Review CPSC 321

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ReviewCPSC 321

• Andreas Klappenecker

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Administrative Issues

• Midterm is on October 12
• Allen Parishs help session Friday 1015-1215

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Questions? Project partners?
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Todays Menu

• What happened so far...

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History
One of the first calculation tools was the
abacus, presumably invented sometime between
1000-500 B.C.
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Early History

• around 1600, John Napier invents the Napier
  bones, a tool that helps in calculations
• 1621, William Oughtred invents the slide rule
  that exploit Napiers logarithms to assist in
  calculations
• 1625 Wilhelm Schickard invents a mechanical
  device to add, subtract, multiply and divide
  numbers
• 1640 Blaise Pascal invents his Arithmetic Machine
  (which could only add)
• 1671 Wilhelm von Leibniz invents the Step
  Reckoner, a device that allows to perform
  additions, subtractions, multiplications,
  divisions, and evaluation of square roots (by
  stepped additions)

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Early History

• Charles Babbage proposes in 1822 a machine to
  calculate tables for logarithms and trigonometric
  functions, called the Difference Engine.
• Before completing the machine, he invents in 1833
  the more sophisticated Analytic Engine that uses
  Jacquard punch cards to control the arithmetic
  calculations
• The machine is programmable, has storage
  capabilities, and control flow mechanisms it is
  a general purpose computer.
• The Analytic Engine was never completed.
• Augusta Ada Lovelace writes the first program for
  the Analytical Engine (to calculate Bernoulli
  numbers). Some consider her as the first
  programmer.

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Z1

• The Z1 computer was clocked at 1 Hz. The memory
  consists of 64 words with 22 bits. Input and
  output is done by a punch tape reader and a punch
  tape writer.
• The computer has two registers with 22 bits and
  is able to perform additions and subtractions (it
  is not a general purpose computer).

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Z3
(Art and photo courtesy of Horst Zuse)

• Zuse constructed the Z3, a fully programmable
  general purpose computer, in 1939-1941.
  Remarkably, it contained a binary floating point
  arithmetic. It was clocked at 5.33 Hz, based on
  relays, and had 64 words of 22 bits.
• The small memory did not allow for storage of the
  program.

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Performance

• Response time time between start and finish of
  the task (aka execution time)
• Throughput total amount of work done in a given
  time

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Performance
(Absolute) Performance
Relative Performance
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Amdahls Law

• The execution time after making an improvement to
  the system is given by
• Exec time after improvement I/A E
• I execution time affected by improvement
• A amount of improvement
• E execution time unaffected

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Assembly Language
.text code section .globl main main li
v0, 4 system call for print string la a0,
str load address of string to
print syscall print the string li v0,
10 system call for exit syscall
exit .data str .asciiz Hello world!\n
NUL terminated string, as in C
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Things to know...

• Instruction and pseudo-instructions
• Register conventions (strictly enforced)
• Machine language instruction given, find the
  corresponding assembly language instruction
• Code puzzles
• Solve a small programming task

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Instruction Word Formats

• Register format
• Immediate format
• Jump format

op-code rs rt
rd shamt funct
6 5 5 5 5
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op-code rs rt
immediate value
6 5 5 16
op-code 26 bit current
segment address
6 26
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Machine Language
What does that mean?

• Machine language level programming means that we
  have to provide the bit encodings for the
  instructions
• For example, add t0, s1, s2 represents the
  32bit string
• 00000010001100100100000000100000
• Assembly language mnemonics usually translate
  into one instruction
• We also have pseudo-instructions that translate
  into several instructions

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Watson, the case is clear

• add t0, s1, s2
• 00000010001100100100000000100000
• 000000 10001 10010 01000 00000 100000
• Operation and function field tell the computer to
  perform an addition
• 000000 10001 10010 01000 00000 100000
• registers 17, 18 and 8

op-code rs rt
rd shamt funct
6 5 5 5 5
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Number Representations

• Signed and unsigned integers
• Number conversions
• Comparisons
• Overflow rules

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Detecting Overflow

• No overflow when adding a positive and a negative
  number
• No overflow when signs are the same for
  subtraction
• Overflow occurs when the value affects the sign
• overflow when adding two positives yields a
  negative
• or, adding two negatives gives a positive
• or, subtract a negative from a positive and get a
  negative
• or, subtract a positive from a negative and get a
  positive

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Detecting Overflow
Operation Operand A Operand B Overflow if result
AB gt0 gt0 lt0
AB lt0 lt0 gt0
A-B gt0 lt0 lt0
A-B lt0 gt0 gt0
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Logic Design Build ALU, etc.
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Logic Design

• Determine truth tables of combinatorial circuits
• Determine combinatorial circuits from truth
  tables
• Determine critical path
• Overflow detection in ALU

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SLT

• 4 operations
• subtraction output available
• Connect
• MSB set output
• w/ LSB less

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Adders

• Ripple carry
• Carry-lookahead

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Fast Adders

• Iterate the idea, generate and propagate
• ci1 gi pici
• gi pi(gi-1 pi-1 ci-1)
• gi pigi-1 pipi-1ci-1
• gi pigi-1 pipi-1gi-2 pipi-1 p1g0
• 
  pipi-1 p1p0c0
• Two level AND-OR circuit
• Carry is known early!

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Multiplication

• 0010 (multiplicand)
• __ x_1011 (multiplier)
  
• 0010 x 1
• 00100 x 1
• 001000 x 0 0010000 x 1
  0010110

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Booth Multiplication

• Current and previous bit
• 00 middle of run of 0s, no action
• 01 end of a run of 1s, add multiplicand
• 10 beginning of a run of 1s, subtract mcnd
• 11 middle of string of 1s, no action

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Example 0010 x 0110
Iteration Mcand Step Product
0 0010 Initial values 0000 0110,0
1 0010 0010 00 no op arithgtgt 1 0000 0110,0 0000 0011,0
2 0010 0010 10 prod-Mcand arithgtgt 1 1110 0011,0 1111 0001,1
3 0010 0010 11 no op arithgtgt 1 1111 0001,1 1111 1000,1
4 0010 0010 01 prodMcand arithgtgt 1 0001 1000,1 0000 1100,0
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IEEE 754 Floating Point Representation

• Float 1 sign bit, 8 exponent bits, 23 bits for
  significand.
• seeeeeeeefffffffffffffffffffffff
• value (-1)s x F x 2E-127
• with F 1 .ffffffff .... fff
• Double 1 sign bit, 11 exponent bits, 52 bits
  for significand

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Processor

• Be able to build the datapath
• Be able to explain issues concerning datapath and
  control

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Control

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Single- versus Multicycle Processor

• What are the differences?
• What is executed during the 7th cycle?
• How many cycles do we need?

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Summary
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Need for Speed

• You need to be able to answer the question in a
  short time (75 minutes)
• Routine calculations, such as number conversions,
  should not slow you down
• Read the chapters very carefully!
• Many repetitions will help you to gain a better
  understanding