1. Java Coding – part 2 David Davenport Computer Eng. Dept.,
data representations
David Davenport
Computer Eng. Dept.,
Bilkent University Ankara - Turkey.
Last updated: separated out the Communications/DataRepresentations part from original slides!
Previously: 08/10/2015 (little tidy up & recreated slide messed up by PowerPoint 2013!)
Previously: 02/11/2014 (added all communication stuff at end)

2. IMPORTANT… Students… Instructors…
This presentation is designed to be used in class as part of a guided discovery sequence. It is not self-explanatory! Please use it only for revision purposes after having taken the class. Simply flicking through the slides will teach you nothing. You must be actively thinking, doing and questioning to learn!
Instructors…
You are free to use this presentation in your classes and to make any modifications to it that you wish. All I ask is an saying where and when it is/was used. I would also appreciate any suggestions you may have for improving it.
thank you, David.

3. In more depth…
Data & DATA Types

4. Communication… Communication requires:
+ something that can be in more than one state
+ being able to detect a change of state (flag up rather than down)
+ a prior agreement on what the message is (enemy approaching, come for a drink, etc.)

5. Communicating… One man multiple messages Many men multiple messages
How to communicate multiple messages
+ allow flag to be in multiple states (still one message at a time)
(is there a limit to the number of messages?)
+ have multiple flags (considered separately or as one?)
(if taken as single state how can you know when they are “ready”?)
One other option…
+ one man, sends sequence of signals which are combined to form complete message
(Problem of synchronization –start and end?
Also really need at least three states?)
One man multiple messages
Many men
multiple messages
combine state for single message?

6. Communicating… Can use anything… Abstractions Up / down On / Off X / O
True / False
1 / 0
Man with flag…
+ held up or down
+ held at say 8 positions
+ held at say 200 positions?
Need to be able to detect each possible state
Need a pre-determined convention to give meaning to each state.
Any physical state could be used, e.g. water bottle, voltage, magnetic field, …
Minimal setup would be something with just two states
+ map physical state to abstract symbol, e.g. T/F. 0/1, +/-, ?/*, …
Can you differentiate (compare & contrast)
+ analogue vs. digital
+ parallel vs. serial

7. Data Types For now, use only the following… Primitive Non-primitive
int (for numeric integer, e.g. 5, -27, 0, 510…)
double (for numeric real, e.g. 5.75, 3.0, -2.6…)
char (for any character, e.g. A, a, B, b, 3, ?, &, … )
boolean (for true / false only)
Non-primitive
String (for any sequence of zero or more characters e.g. “CS101”, “A”, “Well done!”, … )
Note: Use only these limited Java primitive types & String for now.
Will introduce other primitive & non-primitive (object) types later (& discuss them).

8. Numeric representations
Number bases
Base 2 - binary
digits 0 & 1
2n values
0  (2n – 1)
000
001
010
011
100
101
110
111 00 01 10 11
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111 1
Normally use base 10, all digits from 0 up to 9 i.e 10-1
+ for any base, numbers have digits from 0 up to the base-1
Can also have number bases greater than 10,
eg. 16… hexadecimal use “digits” 0..9, A, B, C, D, E, F
n-bits gives 2n values, 0 through 2n – 1
What about negative numbers?
+ in base 10, just put + or – in front (only need one bit to represent it!)
+ so in base 2, could use msb as sign, so +/- 2n-1
But then have +/- zero
Alternatives include 1’s complement and 2’s complement… see ???
Note: octal and hexadecimal often used as cognitive aid for binary!

9. Data Types Primitive Non-primitive
byte, short, int, long (numeric integer)
float, double (numeric real)
char - any character, e.g. A, a, B, b, 3, ?, &, … (Java uses ISO Unicode standard, 16 bit/char)
boolean - true / false
Non-primitive
String - any sequence of zero or more characters
enum – an ordered set of user-defined values
anything & everything else! (we will come to these shortly)
Note: Use only these Java primitive types & String for now. Will introduce other non-primitive (object) types later.

10. Primitive Numeric Types
byte
short
int
long
float
double
Storage
8 bits
16 bits
32 bits
64 bits
Min Value
-128
-32,768
-2,147,483,648
-9 x 1018
±3.4 x 10±38
±1.7 x 10±308
Max Value
127
32,767
2,147,483,647
9 x 1018
7 significant digits
15 significant digits
integer
real
min & max are not exactly same… why? (because only one zero!)
Real values comprise mantissa & exponent mantissa 0 upto 1.0, exponent times 10 to power of … each one is effectively a binary number (like integer)
Result is limited precision….
For example, if a type could only represent 4 significant digits, a value would become i.e. the other digits would be zero. Note that the next values would be , then , the previous ones would be , , , …
So, always have potential error in representation of real values - not always obvious which ones are in error, since decimal input is converted to binary!
Some values cannot be represented exactly in decimal either
e.g. 2/3 written in decimal is … (forever; cannot write on paper!)
same for PI
Limits on values is a major “feature” –problem/concern– in computation!
What happens when limits of representations are reached?
- eg. try to add/subtract one more to integer values (see previous sequences of 4 bit binary numbers…) Answer: goes from max pos to max neg (& vice versa)!
Division by zero? ~ In integer? In real?

11. Data Types Primitive Non-primitive
byte, short, int, long (numeric integer)
float, double (numeric real)
char - any character, e.g. A, a, B, b, 3, ?, &, … (Java uses ISO Unicode standard, 16 bit/char)
boolean - true / false
Non-primitive
String - any sequence of zero or more characters
enum – an ordered set of user-defined values
anything & everything else! (we will come to these shortly)
Note: Use only these Java primitive types & String for now.
Will introduce other non-primitive (object) types later & even create our own.
Consider…
? Why have numeric & string – can write 27.5 as string!
? Why have integer & real types (eg. int & double) – can write 3.0!
Remember Characters in Java are Unicode, not ASCII – discuss representations.
need to standardize code if we are to communicate.
ASCII is 7 bit, actually use 8 bits with additional code page for national characters…
UNICODE is 16 bit, 65K characters… but not enough! Currently ~110,000 characters!
Note: we introduced type restrictions as a way of avoiding/detecting mistakes in program, but these types are insufficient to handle most cases. Java allows us to define our own types, which we will do later!

12. Characters… Coding Size…? Standard Codes ASCII UNICODE 7 bit,
0100 — ‘+’
0101 — ‘-’
0110 — ‘*’
0111 — ‘/’
1000 — ‘0’
1001 — ‘1’
1010 — ‘2’
1011 — ‘3’
1100 — ‘ ’
1101 — ‘x’
1110 — ‘y’
1111 — ‘z’
ASCII
7 bit,
English only!
UNICODE
16 bit
All languages!
Sharing information requires all parties use same code…
ASCII – American Standard Code for Information Interchange
UNICODE – first 128 characters same as ASCII
(see unicode.org)
‘A’.. ‘Z’  26
‘a’.. ‘z’  26
‘0’.. ‘9’  10
punc.  ?? 62
26 = 64
27 = 128
28 = 256

13. Misc… Why so many numeric types? Error in reals? Typecasting
int into double, but not double into int!
Overflow/underflow
Division by zero
Why not use String for everything?
memory, processing time, error, …
i = (int) d; also d = (double) i / j; // forces real division
What happens if add one to maxint or subtract one from –maxint? (Try it!) Or multiply two large values, or divide small by large…?
What happens if divide int’s by 0, doubles by zero? (Try it!)