1. Coding Schemes and Number Systems
Coding Schemes
and
Number Systems

2. Quote
"There are only 10 types of people in the world - those who understand binary, and those who don't." -unknown
Worksheet with questions similar to those on the quiz
Feel free to work together
When doing quiz: Do not simply use a conversion app on the web. Do the conversions on your own first! Then if you want to check your answer, you can check it.

3. Coding Schemes
At the lowest level, everything in a computer is represented by 1s and 0s, called bits
Numbers
Characters
Complex data
Bit – binary digit
A coding scheme is used by a computer to represent characters
Images
Audio
Networking
A bit is the smallest element of computer storage
The way a bit of information is actually stored depends on the storage medium
We will learn more about that in Chapter 7: Storage

4. Coding Schemes ASCII – most widely used coding scheme
EBCDIC – used on some mainframes and high-end servers
Unicode – used by several operating systems and programming languages
Contains ASCII as a subset
ASCII = American Standard Code for Information Interchange

5. Coding Schemes ASCII, EBCDIC Store each character in one byte (8 bits)
256 characters represented
Characters for English and western European languages represented
ASCII
Symbol
EBCDIC 7 8 9 A B C D E
Complete ASCII table:
My favorite:

6. Coding Schemes Unicode Store each character in two(+) bytes (16 bits)
65,536+ characters represented
First 256 codes are same as ASCII codes
Includes codes for ideograms – symbols used in Asian and other languages – allows more languages/characters than only ASCII
Anyone know what languages these are from?

7. Coding Schemes: Conversion Exercise
Try these exercises using
Convert to ASCII binary codes:
Tree
Convert to ASCII decimal codes:
Go Team!
Decipher ASCII codes from binary:
Decipher ASCII codes from decimal:
Show ASCII Code chart on course web site: decimal and binary codes
Tree =
Go Team! = =
= StAr

8. Coding Schemes: Conversion Exercise
Check your answers:
Convert to ASCII binary codes:
Tree
Convert to ASCII decimal codes:
Go Team! *
* What does 32 stand for?
Decipher ASCII codes from binary:
S t a r
Decipher ASCII codes from decimal:
C I S @ P C C
Discovering Computers 2011: Living in a Digital World Chapter 2

9. Number Systems Decimal Base 10 Binary Base 2 Hexadecimal Base 16
Three number systems are commonly used with computers
Decimal
Base 10
Binary
Base 2
Hexadecimal
Base 16
1, 2, 3, … 10, 11, 12
1, 10, 11, …
1010, 1011, 1100
1, 2, 3, … A, B, C

10. 1 2 3 Number Systems Decimal Number System “deci” prefix = 10
10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Base 10 number system
Show cycling through digits as one counts up: 0, 1, 2, … 9, 10 (move over one place value and start again)
123 in the decimal number system represents the quantity one hundred and twenty three
The number we use are just symbols – distinction between the symbol used and the quantity represented
Other examples (on board):
4018 = 4* * * *100
312,000 = …
Now that we understand the decimal number system, we can see that other number systems act the same way, just using a different base value.
102
101
100
= 1* * *100 =

11. Discovering Computers 2011: Living in a Digital World Chapter 2
Number Systems
Each number system has a set of place values.
Any number (except zero) raised to the zero power = 1
Any number raised to the 1st power is itself
Any number raised to the 2nd power is that number times itself
You should know the place values for the decimal system we use every day. See Binary Place_Values and Hexadecimal Place Values
Number Systems
See Number Conversion
Discovering Computers 2011: Living in a Digital World Chapter 2

12. 1 0 1 Number Systems Binary Number System “bi” prefix = 2
2 digits: 0, 1
Base 2 number system
Everywhere we had a 10 on the previous slide, we can replace with a 2
Write table on board: 22 = 4, 23 = 8, …
Do other examples on board:
1011 = 1*23 + 0*22 + 1*21 + 1*20
= = = 640 22 21 20
101 = 1*22 + 0*21 + 1*20 =
= 5

13. 1 2 3 Number Systems Hexadecimal Number System aka Hex
“hexadeci” prefix = 16
16 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
In the Hexadecimal (Base 16) number system we use the letters A-F to represent the additional 6 digits.
We have to add symbols to get 16 digits
The symbols 123 in hex represent the quantity 291
Write table on board: 161 = 16, 162 = 256, 163 = 4096
Do other examples on board:
AB = 10* *160 = = 171
300F = 3* *160 = 3* = = 12303
162
161
160
123 = 1* * *160 =
= 291

14. Number Systems Converting between number systems
Binary or hex to decimal: Use place values
Decimal to binary : Write number as a sum of powers of 2
200 to binary
200 = – 128 = 72
200 = – 64 = 8
200 =
200 =
Anything to decimal: use place values just like we have shown
-> Show place value pages on our web site (Assign 2 assistance)
200 to binary: check chart: 128 is largest less than 200, …
Other examples: 512 = 29 =
513 =

15. Number Systems
Converting between number systems
Decimal to hex: Convert decimal to binary, then to hex
Binary to hex and hex to binary: 4 binary digits = 1 hex digit (see Binary to Hex Conversion)
Binary – Hex Chart on web site
Why does 4 binary digits = 1 hex digit?
16 is a power of 2: 16 = 24
B F

16. Number Systems Why hex? Network mask
More compact representation of binary numbers
Network mask
Host:
Mask:

17. Exercises
Convert the following binary numbers to hexadecimal:
Worksheet with questions similar to those on the quiz
Feel free to work together
When doing quiz: Do not simply use a conversion app on the web. Do the conversions on your own first! Then if you want to check your answer, you can check it.

18. Discovering Computers 2011: Living in a Digital World Chapter 2
Check your answers. 4F
7A D B
6C B7
Discovering Computers 2011: Living in a Digital World Chapter 2

19. Exercises Worksheet with questions similar to those on the quiz
Complete the following table using ASCII code (You may use an online calculator or PC calculator for the numbers). Write binary numbers using 8 bits.
Decimal
Binary
Hex
ASCII char 81 48 @ 61 70 m
Worksheet with questions similar to those on the quiz
Feel free to work together
When doing quiz: Do not simply use a conversion app on the web. Do the conversions on your own first! Then if you want to check your answer, you can check it.

20. Exercises Check your answers:
Decimal
Binary
Hex
ASCII char 81 51 Q 72 48 H 64 40 @
103 67 g 61 3D =
112 70 p
109 6D m 54 36 6
Worksheet with questions similar to those on the quiz
Feel free to work together
When doing quiz: Do not simply use a conversion app on the web. Do the conversions on your own first! Then if you want to check your answer, you can check it.

21. Quote
"There are only 10 types of people in the world - those who understand binary, and those who don't." -unknown
Worksheet with questions similar to those on the quiz
Feel free to work together
When doing quiz: Do not simply use a conversion app on the web. Do the conversions on your own first! Then if you want to check your answer, you can check it.

22. Coding Schemes and Number Systems
Coding Schemes
and
Number Systems