1. CPS120: Introduction to Computer Science
Midterm Exam Review

2. Introduction To Computers

20. 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

21. 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

22. Instruction Format
Difference between immediate-mode and direct-mode addressing

23. Some Sample Instructions
Subset of Pep/7 instructions

24. Figure 7.5 Assembly Process

37. Algorithm and Program Design

38. 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

39. A General Example Planning a large party
Subdividing the party planning

40. Flowchart
A graphical representation of an algorithm.

41. Pseudocode
Uses a mixture of English and formatting to make the steps in the solution explicit

42. Logic Flowcharts
These represent the flow of logic in a program and help programmers “see” program design.

43. Common Flowchart Symbols
Terminator. Shows the starting and ending points of the program. A terminator has flow lines in only one direction, either in (a stop node) or out (a start node).
Data Input or Output. Allows the user to input data and results to be displayed.
Processing. Indicates an operation performed by the computer, such as a variable
assignment or mathematical operation. With a heading – an internal subroutine
Decision. The diamond indicates a decision structure. A diamond always has two
flow lines out. One flow lineout is labeled the “yes” branch and the other is labeled the
“no” branch.
Predefined Process. One statement denotes a group of previously defined statements.
Such as a function or a subroutine created externally
Connector. Connectors avoid crossing flow lines, making the flowchart easier to read.
Connectors indicate where flow lines are connected. Connectors come in pairs, one with
a flow line in and the other with a flow line out.
Off-page connector. Even fairly small programs can have flowcharts that extend several
pages. The off-page connector indicates the continuation of the flowchart on another
page. Just like connectors, off-page connectors come in pairs.
Flow line. Flow lines connect the flowchart symbols and show the sequence of operations during the program execution.
Common Flowchart Symbols

44. 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)

45. 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

46. Rules for Pseudocode Make the pseudocode language-independent
Indent lines for readability
Make key words stick out by showing them capitalized, in a different color or a different font
Punctuation is optional
End every IF with ENDIF
Begin loop with LOOP and end with ENDLOOP
Show MAINLINE first; all others follow
TERMINATE all routines with an END instruction

47. Gates and Boolean Logic

48. Gates
Six types of gates
NOT
AND OR
XOR
NAND
NOR

49. NOT Gate
A NOT gate accepts one input value and produces one output value
Various representations of a NOT gate

50. 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

51. 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

52. 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

53. 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

54. XOR Gate
Various representations of an XOR gate

55. 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

56. 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

57. 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

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

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

60. Adders sum = A  B carry = AB
Circuit diagram representing a half adder
Two Boolean expressions:
sum = A  B
carry = AB
Page 103

61. Adders
A circuit called a full adder takes the carry-in value into account
A full adder

62. Computer Mathematics

63. 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
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,

64. 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
C 6C 6F F C 64
ASCII is a subset of the Unicode character set

65. 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
Number the bits beginning on the right using superscripts beginning with 0 and increasing as you move left
Use each superscript as an exponent of a power of 2
(1*27)+(1*26)+(0*25)+(0*24)+(1*23)+(1*22)+(0*21)+(1*20)
Multiply the value of each bit by its corresponding power of 2
(1*128)+(1*64)+(0*32)+(0*16)+(1*8)+(1*4)+(0*2)+(1*1)
Add the products obtained
= 205

66. 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
becomes
Step 2: Replace each four-bit group by its hexadecimal equivalent
19EAA7(16
Note: Octal is done in groups of threes

67. 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
Step 1: Divide the number by the base you are converting to (r)
75/8 = 9 remainder
Step 2: Successively divide the quotients by (r) until a zero quotient is obtained
9/8 = 1 remainder 1
1/8 = 0 remainder 1
Step 3: The decimal equivalent is obtained by writing the remainders of the successive division in the opposite order in which they were obtained
1 – 1 – 3
Step 4: Verify the result by multiplying it out:
(1*64) + (1*8) + (3*1) = 75

68. 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
Two’s complement
One’s complement

69. 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

70. 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
What is the sign-magnitude representation of the decimal numbers –75 and 75 if the basic unit is a byte?
and
What is the decimal equivalent of the sign-magnitude binary sequence
-104

71. 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

72. One’s 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
What is the one’s complement of –35
STEP 1: Start with the binary representation of the absolute value
35 =
STEP 2: Complement all of its bits

73. 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

74. Two’s 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

75. Two’s 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
If a "borrow" is necessary in the leftmost place, borrow as if there were another “invisible” one-bit to the left of the minuend