CSI 1101 Lab

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CSI 1101Lab 11 April 4, 2003

• Romelia Plesa
• rplesa_at_site.uottawa.ca

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Agenda

• A9 discussion
• Assembly language
• Switching Algebra
• Assignment 10 discussion

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Assignment 9

• Any Questions?
• Solution
• http//www.site.uottawa.ca/turcotte/teaching/csi
  -1101/assignments/09

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Assembly language

• High level language C, Java, etc
• Low level language
• Assembly language
• Close to the instruction set that the hardware
  can execute.
• Programs are highly dependent on the type of
  processor, and cannot be ported to another
  computer.
• Situations where assembly language is used
• writing drivers
• mix with high level code, the critical parts are
  written in assembly language directly to achieve
  greater speeds (not so true with modern
  compilers)
• writing compilers (back-end) necessitates
  knowledge of the assembly language of the machine
  for which the compiler is written.
• Machine code Number representation of
  instruction and data

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TC-1101 Instruction Set
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Assembly language

• one instruction per line
• mnemonics replace instruction codes
• instructions can be designated by labels
• allows for comments generally prefixed by
• Format of a line
• starts with an optional label
• followed by the mnemonic of the instruction
• followed by a symbolic name for the operand
  (optional, depends on the instruction)

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Machine code

• Reading programs
• Since the instructions and the data are both
  represented as numbers (same format) we cannot
  distinguish one from the other.
• Some instructions have an operand others not,
  this makes it difficult to identify the start and
  end of an instruction.
• Writing programs
• Instructions are using absolute addresses, any
  change to a program implies several changes
  elsewhere in the program.
• Instruction codes are not easy to memorize.

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Machine code vs Assembly language
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ExampleMultiplying two numbers by succesive
additions

• Assembly language
• JMP  1 X    BYTE 06 Y    BYTE
  12Prod BYTE 00 Cst1 BYTE 01 1 
  CLA            STA  Prod     CLA      
       ADD  Y    2 JZ   6     3 
  LDA  Prod    ADD  X         STA  Prod
  4  LDA  Y          SUB  Cst1     
  STA  Y      5   JMP  2     6
    DSP  Prod      HLT         

• Java code
• public static int mult (int x, int y)     int
  res 0    while (y gt 0)         res res
  x        y y - 1        return res

• pseudo-code
• 1. set prod to 02. if y 0 goto 63. add x
  to prod4. decrement y5. goto 26. halt

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Translating the assembly program to machine code

• There is a 1-to-1 correspondence between assembly
  and machine language.
• 2 steps process
• Translate the mnemonics to codes
• Translate the symbolic operands to absolute
  addresses (need symbol table)

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Symbol table

• Its a table that associates to each symbol a
  memory address.
• The symbols correspond to the labels of the
  statements, variables and constants.

• Mnemonic Opcode
• JMP 15
• CLA 08
• STA 39
• ADD 12
• JZ 15
• LDA 91
• SUB 61
• DSP 01
• HLT 64

Symbol Table Label Address 1 00 07 2 00
15 3 00 18 4 00 27 5 00 36    
6 00 39 X 00 03 Y 00 04 Prod 00
05 Cst1 00 06
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Translating the assembly program to machine code

• Assembly-code Address OpCode OpAddr H-L
  JMP  1 00 00 15 
        00 07  X   BYTE 06 00 03
       06Y    BYTE 12 00 04
      12Prod BYTE 00 00 05
        00Cst1 BYTE 01 00 06      
  011  CLA        00 07
  08     STA  Prod 00 08
  39    00 05    
  CLA       00 11        08    
  ADD  Y    00 12         99
         00 042  JZ   6      00
  15 17       00
  393  LDA  Prod 00 18
  91      00 05     ADD 
  X    00 21 99     
  00 03     STA  Prod 00 24
  39       00 054 
  LDA  Y      00 27 91      
  00 04     SUB  Cst1   00 30    
  61     00 06    
  STA  Y       00 33 39
     00 045  JMP  2     00 36
  15     00
  156  DSP  Prod   00 39
  01      00 05    
  HLT           00 42 64

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Switching Algebra

• Definition
• A Boolean function of N variables (or inputs) is
  a function that has N input variables and
  produces 1 output.
• "Boolean" means the variables and outputs can
  have only two possible values
• usually these are called FALSE and TRUE, but
  because we want to use Boolean functions to do
  Binary arithmetic, we equate FALSE with the value
  0 and TRUE with the value 1.  
• We will look at 3 different ways of writing down
  Boolean functions
• a) functional notation, e.g. (X AND Y) OR (NOT
  Z)
• (exactly like a Boolean expression in Java,
  except we use words for the operators, or math
  symbols ( ) not the Java operators.)
• b) truth tables
• c) logic circuits
• truth table --gt functional notation --gt logic
  circuit

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Switching Algebra

• Propositional logic consists of an ensemble of
  values, TRUE(1),FALSE(0) and the following 3
  operators
• AND, OR and NOT

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Truth Tables

• A truth table is a simple way of representing a
  boolean function
• it is very convenient as long as the function
  does not have too many inputs.
• A truth table has one column for every input
  variable, and one extra column for the function
  output.
• It has one row for every possible combination of
  inputs (2-to-the-N).
• In the "input" columns you write down the
  particular input values (for the particular
  combination/row you're looking at)
• in the function column you put the output of the
  function given that input.

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Truth Tables
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Using truth tables to prove a property

• Show that
• a a.b a b

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Using truth tables to prove a property

• Show that
• a a' 1

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Using truth tables to prove a property

• Show that
• a.(bc) a.b a.c

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16 different 2-input Boolean functions
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Logic Gates

• 2-input boolean functions are the building blocks
  out of which almost all computer circuits are
  made. When we draw these circuits, we have
  special ways of drawing the most important
  functions

You dont have to memorize the symbols for the
final, there will be an appendix
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Logic Gates

• We imagine that the values flow along wires. So
  if we want to make a more complex circuit we just
  connect the output of one logic gate to the input
  of another.
• Example
• suppose we wanted to test if X and Y and Z were
  all true.
• Assuming we only have 2-input AND gates, we'd
  have to use several gates.
• We'd break the expression down into (X AND Y)
  AND Z.
• The AND in brackets would be done with one gate,
  and its output would be connected to one of the
  inputs of a second AND gate (Z would be connected
  to the other input).

X
Y
Z
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Logic Gates Special Symbols
NOR gate
NAND gate
XOR gate
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Rules for Logic Circuits Drawing

• There is one vertical line per input variable
• The gates are connected to those lines with
  horizontal lines       
• A connection is shown as a dot at the
  intersection of a vertical and horizontal line

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Rules for Logic Circuits Drawing
a a.b
a.b
aa.b
b
a
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Exercises

• a) Draw a circuit for the following expression
  (a c)(b d))
• b) Simplify the circuit to have only single
  variables inverted.
• 2. Construct a circuit that implements the
  expression AB CD using only NAND gates
• 3. Using only NAND gates, construct the circuit
  for the expression
• A BC

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Assignment 10

• Question 1 For the giving Java code(adding the
  odd numbers from 1 to 2N-1 )
• - write the line to line assembly
  language program
• - transform the assembly language into
  machine code
• Question 2 1. 3-way jump
• 2. translate the assembly code into machine
  code