1. Bits and Bytes
Bits and Bytes
Chapter 1

2. Bits OR Bit = Binary Digit (or Binary Digit) = {0, 1} Off On
Bits & Bytes
Bits
Bit = Binary Digit (or Binary Digit) = {0, 1}
Assume you wish to send a message using a Light Switch
A binary condition since the light switch can be either: OR
Off On
Any binary condition can be represented with a single light switch :
Good
Bad
Yes No OR OR
Male
Female
Dead
Alive OR OR

3. If there are 2 light switches, the total combinations are:
But, what if there are more than two states? What if I want to represent the conditions GOOD, SO-SO, and BAD????
Simple …..
Add more Light Switches
If there are 2 light switches, the total combinations are: #1 #2 #3 #4
Off
Off On 1
Off On 1 On 1
Interpreted as:
Bad
Interpreted as:
So-So
Interpreted as:
Good
Not Used

4. Bits and Bytes
If I can transmit 4 messages with two bits, how many could I transmit if I had 3 bits? Or 4 bits?
With 3-bits, there are 8 possible combinations:
And, with 4-bits, there are 16 possible combinations:

5. Bits and Bytes
Is there any way to know how many messages we could transmit for a given number of bits without having to test all possible combinations??
As in Decimal (base 10), it is possible to determine how many messages can be transmitted for any number of decimal places. In Binary (base 2), the same calculations are made, but using bits (instead of decimals).
Decimal Number Number Number
Places Messages Bits Messages
= = 1
= = 2
= = 4
= 1, = 8
= 10, = 16
= 100, = 32
= 1,000, = 64
= 10,000, = 128
= 100,000, = 256
= 1,000,000, = 512
= 10,000,000, = 1,024

6. The General formula is:
Bits and Bytes
The General formula is:
I = Bn where: I = The amount of Information (messages) available
B = The base we are working in (Decimal or Binary)
n = The number of digits (decimals or bits) we have
Applying the formula to both decimal and binary values:
100 = = 1
101 = = 2
102 = = 4
103 = 1, = 8
= 10, = 16
105 = 100, = 32
= 1,000, = 64
107 = 10,000, = 128
108 = 100,000, = 256
109 = 1,000,000, = 512
1010 = 10,000,000, = 1,024

7. Just reverse the process.
Bits and Bytes
What if I Know how much information (I = Number of Messages) I want to transmit. How do I determine the number of bits I need?
Just reverse the process.
If I = 10n (decimal) OR I = 2n (binary)
then log(I) = n log(10) log(I) = n log(2)
log(I) log(I) log(I) log(I)
And n = = n = =
log(10) log(2)
= log(I) Since = 2
Information Decimals Needed Bits Needed
log(10) = log(10)/log(2) = 1.000/ =
log(50) = log(50)/log(2) = 1.699/ =
log(100) = log(100)/log(2) = 2.000/ =
log(500) = log(500)/log(2) = 2.699/ =
1, log(1000) = log(1000)/log(2) = 3.000/ =
10, log(10000) = log(10000)/log(2) = 4.000/ = 13.29

8. Bits and Bytes
How can we have partial bits (or decimals)? For example, how can we have 5.64 bits to represent 50 messages?
We Can’t
The formula given should have been:
log(I) log(I) Where:
n = =
log(2) is the ceiling of the result (i.e., rounded up)
And the number of bits needed would be:
Messages Bits Needed
log(10)/log(2) = / = = 4
log(50)/log(2) = / = = 6
log(100)/log(2) = / = = 7
log(500)/log(2) = / = = 9
1, log(1000)/log(2) = / = = 10
10, log(10000)/log(2) = / = = 14

9. They either remain unused, or are available for future use
Bits and Bytes
Notice that we could have predicted that, for example, it would take 6 bits to represent 50 pieces of information since:
25 = and = 64
If we need 6 bits to represent 50 pieces of information, and we could represent 64 pieces of information, what happens to the remaining 16 pieces of information??
They either remain unused, or are available for future use

10. What does this have to do with Computers?
Bits and Bytes
What does this have to do with Computers?
If we were to look inside a computer (especially earlier ones) we might see a series of ‘doughnuts’:
Which were merely metal rings with wires running through them
Depending on whether there was voltage running through them or not (actually, high voltage or low voltage) the series represented a sequence of messages.
A BINARY SITUATION!

11. Where and represent the different voltage states
Bits and Bytes
Notice that since there are 5 ‘doughnuts’, there are 25 or 32 Combinations
Where and represent the different voltage states

12. How Many bits (or ‘doughnuts’) do we really need?
Bits and Bytes
How Many bits (or ‘doughnuts’) do we really need?
Good question! What symbols/information do we wish to convey?
Pieces of Information
The digits (0, …, 9)
The alphabet (a, …, z)
The upper case alphabet (A, …, Z) 26
Special characters (! + ( ) . ? / * - % & # =, etc.) 32 (?) 94
Since: n = log(I)/log(2) = log(94)/log(2) = / =
we need 7 bits, which we could have predicted since:
26 = and = 128

13. What about the remaining 34 (128 - 94) bits?
Bits and Bytes
What about the remaining 34 ( ) bits?
There are a number of additional special characters and a number of ‘hidden’ characters which we didn’t account for:
Carriage Return (CR)
Back Space (BS)
End of File (EOF)
etc.
So the additional bits will be used.
Are 7 bits normally used to represent a character set?
Yes. The Standard coding scheme consists of 128 characters

14. Bits and Bytes
LIAR!! LIAR!! PANTS ON FIRE !!!
Doesn’t a byte represent a character? And isn’t a byte equal to 8 bits, not 7?
Yes - sort of.
1-Byte = 8-bits
A Byte is used to represent a character
A Byte is the basic addressable unit in RAM
BUT, the standard character still contains only 128 characters, which requires 7-bits
Then Why does a byte contain 8-bits?

15. The Parity Bit There were problems with storage and data transmission
Bits and Bytes
There are a few reasons. Primarily, however, it is because earlier machines suffered some reliability problems (remember what the term debugging really means)1:
There were problems with storage and data transmission
One additional bit was added to help detect errors:
The Parity Bit
How does adding one additional bit help detect errors?
1 In the days of vacuum, tubes, bugs were attracted to the heat given off by the tubes. Programmers frequently spent much of their time scrapping dead bugs off the circuitry, or ‘de-bugging’.

16. Bits and Bytes
Assume that we wished to send the series of bits:
But, because of transmission errors, actually sent the message:
How can we tell that an error was made? How do we know that the sequence was not the true message?
As it stands now, we can’t.

17. 1001100 1 If we were to send a transmission using an extra bit:
Bits and Bytes
If we were to send a transmission using an extra bit: 1
Parity-Bit
We could determine if the message was correctly transmitted by counting the total number of on bits
E.G. If the total number of on bits is an EVEN number, the message was correctly transmitted.
Since the message sent contains 4 bits (an even number) the message sent was correct.

18. Other examples using EVEN Parity:
Bits and Bytes
IF, however, we received the message: 1
Parity-Bit
We know it is incorrect because the message contains 5 (an odd number) bits
Other examples using EVEN Parity:
Message Sent:
Mess. Received:
No. Bits: 1 1
6 (Even)
Correct
3 (Odd)
Incorrect 1 1
5 (Odd)
Incorrect
4 (Even)
Correct

19. All it takes is one incorrect message.
Bits and Bytes
What gives? The last message:
Message Sent:
Mess. Received:
No. Bits:
4 (Even)
Correct
Was NOT correct, even though the total number of on bits received was even???
Yes - The system is NOT perfect, but if there are thousands or millions of messages sent, it is highly unlikely that mistakes will not be caught.
All it takes is one incorrect message.

20. Notice that errors can still go undetected.
Bits and Bytes
Must Parity always be equal??
No, it can be ODD (or there can be NO parity). That decision is made by the software designer.
If we look at our previous examples using ODD parity:
Message Sent:
Mess. Received:
No. Bits:
5 (Odd)
Correct 1 1
4 (Even)
Incorrect
4 (Even)
Incorrect 1 1
5 (Odd)
Correct
Notice that errors can still go undetected.

21. Given the binary sequences:
Bits and Bytes
There was one other problem with bytes:
Compatibility
Given the binary sequences:
Manufact.
#1:
Manufact.
#2:
Manufact.
#3: A + B 1 - C 2 * D 3 ?
  
  
  
   6 v
TAB 7 x CR 8 y LF 9 z FF
Manufacturers Interpreted them differently

22. ASCII Which is the Correct Interpretation??? What’s the Solution ???
Bits and Bytes
Which is the Correct Interpretation???
Each is equally Correct
Could be either a ‘C’ OR a ‘2’
The letter ‘C’ Could be pronounced either ‘cee’ OR ‘ess’
What’s the Solution ???
ASCII
The American Standard Code for Information Interchange

23. Sample ASCII Codes: Binary Sequence Value Character Description .
Bits and Bytes
Sample ASCII Codes:
Binary Sequence
Value
Character
Description
NULL
NULL/Tape feed
  
  
  
   7
BEL
Rings Bell 8 BS
Back Space
  
  
  
   13 CR
Carriage Return
  
  
  
   27
ESC
Escape
  
  
  
   32 SP
Space
  
  
  
   48
Zero 49 1
One
  
  
  
   65 A
Capital ‘A’ 66 B
Capital ‘B’
  
  
  
   97 a
Lower Case ‘a’ 98 b
Lower Case ‘b’

24. A Preview of Things to Come:
Bits and Bytes
A Preview of Things to Come:
For the first Exam Memorize the Numeric Values for:
NULL Value: 0
BEL (Ring The Bell) Value: 7
BS (Backspace) Value: 8
CR (Carriage Return) Value: 13
ESC (Escape) Value: 27
SP (Space) Value: 32
The digits (0, 1, …, 9)
NOTE: The Digit 0 (zero) has the value: 48
The Uppercase Alphabet
NOTE: The Character ‘A’ has the value: 65
The Lowercase Alphabet
NOTE: The Character ‘a’ has the value: 97

25. Are We limited to only 128 (= 27) characters ??
Bits and Bytes
Are We limited to only 128 (= 27) characters ??
Yes and no:
The STANDARD ASCII Character Set Consists of 128 Characters (as given in Addendum 1.1)
There is an EXTENDED ASCII Character set which uses ALL 8-bits (1-byte) available (parity is NOT an issue)
The extended ASCII Character set consists of (= 28) characters (See Addendum 1.2)
The Majority of the characters included in the extended ASCII character set are extensions of the Greco-Roman Alphabet (e.g., ß, Ü, å) or ‘graphics’ characters (e.g., )

26. What does the term ‘ASCII file’ Mean ??
Bits and Bytes
What does the term ‘ASCII file’ Mean ??
An ASCII File assumes that every 8-bits (1-byte) in the file are grouped together according to the ASCII tables
Aren’t ALL Files ASCII Files ??
NO - As we will see later, not all data is stored according to ASCII formats
That Helps (sort-of) to explain why when we display non-ASCII files we sometimes get characters such as ,  , , , , and 

27. Do ALL computers use ASCII to Represent Symbols???
Bits and Bytes
Do ALL computers use ASCII to Represent Symbols???
NO - Although most do.
IBM had the first Coding Scheme (dating back to 1880)
EBCDIC
Extended Binary Coded Decimal Interchange Code
EBCDIC is still used (?) in IBM Mainframes and to store data on large reel-to-reel Tape Drives

28. There is only ASCII and EBCDIC ??
Bits and Bytes
And so that’s it ??
There is only ASCII and EBCDIC ??
Well, … No
It became obvious that Even the Extended ASCII and Character Sets were insufficient
How So – Kimo Sabi ??
Suppose you wanted to represent ALL the characters used by ALL the languages in the World ---
How Many Are there ????
I Don’t know, How Many ??
I Don’t know, Either --
But it’s a lot !!!

29. AHA!! So Everyone is using Unicode now -- Right ??
Bits and Bytes
Enter Unicode (1990):
If we were to use 16-bits, instead of 8, to represent characters we could represent:
216 = 65,536 Characters
AHA!! So Everyone is using Unicode now -- Right ??
Well, … No
Well, why not ??
Life is not so simple …

30. (No fonts – No Characters)
Bits and Bytes
There are a lot of problems still be worked out:
There is a lot of disagreement about what should be included
(Even though there are 65,536 combinations, you would be surprised at how quickly those combinations can be used up)
The large number of characters in this set poses a severe problem for a font vendor
(No fonts – No Characters)
By doubling the number of bits (or bytes), we are doubling the storage and processing requirements
Result: It will take years to get this straightened out

31. Do I have to know this stuff ??
Bits and Bytes
SO – What have we learned ????
What a bit is
How a bit corresponds to computer architecture
How combinations of bits can be used to store information
How to calculate how much information a given number of bits yields
How to calculate how many bits we need to store information
What a byte is and why it is 8-bits
What parity is and why it is/was necessary
What ASCII is and why it was developed
What EBCDIC is
What Unicode is and why it was developed
… And many other things in between …
Do I have to know this stuff ??
Of Course not !! – I just like to waste my time and yours !!

32. ??? Any Questions ??? (Please!!)
Bits and Bytes
So what do we need to do ??
Make sure you THOUROGHLY understand ALL of the concepts covered in these slides
Answer ALL of the relevant questions on the Review Page
Memorize the assigned ASCII codes
Submit your References
Submit your Question(s)
Look at the Bits/Bytes/ASCII C/C++ Programming Assignment (it’s not due yet, but it can’t hurt to look at it)
??? Any Questions ??? (Please!!)

33. Bits and Bytes