBF
(a) Using general register computer with OLA
three address instruction. : STORET
(2) Using general register computer with 490 LOAD A
‘ess instruction. SUBB
@ 1g general register computer with one ADD T AC—AC+ M7]
ness instruction. Fee STORET ances
@ Write « program to evaluate the arithmetic ROADIE, ri
statement: : MULK ACH
X=(A-B+ 0" D*E- PG + HE ADDG aoe = iMG
Using a general register computer with 1100 STORE X 4] AC
adress instruction. 01617) LOAD 7 AG
Divx AC — AC) 32]
yy AcBeCND*E-P) storex my ao
ir G+H*K a :
(2) Three-Address Instruction + seuss immediate addressing with le.
SUB Ri, A, B Rie MA] - MIB) a : “oan
MUL R2, D, E ‘R2— MUD) * MIB) © Explain different tynes of displacement
SUB R2, R2, F Ra R2— MIA addressing modes with examples. (2020-21)
MUL R2, R2, C R2— R2* MIE) ‘@ Explain Addressing es
ADD RI, Ri, R RUC EIS Re types. Design ¢bit Bidivouttonel ait egie
MULRO, HK Ro- MUM" MK) it bi-directional shift register.
ADD R2, G, R2 R2— M{G] + R2 (2018-19)
DIVX, RI, RY ‘MIXI— RIR2 REET
The program using general register computer with
two address instruction is as follows =
(2) Two Address Instructions
‘The operation field of en inst
Id of on instruction specifies the
operation to be performed. This operation will be executed
on some data which is stored in computer registers or the
MOV RIA Rie MA} ‘main memory. The way any operand is soleet
SUB Ri, B Ric R1-MIB} proptam exozcion i depenienton tne at erian ane
MOV #2, D F2
specified address to the
instruction has the format
POP
stack. The POP24
[EGE ronmica
CowPUTeR ORGANZATION ANO ARCHMTECTURE A295
SPE SP
Spe
13. Explain how processor responda to an interrupt,
(2011-12)
wet ca) vo species eres
swe the effects of these two operatior
‘The POP operat
aTopetstack
(Figure)
vantages : i
@ ‘Sfhelent computation of complex arith
expressions. ie es
to) Exvcutve of instructions is fas, rome crore
(©) Tits are etored in eoncecative memory loca :
(c) Since instructions do not have address field, the
length of instructions i short
Disadvantages : Program size lengthens.
12.
an address space is specified by 24 bits and
esponding memory space by 16 bits:
Gy "How mony words ere there in the address
(2) Hoe many words are there tn the memory
space?
(3) If @ page consists of 2K words, how many |*
there in the system?
pete Se ee (2010-11, 2011-12)
24= 16M words
(2) Memory space = 16 bits, 21° = 64 K words
(1) Address space = 24 bits,
Maskable Interrupts allow a programmer to specify that
the CPU does ignore it, while Non-Maskeable Interrupt
Tequests must be serviced.
1s is important to note that an Interrupt is a way to
{ummunicate asynchronously with the CPU - very much
like sending an email.
When you send an email to a person, you cannot
know at which time the person reads the message, let
~ alone when the person reacts,
A phone call, on the other hand is synchronous
(happening at the same time): when I eall you, you nace
answer right now.
Interrupts where introduced to allow tg is emaillike
Themunication with slower hardware, like a hard-disk,
‘This way, the CPU can order something from the HD lice
jf to this location’, the CPU can then return to more
f portant stuff, while the HD seeks. When the HD is done,
it sende the CPU an IRQ, which tells the CPU “I an done,
talk to me”,
all the data it was working on earlier in some secure
112% normally on the stack and then begin to execute
the so-called Interrupt. Handler, a piece of
associated with the number of the
After executing it, it can carry on doing what it did
earlier (after having loaded all the data back into its
registers).[EGE ror mica
Computer OncavizAnion avo ARCHIE
Local Bus
in each field of the [Networ tC
rand give a general encoding | ay ls =a =
| a
that specify the le Cisse]
Eipanson Be
(Figure)
High Performance Hierarchical Bus Ar
Q) Incorporates a high-speed bus specific
support high-capacity 1/0 devices,
(2) Bring high-demand devi
RnE high
stack and that
‘The stack pointe!
zero, the stack is empty,
|
receives the I
erroneous operation Ww:
FULL = 1 or popped w!
a
ARITHMETIC AND
nce
1. Show the block di
loge sie nt nd cleo expla is fase
sie ‘plain its functional
@or12)
TSE Cn
Bo ereea| design of arithmetic and logic circuits
ferasinnle ALU. Dy combining both circuits with the help
of multiplexer we can got the arithmetic and logic cireuit
as ghown in the Fig. The Fig. chows one stage of
sic shift unit, The subscript 1 designates a
typical stage. Inputs A.
arithmetic i are applied to
tenet and oie unite Inputs Sand Se aed
‘a particular micro-operation. jo sre-uused to
PLLE
{=} One stage of.
arithmetic circuit [%
is (Faure 1 One Stage Logic Shift Circuit)
woe Ad multiplexer at the output chooses between ai
ic output in ¥; and a logic output in Zi. The data inKGB ron ica
for ehift left operation and Av for shift |
‘rtant to note that the diagram |
shows just one typical stage. The circuit |
ge must be repeated n times for an n-bit |
ave ALU, the output carry of a previous
must be connected to the input carry C; of |
performed using ‘arithmetic logic shift circuit)
how in Fig.
Function Table For Arithmetic Logie Shift Circult
Subject inputs ‘Operation Function zi er
STS | S| S| ee (igure)
3 F=R Transtar
eee lol tl reas Increment A How the fast adders are designed? Discuss.
spetett Lo | Fars | Add Aang. (2020-21)
o SPT) FSAe Bet | Aaa A ond B wih
: @) A carry-look ahead adder (CLA) or fast adder is a
B type of adder used in digital k
a ary ital logic.
EALe (@) Acarry-look ahead adder improves speed by reducing
TTO Tt} oO] 1 | Feasiet the amount of time required to determine carry bits.
Tpept[ap oy} Feat Decrement (Ie can be contrasted wi
apetatay4 Zz Transfer A Hipple-carry adder
opr polo] x] FA AB ‘AND, calculated aloi bit, and each stage
Shown in” the Table first eight| wait unt previous carry bit has been
calculated to begin calculating its own sum bit and
operation are arithmetic operations and are selected when}
S,S,=00. The next four are logic operatio
and are selected when S,$)=01. The last two operations}
‘are chift operatins and are selected when S,S,=10
and $,S,=11. The carry inputs has no effe
during logic and shift operations and hence marked
don't care.
Design the 16-bit Carry Look-ahead adder using|
four 4-bit Carry Look-ahead adders you have
discussed. (2010-11) |
carry bit.
() The carry-lookahead adder eal
carry bits before the sum, which reduces the wait
time to calculate the result of the larger-value bits of
the adder
(5) Accarry-Lookahead adder is « fast parallel adder as it
reduces the propagation delay by more complex
hardware, hence it is costlier.
(8) This method makes usinal
© IEEE standards for floating}
also represent the floating}
1.01101x2" in IEEE. single!
point number
ae
‘rds for representing floating point nur
shave been developed by the instil
of electrical and electronics engineers, referred to as, IEEH
754 standards. Figure shows these IEEE standard form
Single Precision :
}&-———— 2 bits ——
0
M
25-bit
CCouPuTER ORGANZANON 210 ARCIETECTURE ea
Double Precisi
Value Represented = =1
Numerical Solutio
precision format éan bs
mx 2e=+(0.10110
Representation in IEEE Single Pri
Precision Format :
@) 179.125810
179),9=(10110011),
(125810), =(.0010),
=(10110011.9010),
in IEEE single
10110011.0010=1.01100110010«2"
Now represent the above floating point in
single precision & double precision.
Single Precision :
From the above floating point
‘s=0
E=7
‘M= 01100110010
‘The modified exponent F = 127 +E
= 127+ 7= (310
= (10000110)2
Number in single precision format
s1e[w
To an Be
10 [roooorro[ orrc0110070....0]
(Figure)
‘Double Precision :
S=0
E=7
+ M= 01100110010f
Bs
THOOHOOTS
(Figure)
1001110001110.01
=(L111001110
00111001195 x 28
joort100071700111..0]
23
(Figure)
$=0,E= 10011100011100111
E’=E + 1023 = 15 + 1028 + 1038
= (10000001110)2
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Explain how Booth’s algorithms is suitable for}
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to conventional shift an oneal
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algorithm, and also multiply the two numbers)
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Booth’s Algorithi
for multiplying binary integers in signed 2's complement
representation. A powerful algorithm for signed number
multiplication is a booth’s algorithm, which generates a2 n
bits product and treat both positive and negative number
uniformly. In general for Booth’s algorithm recoding
scheme can be given as : “-] times the shifted multiplicand
is selected when moving from 0 to 1, +1 times the shifted
when moving from 1 to 0, and 0
iplicand is selected for none of the
seanned from rig