CDA 3101 Spring 2001 Introduction to Computer Organization

CDA 3101 Spring 2001 Introduction to Computer Organization

CDA 3101 Summer 2007 Introduction to Computer Organization Division 14 June 2007 Review Multiplication can be implemented using simple shift and add hardware Algorithm is similar to the grade-school method Booths algorithm for twos complement Handles all cases of positive/negative operands More efficient than conventional algorithm 2n + 2n-1 + 2n-2 + + 2k = 2n+1 - 2k Further optimization is possible MIPS multiply instructions ignore overflow Multu: Hi = 0 Mult: Hi = replicated sign of Lo Division Long division of unsigned binary integers 00001101 Divisor Partial remainders 1011 10010011 1011 Quotient Dividend

001110 1011 001111 1011 100 Remainder Dividend = Quotient x Divisor + Remainder Unsigned Division M Divisor Q Dividend Count n, A START 0 Shift left: A, Q A A-M No Q0 A < 0? Yes 1 A Count No Q0 0

A+M Count - 1 Count = 0? Yes END Quotient in Q Remainder in A Division Hardware Divisor M31 M0 32-bit ALU 4 Add 2 Subtract 4 write 0 4 write 1 Control 1 SLL 3 ... A31 ... A0 Q31

... Dividend Q0 Examples 7/3: A 0000 0000 1101 0000 0001 1110 0001 0011 0000 0000 0001 1110 0001 Q M = 0011 0111 Initial values 1110 1110 1110 1100 1100 1100 1000 1000 1001 0010 0010 0010

Shift A=A-M A=A+M 1 Shift A=A-M A=A+M 2 Shift A=A-M Q0 = 1 3 Shift A=A-M A=A+M 4 Signed Division Simplest solution Negate the quotient if the signs of divisor and dividend disagree Remainder and dividend must have the same signs Remainder = (Dividend Quotient * Divisor) (+7) / (+3): Q = 2; R = 1 (-7) / (+3): Q = -2; R = -1 (+7) / (-3): Q = -2; R = 1 (-7) / (-3): Q = 2; R = -1 Signed Division Algorithm A, Q Dividend M

Divisor, Count START Shift left: A, Q A31, Count Count - 1 S A A+M No No Restore A No n M31 = A31? S = A31? A A-M Yes Yes A=0 and Q=0 ? No Yes

Count = 0? Yes Q0 END 1 Quotient in Q Remainder in A Examples (1/2) A 0000 0000 1101 0000 0001 1110 0001 0011 0000 0000 0001 1110 0001 Q M = 0011 0111 Initial values 1110 Shift Subtract Restore 1

1110 Shift 1100 Subtract 2 Restore 1100 1000 1001 0010 Shift Subtract Q0 = 1 Shift Subtract Restore 0010 (7) / (3) 3 4 A 0000 0000 1101 0000 0001 1110 0001 0011 0000 0000 0001 1110 0001 Q M = 1101

0111 Initial values 1110 1110 1100 1100 1000 1001 0010 Shift Add Restore 1 Shift Add Restore 2 Shift Add Q0 = 1 3 Shift Add Restore 4 0010 (7) / (-3) Examples (2/2) A 1111 1111

0010 1111 1110 0001 1110 1100 1111 1111 1111 0010 1111 Q M = 0011 1001 Initial values 0010 0010 0100 0100 1000 1001 0010 Shift Add Restore Shift Add Restore Shift Add Q0 = 1 Shift Add Restore 0010 (-7) / (3) 1

2 3 4 A 1111 1111 0010 1111 1110 0001 1110 1100 1111 1111 1111 0010 1111 Q M = 1101 1001 Initial values 0010 0010 0100 0100 1000 1001 0010 Shift Subtract Restore 1 Shift Subtract Restore

2 Shift Subtract Q0 = 1 3 Shift Subtract Restore 4 0010 (-7) / (-3) MIPS Multiply and divide use existing hardware ALU and shifter Extra hardware: 64-bit register able to SLL/SRA Hi contains the remainder (mfhi) Lo contains the quotient (mflo) Instructions Div: Divu: signed divide unsigned divide MIPS ignores overflow ? Division by 0 must be checked in software MIPS Processor Registers 32

0 Sign extend 16 1 IR: M Sub ALU Operation Control Unit Zero Overflow 0 1 Hi 2 Memory address Lo SLL/SRA Have a Great Weekend!!

Recently Viewed Presentations

  • U.S. Department of Labor Workforce Integrated Performance System

    U.S. Department of Labor Workforce Integrated Performance System

    Users should submit all support request through the requested ticket submission template (shown next slide). All emails will be answered by the Level 1 support team or triaged out to the appropriate Program and Technical points of contact when necessary....
  • Chapter 11 Section 1 - North Allegheny

    Chapter 11 Section 1 - North Allegheny

    Examples. Fishes, Amphibians, Reptiles. Birds,Mammals. Definition. an animal whose body does not produce much internal heat, body temperature changes depending on temperature of environment. An animal whose body regulates it own temperature by controlling the internal heat it produces, body...
  • Science Fiction

    Science Fiction

    Dystopian Film This sub-genre often holds the same themes and characteristics of a post-apocalyptic film. Generally, the common themes within Dystopian films include dehumanization, the repression of individuality, and uniformity at the cost of human rights. Examples: V for Vendetta,...
  • SCM and Logistics Dickson K.W. Chiu PhD, SMIEEE,

    SCM and Logistics Dickson K.W. Chiu PhD, SMIEEE,

    SCM and Logistics Dickson K.W. Chiu PhD, SMIEEE, SMACM Text: Ballou - Business Logistics Management, 5/E (Chapter 1) Learning Objectives To familiarize with basic concepts of logistics and supply chain management To understand recent evolvement of logistics To understand the...
  • Diabetes and Reproductive Health: Pharmacological Treatment ...

    Diabetes and Reproductive Health: Pharmacological Treatment ...

    Share the definition of a migraine with aura: Recurrent attacks, lasting minutes, of unilateral fully reversible visual, sensory or other central nervous system symptoms that usually develop gradually and are usually followed by headache and associated migraine symptoms. From international...
  • Schizophrenia

    Schizophrenia

    The Million Dollar Question. We believe that mental illness is a brain disorder, although there is evidence that our immune systems, our hormone levels, inflammation, heart disease, cancer, and even the bacteria in our gut can affect our moods and...
  • ETHICS CONSIDERATIONS IN A SOCIAL MEDIA WORLD Liz

    ETHICS CONSIDERATIONS IN A SOCIAL MEDIA WORLD Liz

    Model Rule 8.2(a) states: A lawyer shall not make a statement that the lawyer knows to be false or with reckless disregard as to its truth or falsity concerning the qualifications or integrity of a judge, adjudicatory officer or public...
  • Soc3306a - University of Western Ontario

    Soc3306a - University of Western Ontario

    Soc3306a Individual Assignment 6