CPS120: Introduction to Computer Science

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CPS120 Introduction to Computer Science

• Midterm Exam Review

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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. Show MAINLINE first all others follow
8. 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

• 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
• Arithmetic operations, particularly subtraction
  raise the possibility that the result might be
  negative
• 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

• For a basic unit of N bits, the leftmost bit is
  used exclusively to represent the sign
• The remaining (N-1) bits are used for the
  magnitude

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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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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
• The range of negative numbers is one larger than
  the range of positive numbers
• Given a negative number, to find its positive
  counterpart, use steps 2 3 above

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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