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 OR 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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How to make registers

• Switches can be connected to make a memory device
• Latches and Flip-Flops

Reset
NOR
NOR
Set
A register is a set latches grouped together
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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 multiplexers
• Also, must decide when the count has reached M
• How to tell when to connect which input to the
  adder??

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Multiplexers

• Multiplexers connect one of their inputs to the
  output,
• and allow one to choose which ones to select
• can be implemented with gates as well

Input
Control
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Instructions and Stored Program

• Let us have a control unit
• Tells which inputs are to be 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,

Instructions
Multi plexor
Registers
Adder
Control Unit
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The SIS CPU
Registers
Multi plexor
Adder
Instructions memory with multiplexor
Multi plexor
PC Program Counter
Control Unit
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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

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The SIS CPU
Data Memory
Registers
Multi plexors
Adder
Instructions memory with multiplexor
Multi plexor
Load and Store Unit
PC
Control Unit
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The instruction set so far

• Add R1, R2, R3
• Add contents of registers R1 and R2 and store
  result in R3
• Load R1, R2
• Load contents of R2 with memory location
  indicated by R1
• Store R1,R2
• Store contents of R2 in memory location indicated
  by R1
• Need to decide when to stop adding (for squaring)
• It suffices to compare two registers, and change
  PC based on the result
• BEQ R1,R2, R3
• If contents of R1 and R2 are identical, change PC
  to contents of R3

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A few more instructions

• Loading fixed numbers into registers
• have to be careful instructions have only 16
  bits, of which 4 are opcode
• LoadThis R1, Data
• It is called LoadImmediate (LDI R1, Data)
• Data can be 8 bits only
• Where does it go? In the lower order 8 bits of
  the register?
• A couple more branching instructions
• BNE R1, R2, R3 // branch to R3 if not equal
• BR R1 // unconditional branch

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The machine language

• Each instruction is
• 16 bits
• 1 3-4 bit field to specify operation (need only 3
  for now)
• 3 4-bit fields to identify operand registers
• Assign meanings to opcode bit combinations

0001 Load 0010 Store 0011 Add 0100 BEQ 0101
BNE 0110 BR
1000 Input 1001 Output 1010 LDI 1011 SetZero
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The squaring program

• Read N
• and output square of N

Input R1 setzero R2 // count 0 setzero R3 //
result 0 LDI R5, 00001010 // ten LDI R4,
00000001 // R4 has one add R1, R3, R3 ADD R4,R2,
R2 BNE R1,R2, R5 Output R3 Stop
0 2 4 6 8 10 12 14 16 18
1000 0001 xxxx xxxx Complete the program
Question is this program correct? Check it and
report correct if needed
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The point of this exercise

• Get the big picture
• Bottom up
• we know exactly how the whole machine works,
  assuming only that a controllable switch is
  available
• The entire machine architecture, with all the
  fundamental components is introduced in a simple
  setting
• A simpler machine language to get you started
• Later (soon!)
• We switch to a real machine language (MIPS, in
  Chapter 3)
• Chapter 3 is about instruction set architecture,
• So we will then ignore how it can be implemented
• return to implementation in Chapter 5

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Another program

• Suppose we want to print squares of M numbers,
  starting with N
• input sequence 5, 3
• output sequence 25, 36, 49
• Write in Higher language
• Then
• convert to symbolic lang.
• then to machine language
• We will program in
• The symbolic language
• Called the assembly language
• Assemblers translate this

Higher level language read n, m x n while
(xltm) r0 c0 while (c!x) r
rx c c1 output r x x1
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Printing a range of squares
Higher level language read n, m x n while
(xltm) r0 c0 while (c!x) r
rx c c1 output r x x1
Input R1 // n is in R1 Input R2 SetZero R3 Add
R3,R1,R3 // x n SetZero R4 // r0 SetZero R5
// c 0 add R4, R3, R4 // r rx LDI
R6,00000001 // R6 has 1 add R6,R5, R5 //
cc1 LDI R6, 00001010 // branch destn. BNE
R3,R5, R6 ... ...
0 2 4 6 8 10 12 14 16 18 20 22 24