CPS120:%20Introduction%20to%20Computer%20Science

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CPS120 Introduction to Computer Science

• Session 5

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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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Converting Binary to Octal

• Groups of Three (from right)
• Convert each group
• 11010010 110 100 010
• 6 4 2
• 110100010 is 642 in base 8

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Converting Octal to Decimal
What is the decimal equivalent of the octal
number 642?
6 x 8² 6 x 64 384 4 x 8¹
4 x 8 32 2 x 8º 2 x 1
2 418 in base 10
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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
• 110111101111 becomes
• 1101 1110 1111
• Step 2 Replace each four-bit group by its
  hexadecimal equivalent
• DEF(16

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Converting Hexadecimal to Decimal
What is the decimal equivalent of the hexadecimal
number DEF?
D x 16² 13 x 256 3328 E x 16¹
14 x 16 224 F x 16º 15 x 1
15 3567 in base 10
Remember, base 16 is 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E
,F
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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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Converting Decimal to Hexadecimal
222 13 0
16 3567 16 222 16 13 32
16 0
36 62 13 32 48
47 14 32
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D E F
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CPS120 Introduction to Computer Science

• Pseudocode

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Sample Program Flowchart
Start
Terminal Symbol
Initialize Variables
Preparation Symbol
or
Variables
Open Files
I/O Symbol
Read a Record
No
More items?
Process Record (Total Time)
Close Files
Stop
Decision Symbol
Yes
Process Record (Detail Time)
Process Symbol
Write Record
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Common Flowchart Symbols
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Rules for Drawing Flowcharts

• Top to bottom and left to right
• Draw the flowchart the way you like to read
• Use arrowheads on flow lines whenever the flow is
  not top to bottom, left to right
• Be neat ! Use graphics software
• Avoid intersecting lines

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Programs

• A program is a set of step-by-step instructions
  that directs the computer to do the tasks you
  want it to do and produce the results you want.

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What Can a Program Do?

• A program can only instruct a computer to
• Read Input
• Sequence
• Calculate
• Store data
• Compare and branch
• Iterate or Loop
• Write Output

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Sequence Control Structures

• Sequence control structures direct the order of
  program instructions.
• The fact that one instruction follows anotherin
  sequenceestablishes the control and order of
  operations.

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Calculate

• A program can instruct a computer to perform
  mathematical operations.

Add 1 to Counter
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Store

• A program will often instruct a computer to store
  intermediate results.

Place 1 in Counter
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Compare and Branch

• A program can instruct a computer to compare two
  items and do something based on a match or
  mismatch which, in turn, redirect the sequence of
  programming instructions.
• There are two forms
• IF-THEN
• IF-THEN-ELSE

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IF-THEN
Test condition p
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IF-THEN-ELSE
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Iterate

• A program loop is a form of iteration. A computer
  can be instructed to repeat instructions under
  certain conditions.

No
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Iteration Control Structures

• Iteration control structures are looping
  mechanisms.
• Loops repeat an activity until stopped. The
  location of the stopping mechanism determines how
  the loop will work
• Leading decisions
• Trailing decisions

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Leading Decisions

• If the stop is at the beginning of the iteration,
  then the control is called a leading decision.
• The command DO WHILE performs the iteration and
  places the stop at the beginning.

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DO WHILE Loop
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Trailing Decisions

• If the stop is at the end of the iteration, the
  control mechanism is called a trailing decision.
• The command DO UNTIL performs the iteration and
  puts the stop at the end of the loop.

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DO UNTIL Loop
Loop statement a
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Pseudocode

• Pseudocode is an artificial and informal language
  that helps programmers develop algorithms.

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Pseudocode

• This device is not visual but is considered a
  first draft of the actual program.
• Pseudocode is written in the programmers native
  language and concentrates on the logic in a
  programnot the syntax of a programming language.

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Writing Pseudocode

• You need to reach a balance between excessive and
  insufficient detail.

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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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A Computer Example

• Problem
• Create an address list that includes each
  persons name, address, telephone number, and
  e-mail address
• This list should then be printed in alphabetical
  order
• The names to be included in the list are on
  scraps of paper and business cards

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A Computer Example
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A Computer Example
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A Computer Example
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A Computer Example
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A Computer Example
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CPS120 Introduction to Computer Science

• Boolean Logic

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Decision Making In Computers

• A circuit quite simply allows one out of two
  choices to be made depending on its inputs
• When decisions are made in a computer program,
  they are simply the result of a computation in
  which the final result is either TRUE or FALSE
• The value zero (0) is considered to be FALSE. Any
  positive or negative value is considered to be
  TRUE (usually represented by 1)

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I Know This Concept

• If you have ever taken a True or False test, you
  have used Boolean logic.
• In the Boolean system an object can exist in only
  one of two states, there is no third choice
• This is a central concept in programming.

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Computers and Electricity

• A gate is a device that performs a basic
  operation on electrical signals
• Gates are combined into circuits to perform more
  complicated tasks

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Computers and Electricity

• There are three different, but equally powerful,
  notational methods for describing the behavior
  of gates and circuits
• Boolean expressions
• logic diagrams
• truth tables

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Computers and Electricity

• Boolean algebra expressions in this algebraic
  notation are an elegant and powerful way to
  demonstrate the activity of electrical circuits

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Computers and Electricity

• Logic diagram a graphical representation of a
  circuit
• Each type of gate is represented by a specific
  graphical symbol
• Truth table defines the function of a gate by
  listing all possible input combinations that the
  gate could encounter, and the corresponding output

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Truth Tables

• Use this truth table to determine the results of
  the logical operators. In this table, 1
  represents TRUE and 0 represents FALSE.
• Note that the ! symbol (the logical NOT operator)
  changes a TRUE to a FALSE.

1

0

1




1

1

1



1

1

1





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Gates

• Lets examine the processing of the following
  six types of gates
• NOT
• AND
• OR
• XOR
• NAND
• NOR
• Typically, logic diagrams are black and white,
  and the gates are distinguished only by their
  shape

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NOT

• Reverses the input. If TRUE is input, the result
  id FALSE if FALSE is input, the result is TRUE.
• 1 would evaluate to FALSE
• 0 would evaluate to TRUE

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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
• A NOT gate is sometimes referred to as an
  inverter because it inverts the input value

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AND

• Two or more items must agree(be evaluated to the
  same result) for the expression to be true.
• 1 AND 1 would evaluate to TRUE
• 0 AND 1 would evaluate to FALSE
• 1 AND 0 would evaluate to FALSE
• 0 AND 0 would evaluate to FALSE
• 1 AND 1 AND 1 would evaluate to TRUE
• 1 AND 1 AND 0 would evaluate to FALSE

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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

• One, both or more items must agree. If both
  inputs are FALSE, the result it FALSE.
• 1 OR 1 would evaluate to TRUE
• 0 OR 1 would evaluate to TRUE
• 0 OR 0 would evaluate to FALSE

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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 (eXclusive OR)

• Only one input may be TRUE, if both are TRUE the
  entire result id FALSE.
• 1 XOR 1 would evaluate to FALSE
• 1 XOR 0 would evaluate to TRUE
• 0 XOR 1 would evaluate to TRUE
• 0 XOR 0 would evaluate to FALSE

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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 (Not AND)

• This basically negates AND
• 1 NAND 1 would evaluate to FALSE
• 1 NAND 0 would evaluate to TRUE
• 0 NAND 0 would evaluate to TRUE
• 0 NAND 1 would evaluate to TRUE

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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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Using Logical Operators

• When complex decisions must be coded into an
  algorithm, it may be necessary to "chain
  together" a few relational expressions (that use
  relational operators)
• This is done with logical operators (also called
  Boolean operators.)

is the logical AND operator
is the logical OR operator ! is the
logical NOT operator