CS 232: Computer Architecture II

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CS 232 Computer Architecture II

• Prof. Laxmikant (Sanjay) Kale

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CS 232 Objectives

• Learn about how a computer system, and
  specifically its processor, works
• Assembly language programming
• Instruction Set Architecture
• Basic Processor design Data-path and control
• An overview of advanced topics
• with specific topics covered in depth
• Example Pipelining, Caches, I/O, Multiprocessors

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Some of the Dos and Dont

• Must use the class web page regularly
• Important announcements, syllabus, lecture notes
  (slides), assignments
• Also, must read the class newsgroup regularly
• Frequently asked questions
• Timely response
• Make sure you dont post solutions
• No trash tolerated!

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Lets begin with numbers

• Say you wanted to build a machine that calculates
  the exact square of any given number quickly.
• 100 years ago
• May want to use the same idea for other things
• calculate cubes?
• Other number calculations?
• Need to decide
• How are you going to represent the numbers?
• What are you going to build the machine out of?
• Need a basic smart component

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Representing numbers

• Focus on integers
• Examine our decimal number system
• Much nicer compared to roman numbers
• How do you add two large numbers in roman
  representation?
• With weighted positions (ones, tens, hundreds)
  addition is easy.
• In fact, we can describe a simple procedure
  (algorithm) for doing it.
• But choice of 10 as the base is somewhat
  arbitrary
• What base is better for our machine?
• Base 10 need 10 symbols
• Base 2 need 2 symbols (0,1)
• We can probably make machines that can represent
  0 and 1
• so that they dont mix with each other

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Binary number representation

• You have done this in CS231
• 11011 is 27
• 35 is 100011
• Addition and subtraction rules are the same as
  decimal numbers
• Let us agree to use this in our machine
• Still have the problem of having to translate
  between decimal system (that we understand) and
  binary system, that our machine understands
• Assume we will do it manually, for now

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Smart component Switch

• A switch is either on or off
• To really compose switches to build a machine, we
  need to be able to control a switch
• (I.e. if switch A is ON, it will also change
  switch B to the ON position).
• Let us assume we have electricity
• Basics Voltage, Current, Flows if switch is on
• Make a controllable switch
• such that if input voltage is High, the switch
  is ON (closed)
• Let us assume High Voltage represents 1 and
  Low 0.

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Gates

• We can now connect switches together
• Two switches (A and B) connected in series
• If both are ON, the output is HIGH
• So, if the input to both switch A and switch B is
  High, the output of the composite circuit is High
• Let us call this the AND circuit (or AND gate)
• You can also connect switches such that
• If either of the switch is ON, the output is HIGH
• Connect the switches in parallel
• So, if input to A is HIGH or input to B is HIGH,
  output is High AND gate
• NOT gate
• Input High, Output Low, and vice versa

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Gates to Adders

• We can now connect gates together to make an
  adder
• Half adder (ignores carry)
• Given two inputs, if exactly one of them 1, then
  output 1
• Also output carry if both are 1
• How can we connect gates together to make this
  circuit?
• Full adder
• uses carry
• 3 inputs lines, two output lines
• Multi-bit adder
• Feed the carry of least significant bit to the
  next higher one

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So, we have an adder

• But we needed to square a number.
• The adder is just a simple calculating device
• We could connect a lot more of those to make a
  multiplier, or a squarer.
• But, we can reuse the same hardware.
• Challenge just use one adder (say 32 bit adder).
• We need one more type of device
• to store intermediate results
• Memory or registers
• We tell the adder to repeatedly add M to a
  running total.
• So, we need to store the running total and M
  somewhere
• Also need to to remember how many times to add
  (Count)

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What does it look like now?

• We have
• 3 32 bit registers M, result, count
• 1 32 bit adder
• How are they connected?
• We need to bring back M and result to the inputs
  of the adder
• Store the sum back in result
• bring count and 1 to the adder
• store sum in count
• We can use gates to select which register is
  connected to the input of the adder
• Also, must decide when the count has reached M
• How to tell when to connect which input to the
  adder??

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Instructions and Stored Program

• Let us have a control unit
• Tells which inputs are connected,
• Where to store the output
• How does the control unit know what to do?
• Store instructions for it in another set of
  registers?
• What is an instruction?
• Identifies Input registers, and output register

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Let us add memory

• When the amount of data is large
• Cant keep on adding registers
• Memory a linear, random-access storage
• Cheaper, slower than registers
• Now we need to bring the data from memory into
  registers and vice versa