Information system lectures

1. Chapter 0 1
Numbers & Logic
Bits & Pieces

2. Chapter 0 2
Base 10 example
• Decimal Number 9 7 0 1
• Place 4 3 2 1
• Place - 1 3 2 1 0
• 10(place - 1) 103 102 101 100
• ===============================
• = 9*1000 + 7*100 + 0*10 + 1*1
• = 9701

3. Chapter 0 3
Numeric Values
– The numeric value of a set of digits is
determined as:
• The sum of the products of each digit and its
corresponding place value,
• where the place value is the numeric-base raised to
the place - 1.

4. Chapter 0 4
Base 2 example
• Binary Number 0 1 0 1
• 2(place - 1) 23 22 21 20
• ===============================
• = 0*8 + 1*4 + 0*2 + 1*1
• = 5

5. Chapter 0 5
A general example
Base n
• Binary Number 0 1 0 1
• n(place - 1) n3 n2 n1 n0
• ===============================
• 0*(n * n* n) + 1*(n*n) + 0* n + 1*1

6. Chapter 0 6
Commonly Used Systems
• Binary Base 2
• Octal Base 8
• Decimal Base 10
• Hexadecimal Base 16

7. Chapter 0 7
Legal Digits
• What are the legal digits?
• Start at zero and stop at the base - 1
• Binary 0, 1
• Octal 0, 1, 2, 3, 4, 5, 6, 7
• Decimal 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Hex 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

8. Chapter 0 8
What is the decimal value of?
• 10101 base 2
• 10101 base 8
• 10101 base 10
• 10101 base 16

9. Chapter 0 9
• 0000 00 00 0
• 0001 01 01 1
• 0010 02 02 2
• 0011 03 03 3
• 0100 04 04 4
• 0101 05 05 5
• 0110 06 06 6
• 0111 07 07 7
• 1000 10 08 8
• 1001 11 09 9
• 1010 12 10 A
• 1011 13 11 B
• 1100 14 12 C
• 1101 15 13 D
• 1110 16 14 E
• 1111 17 15 F
• Counting in Binary,
Octal, Decimal and
Hexadecimal
• A single Hex digit
can be used to
represent the value of
four binary digits

10. Chapter 0 10
Hex = Binary Shorthand
• Hexadecimals are often used as a shorthand
for large binary values.
• This shorthand is useful for specifying
memory locations, e.g.
• Decimal - 16,274,482
• Binary - 111110000101010000110010
• Hex - F85432

11. Chapter 0 11
Binary to Hex
• Each Hexadecimal digit represents four
binary digits
• 1111 1000 0101 0100 0011 0010
• F 8 5 4 3 2

12. Chapter 0 12
Binary to Octal
• Each Octal digit represents three binary
digits
• 111 110 000 101 010 000 110 010
• 7 6 0 5 2 0 6 2

13. Chapter 0 13
ASCII & EBCDIC
• American Standard Code for Information
Interchange
– ASCII @ Wikipedia
• Binary Coded Decimals
– Binary Coded Decimals
• Extended Binary Coded Decimals
– EBCDIC @ Wikipedia
• Unicode
– Unicode @ Wikipeda

14. Chapter 0 14

15. Binary Coded Decimals
• BCD takes advantage of the fact that any
one decimal numeral can be represented
by a four-bit pattern. The most obvious
way of encoding digits is Natural
BCD (NBCD), where each decimal digit is
represented by its corresponding four-bit
binary value, as shown in the following
table. This is also called "8421" encoding.
Chapter 0 15

16. Chapter 0 16
Boolean Logic
• A two valued logic often used in computers
and information systems.
• The only legal values in Boolean Logic are
– TRUE
– FALSE

17. Chapter 0 17
Logical Values
• Logical values can only be True or False
• Similar to numeric values, logical values
can be combined into logical expressions
using logical operators.
• The logical operators are:
not and or < <= = >= >

18. Chapter 0 18
Logical Expressions
• a logical-expression is any expression that
evaluates to False or True
• False
• True
• notlogical-expression
• logical-expression and logical-expression
• logical-expression or logical-expression

19. Chapter 0 19
Logical Expressions
are not unlike
Numerical Expressions
• A numerical-expression is any expression that
evaluates to a legal numerical value.
• Examples of numerical expressions:
– 3
– -4
– 3 + 8 / 2
– (3 + 8) / 2

20. Chapter 0 20
Numerical Operators
• Unary operators have only one argument
– the positive and negative signs are the unary
numerical operators.
– + -
• Binary operators require two arguments
– addition, subtraction, multiplication, division,
and exponentiation are the binary operators
– + - * / ^

21. Chapter 0 21
You’ve probably already used
logical expressions
• The relational operators > >= = < <=
evaluate to logical results.
• Example
– the expression 3 + 5 <= 8 - 4 evaluates to a
value of False, so it is a logical expression.
– Note that here we have combined numerical
expressions with relational operators to form a
logical expression.

22. Chapter 0 22
Logical Operators
• Unary operators have only one argument
– not is the only unary logical operator.
– not
• Binary operators require two arguments
– conjunction and disjunction are the binary
operators
– and or

23. Chapter 0 23
Truth Tables
A NOT A
F T
T F
A B A AND B
F F F
F T F
T F F
T T T
A B A OR B
F F F
F T T
T F T
T T T

24. Chapter 0 24
Operator Precedence
• Higher precedence evaluate first,
• Equal precedence evaluate left to right
• Parenthesis can be used to modify the order
of precedence, expressions inside
parenthesis are evaluated first.

25. Chapter 0 25
Operator Precedence
- (unary)
* / mod numerical operators
+ -
< = >= > <= relational operators
not
and logical operators
or

26. Chapter 0 26
Evaluation of Logical
Expressions
• A = True
• B = False
• Given the above evaluate the following:
• A or B => True
• A and B => False
• 3 > 7 or A => TRUE
• (3 < 7) and not A => False

27. Chapter 0 27
Complex Logical Expression
• A = True B = False C = True D =False
• A or not B and not (3 + 7 <= 10 / 2) or C and D

28. Chapter 0 28
Complex Logical Expression
• A = True B = False C = True D =False
• A or not B and not (3 + 7 <= 10 / 2) or C and D
• T or not F and not (3 + 7 <= 10 / 2) or T and F

29. Chapter 0 29
Complex Logical Expression
• A = True B = False C = True D =False
• A or not B and not (3 + 7 <= 10 / 2) or C and D
• T or not F and not (3 + 7 <= 10 / 2) or T and F
• T or not F and not ( 10 <= 5 ) or T and F
• T or not F and not ( F ) or T and F

30. Chapter 0 30
Complex Logical Expression
• A = True B = False C = True D =False
• A or not B and not (3 + 7 <= 10 / 2) or C and D
• T or not F and not ( F ) or T and F
• T or T and T or T and F

31. Chapter 0 31
Complex Logical Expression
• A = True B = False C = True D =False
• A or not B and not (3 + 7 <= 10 / 2) or C and D
• T or T and T or T and F
• T or T or F

32. Chapter 0 32
Complex Logical Expression
• A = True B = False C = True D =False
• A or not B and not (3 + 7 <= 10 / 2) or C and D
• T or T or F
• T or F
• T

33. Chapter 0 33
Normal Forms
• Conjunctive Normal Form
– A and B and C and D and E
– any false value makes the expression false
• Disjunctive Normal Form
– A or B or C or D or E
– any true value makes the expression true

34. Chapter 0 34
Computer Time
• millisecond 10-3 = 1/1,000
• microsecond 10-6 = 1/1,000,000
• nanosecond 10-9 = 1/1,000,000,000
• picosecond 10-12 = 1/1,000,000,000,000
• femtosecond 10-15 = 1/1,000,000,000,000,000
• Conversion of Time Units

35. Chapter 0 35
Computer Units
• Thousand 103 = 1,000
• Kilobyte 210 = 1,024
• Million 106 = 1,000,000
• Megabyte 220 = 1,048,576
• Billion 109 = 1,000,000,000
• Gigabyte 230 = 1,073,741,824
• Trillion 1012 = 1,000,000,000,000
• Terabyte 240 = 1,099,511,627,776

36. Chapter 0 36
Bigger Units
• Trillion 1012 = 1,000,000,000,000
• Terabyte 240 = 1,099,511,627,776
• Quadrillion 1015 = 1,000,000,000,000,000
• Petabyte 250 = 1,125,899,906,842,624
• Quintillion 1018 = 1,000,000,000,000,000,000
• Exabyte 260 = 1,152,921,504,606,846,976
• Sextillion 1021 = 1,000,000,000,000,000,000,000
• Zettabyte 270 = 1,180,591,620,717,411,303,424
• Septillion 1024 = 1,000,000,000,000,000,000,000,000
• Yottabyte 280 = 1,208,925,819,614,629,174,706,176
• Byte Converter – File Size Calculator
• Million, Billion, Trillion

37. Quiz # 01
• Convert the following Number
• (1100110)2 = ()16
• (A7)16 = ()10
• (88)10 = ()2
• (55)8 = ()2
• (62)8 = ()10
Chapter 0 37