CPS120: Introduction to Computer Science

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CPS120 Introduction to Computer Science

• Midterm Exam Review

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Topics

• Von Neumann architecture
• Design of the CPU
• Structure charts
• Flowcharting
• Pseudocode
• Computer logic / truth tables
• Machine language / assembly language
• High level languages
• Computer Math

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Introduction To Computers
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Machine Language

• Every processor type has its own set of specific
  machine instructions
• The relationship between the processor and the
  instructions it can carry out is completely
  integrated
• Each machine-language instruction does only one
  very low-level task

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Assembly Language

• Assembly languages assign mnemonic letter codes
  to each machine-language instruction
• The programmer uses these letter codes in place
  of binary digits
• A program called an assembler reads each of the
  instructions in mnemonic form and translates it
  into the machine-language equivalent

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Instruction Format
Difference between immediate-mode and direct-mode
addressing
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Some Sample Instructions
Subset of Pep/7 instructions
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Figure 7.5 Assembly Process
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Algorithm and Program Design
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Top-Down Design
An example of top-down design

• This process continues for as many levels as it
  takes to expand every task to the smallest
  details
• A step that needs to be expanded is an abstract
  step

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A General Example

• Planning a large party

Subdividing the party planning
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Flowchart

• A graphical representation of an algorithm.

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Pseudocode

• Uses a mixture of English and formatting to make
  the steps in the solution explicit

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Logic Flowcharts

• These represent the flow of logic in a program
  and help programmers see program design.

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Common Flowchart Symbols
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How to Draw a Flowchart

• There are no hard and fast rules for constructing
  flowcharts, but there are guidelines which are
  useful to bear in mind.Here are six steps which
  can be used as a guide for completing flowcharts.
  
• Describe the purpose of the program to be
  created (this is a one-line statement)
• Start with a 'trigger' event (it may be the
  beginning of the program)
• Initialize any values that need to be defined at
  the start of the program
• Note each successive action concisely and clearly
  
• Go with the main flow (put extra detail in other
  charts -- this is the basis of structured
  programming)
• Follow the process through to a useful conclusion
  (end at a 'target' point -- like having no more
  records to process)

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Pseudocode for a Generalized Program
START Intialize variables LOOP While More records
do READ record PROCESS record PRINT
detail record ENDLOOP CALCULATE TOTALS PRINT
total record END
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Rules for Pseudocode

1. Make the pseudocode language-independent
2. Indent lines for readability
3. Make key words stick out by showing them
   capitalized, in a different color or a different
   font
4. Punctuation is optional
5. End every IF with ENDIF
6. Begin loop with LOOP and end with ENDLOOP
7. TERMINATE all routines with an END instruction

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Gates and Boolean Logic
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Gates

• Six types of gates
• NOT
• AND
• OR
• XOR
• NAND
• NOR

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NOT Gate

• A NOT gate accepts one input value and produces
  one output value

Various representations of a NOT gate
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NOT Gate

• By definition, if the input value for a NOT gate
  is 0, the output value is 1, and if the input
  value is 1, the output is 0

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AND Gate

• An AND gate accepts two input signals
• If the two input values for an AND gate are both
  1, the output is 1 otherwise, the output is 0

Various representations of an AND gate
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OR Gate

• If the two input values are both 0, the output
  value is 0 otherwise, the output is 1

Figure 4.3 Various representations of a OR gate
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XOR Gate

• XOR, or exclusive OR, gate
• An XOR gate produces 0 if its two inputs are the
  same, and a 1 otherwise
• Note the difference between the XOR gate and the
  OR gate they differ only in one input situation
• When both input signals are 1, the OR gate
  produces a 1 and the XOR produces a 0

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XOR Gate
Various representations of an XOR gate
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NAND and NOR Gates

• The NAND and NOR gates are essentially the
  opposite of the AND and OR gates, respectively

Various representations of a NAND gate
Various representations of a NOR gate
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Review of Gate Processing

• A NOT gate inverts its single input value
• An AND gate produces 1 if both input values are 1
• An OR gate produces 1 if one or the other or both
  input values are 1

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Review of Gate Processing (cont.)

• An XOR gate produces 1 if one or the other (but
  not both) input values are 1
• A NAND gate produces the opposite results of an
  AND gate
• A NOR gate produces the opposite results of an OR
  gate

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Adders

• At the digital logic level, addition is performed
  in binary
• Addition operations are carried out by special
  circuits called, appropriately, adders

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Adders

• The result of adding two binary digits could
  produce a carry value
• Recall that 1 1 10 in base two
• A circuit that computes the sum of two bits and
  produces the correct carry bit is called a half
  adder

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Adders

• Circuit diagram representing a half adder
• Two Boolean expressions
• sum A ? B
• carry AB

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Adders

• A circuit called a full adder takes the carry-in
  value into account

A full adder
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Computer Mathematics
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Representing Data

• The computer knows the type of data stored in a
  particular location from the context in which the
  data are being used
• i.e. individual bytes, a word, a longword, etc
• 01100011 01100101 01000100 01000000
• Bytes 99(10, 101 (10, 68 (10, 64(10
• Two byte words 24,445 (10 and 17,472 (10
• Longword 1,667,580,992 (10
• ASCII c, e, D, _at_

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Alphanumeric Codes

• American Standard Code for Information
  Interchange (ASCII)
• 7-bit code
• Since the unit of storage is a bit, all ASCII
  codes are represented by 8 bits, with a zero in
  the most significant digit
• H e l l o W o r l d
• 48 65 6C 6C 6F 20 57 6F 72 6C 64
• ASCII is a subset of the Unicode character set

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Decimal Equivalents

• Assuming the bits are unsigned, the decimal value
  represented by the bits of a byte can be
  calculated as follows
• Number the bits beginning on the right using
  superscripts beginning with 0 and increasing as
  you move left
• Note 20, by definition is 1
• Use each superscript as an exponent of a power of
  2
• Multiply the value of each bit by its
  corresponding power of 2
• Add the products obtained

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Binary to Hex / Octal

• Step 1 Form four-bit groups beginning from the
  rightmost bit of the binary number
• If the last group (at the leftmost position) has
  less than four bits, add extra zeros to the left
  of the group to make it a four-bit group
• 0110011110101010100111 becomes
• 0001 1001 1110 1010 1010 0111
• Step 2 Replace each four-bit group by its
  hexadecimal equivalent
• 19EAA7(16
• Note Octal is done in groups of threes

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Converting Decimal to Other Bases

• Step 1 Divide the number by the base you are
  converting to (r)
• Step 2 Successively divide the quotients by (r)
  until a zero quotient is obtained
• Step 3 The decimal equivalent is obtained by
  writing the remainders of the successive division
  in the opposite order in which they were obtained
• Know as modulus arithmetic
• Step 4 Verify the result by multiplying it out

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Representing Signed Numbers

• Remember, all numeric data is represented inside
  the computer as 1s and 0s
• Any numerical convention needs to differentiate
  two basic elements of any given number, its sign
  and its magnitude
• Conventions
• Sign-magnitude
• Twos complement
• Ones complement

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Representing Negatives

• It is necessary to choose one of the bits of the
  basic unit as a sign bit
• Usually the leftmost bit
• By convention, 0 is positive and 1 is negative
• Positive values have the same representation in
  all conventions
• However, in order to interpret the content of any
  memory location correctly, it necessary to know
  the convention being used used for negative
  numbers

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Sign-Magnitude

• The leftmost bit is used exclusively to represent
  the sign
• The remaining bits are used for the magnitude
  (distance from 0)

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Sign-magnitude Operations

• Addition of two numbers in sign-magnitude is
  carried out using the usual conventions of binary
  arithmetic
• If both numbers are the same sign, we add their
  magnitude and copy the same sign
• If different signs, determine which number has
  the larger magnitude and subtract the other from
  it. The sign of the result is the sign of the
  operand with the larger magnitude

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Complements

• Conventions other than sign magnitude are useful
  because the eliminate the problem of two
  representations of zero
• Secondly, they allow us to do addition and
  subtraction (treated as adding a negative)
  without using carry values

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Ones Complement

• Devised to make the addition of two numbers with
  different signs the same as two numbers with the
  same sign
• Positive numbers are represented in the usual way
• For negatives
• STEP 1 Start with the binary representation of
  the absolute value
• STEP 2 Complement all of its bits

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One's Complement Operations

• Treat the sign bit as any other bit
• For addition, carry out of the leftmost bit is
  added to the rightmost bit end-around carry

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Twos Complement Convention

• A positive number is represented using a
  procedure similar to sign-magnitude
• To express a negative number
• Express the absolute value of the number in
  binary
• Change all the zeros to ones and all the ones to
  zeros (called complementing the bits)
• Add one to the number obtained in Step 2

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Twos Complement Operations

• Addition
• Treat the numbers as unsigned integers
• The sign bit is treated as any other number
• Ignore any carry on the leftmost position
• Subtraction
• Treat the numbers as unsigned integers
• If a "borrow" is necessary in the leftmost place,
  borrow as if there were another invisible
  one-bit to the left of the minuend