1) There are several algorithms for performing multiplication and division with signed-magnitude numbers, including array multiplication, Booth's multiplication, restoring division, and non-restoring division.
2) Hardware implementations of these algorithms often involve adders, shifters, and correction logic to handle issues like overflow and producing results in the proper number format.
3) Division algorithms in particular require handling issues like division by zero and divide overflow through detection logic and interrupt-driven error handling.
Search techniques in ai, Uninformed : namely Breadth First Search and Depth First Search, Informed Search strategies : A*, Best first Search and Constraint Satisfaction Problem: criptarithmatic
There are situations, called hazards, that prevent the next instruction in the instruction stream from executing during its designated cycle
There are three classes of hazards
Structural hazard
Data hazard
Branch hazard
Computer Architecture refers to those attributes of a system that have a dire...mayurjagdale4
Computer Architecture refers to those attributes of a system that have a direct impact on
the logical execution of a program. Examples:
o the instruction set
o the number of bits used to represent various data types
o I/O mechanisms
o memory addressing techniques
Search techniques in ai, Uninformed : namely Breadth First Search and Depth First Search, Informed Search strategies : A*, Best first Search and Constraint Satisfaction Problem: criptarithmatic
There are situations, called hazards, that prevent the next instruction in the instruction stream from executing during its designated cycle
There are three classes of hazards
Structural hazard
Data hazard
Branch hazard
Computer Architecture refers to those attributes of a system that have a dire...mayurjagdale4
Computer Architecture refers to those attributes of a system that have a direct impact on
the logical execution of a program. Examples:
o the instruction set
o the number of bits used to represent various data types
o I/O mechanisms
o memory addressing techniques
index of all of the financial accounts in a company's general ledger. In shor...mayurjagdale4
index of all of the financial accounts in a company's general ledger. In short, it is an organizational tool that lists by category and line item all of the financial transactions that a company conducted during a specific accounting period
Implementation and Simulation of Ieee 754 Single-Precision Floating Point Mul...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Multiplecation is a costly operation in terms of hardware resources. Booths algorithm is one of the optimization technique which fulills the requirement of efficient multiplication algorithm and reduces the number of oprations and steps requred for multiplication. There are different versions of Booths algorithm and its implementations which try to make it more efficient. One is radix-4 modified booth algorithm.
http://www.siliconmentor.com/
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
2. Eight Conditions for Signed-
Magnitude Addition/Subtraction
Operation
ADD
Magnit
udes
SUBTRACT Magnitudes
A > B A < B A = B
(+A) + (+B) + (A + B)
(+A) + (-B) + (A – B ) - (B – A ) + (A – B )
(-A) + (+B) - (A – B ) + (B – A ) + (A – B )
(-A) + (-B) - ( A + B)
(+A) - (+B) + (A – B ) - (B – A ) + (A – B )
(+A) - (-B) + (A + B)
(-A) - (+B) - ( A + B)
(-A) - (-B) - (A – B ) + (B – A ) + (A – B )
3. Examples
Example of adding
two magnitudes
when the result is
the sign of both
operands:
+3 0 011
+ +2 0 010
+5 0 101
Example of adding two
magnitudes when the
result is the sign of
the larger magnitude:
-3 1 011
+ +2 0 010
-( +3
011
- +2) 010
5. Addition and Subtraction with Signed-
Magnitude Data Hardware Design
A register
AVF
E
Bs
As
B register
Complementer
Parallel Adder
S
Load
Sum
M
Mode
Control
Input
CarryOutput
Carry
6. Summary of Addition and Subtraction
with Signed-Magnitude Data
The signs use an exclusive OR gate where if
the output is 0, then the signs are the same.
Hence, add the magnitudes of the same
signed numbers. If the sum is an overflow,
then a carry is stored in E where E = 1 and
transferred to the flip-flop AVF, add-
overflow.
Otherwise, the signs are opposite and
subtraction is initiated and stored in A.
No overflow can occur with subtraction so
the AVF is cleared.
If E = 1, then A > B.
However, if A = 0, then A = B and the sign is
made positive.
If E = 0, then A < B and sign for A is
7. BCD Adder
Is a circuit that adds two BCD digits in
parallel and produces the sum in BCD.
Correction logic
11. Operation
Decimal digits are added with input
carry with binary adder.
If output carry is zero, nothing is to be
added to the binary sum.
When output carry=1, 0110 is added to
the binary sum through the next adder.
the next output carry can be ignored..
12. Multiplication
• A complex operation compared with
addition and subtraction
Many algorithms are used, esp. for
large numbers
Simple algorithm is the same long
multiplication taught in grade school —
Compute partial product for each digit
— Add partial products
13. Multiplication Example
1011 Multiplicand (11 dec)
x 1101 Multiplier (13 dec)
1011 Partial products
0000 Note: if multiplier bit is 1 copy
1011 multiplicand (place value)
1011 otherwise zero
10001111 Product (143 dec)
Note: need double length result
15. looking at successive bits of the multiplier, least
significant bit first.
If the multiplier bit is a 1, the multiplicand is
copied down;
otherwise, zeros are copied down.
The numbers copied down in successive lines
are shifted one position to the left from the
previous number.
Add these numbers.
16. Array Multiplier
Positive numbers can be implemented
in a combinational two-dimensional
array
Main component of each cell is a full
adder FA
17.
18.
19. Array multiplier is well known due to its
regular structure. Multiplier circuit is based
on add and shift algorithm. Each partial
product is generated by the multiplication of
the multiplicand with one multiplier bit. The
partial product are shifted according to their
bit orders and then added. The addition can
be performed with normal carry propagate
adder. N-1 adders are required where N is
the multiplier length
24. Booths Multiplication
Algorithms
1. The multiplicand is subtracted from the
partial product upon encountering the first least
significant 1 in a string of 1's in the multiplier.
2. The multiplicand is added to the partial
product upon encountering the first 0 (provided
that there was a previous 1) in a string of O's in
the multiplier.
3. The partial product does not change when
the multiplier bit is identical to the previous
multiplier bit.
29. Hardware Implementation for
Signed-Magnitude Data for
restoring divioin
Instead of shifting the partial product to
the right,the divisor and partial product
are shifted to the right.
For subtraction, perform 2’s
complemented addition.
30.
31. Algorithms steps
Do the following n times
Shift A and Q left one binary position
Subtract M from A, and place the answer
back in A.(2’s complement addition of
divisor)
If E=1 A>=B set Qn=1.
Quotient bit 1 is added in Qn bit of partial
remainder and that is shifted to the left.
32. If E=0,A<B so the quotient in Qn
remains a 0.
The value of B is then added to the partial
remainder and is shifted to the left.
Finally, , the quotient is in Q and final
remainder in A.
33.
34. Divide Overflow
Critical when implemented in hardware
The length of the registers is finite and
will not hold a number exceeds its
length.
When the dividend is twice as long as
the divisor, overflow occurs:
If the high-order half bits of the dividend
constitute a number greater than or equal
to the divisor.
35. Division by zero must be avoided.
detected by DVF(divide overflow
flipflop).
36. Handling Divide Overflow
Duty of the programmer
The occurrence of a divide overflow
stopped the computer (divide stop).
Not recommended(time consuming)
Provide an interrupt request when DVF
is set.
Suspend the current program and branch
to a service routine to take the corrective
actions.
37. Corrective measure:
Remove the program and type an error
message stating the reason.
The best way to avoid divide overflow
is use floating point data.