1. Information Representation

2. Computer Architecture

3. Memory
Memory is a collection of cells, each with a unique physical address for random (direct) access
memory is divided into fixed-length units or words
Information that is stored in memory cells is in binary coded format:
Instructions that make up programs
Data: text symbols, numbers, images, etc.

4. Information Representation
The Binary System: Using On/Off Electrical States to Represent Data & Instructions
The binary system has only two digits--0 and 1.
Bit - binary digit
Byte - group of 8 bits used to represent one character, digit, or other value

5. Representing Information with Bit Combinations
To encode entities (e.g., symbols), we need to assign a unique number to each entity (e.g., social security number). Binary encoding means that we assign a unique combinations of bits to each object.
One bit can be either 0 or 1. Therefore, one bit can represent only two things.
To represent more than two things, we need multiple bits. Two bits can represent four things because there are four combinations of 0 and 1 that can be made from two bits: 00, 01, 10,11.
If we want to represent more than four things, we need more than two bits. In general, 2n bits can represent 2n things because there are 2n combinations of 0 and 1 that can be made from n bits.
Q: how many bits do we need to encode all the 37 people in the class?

6. Information Representation
Kilobyte approx bytes (actually 210 = 1024 bytes)
Megabyte approx. 1,000,000 bytes (one million)
Gigabyte approx. 1,000,000,000 bytes (one billion)
Terabyte approx. 1 trillion bytes
Petabyte approx. 1 quadrillion bytes
FACTOIDs:
The prefix “mega” in “megabyte” comes from the Greek word “megas” meaning “mighty” or “great.”
The prefix “giga” in “gigabyte” comes from a Greek word meaning “giant.”
The prefix “tera” in “terabyte” comes from a Greek word meaning “monster.”
You might think that the largest unit of storage capacity is a petabyte, but in fact, there are also exabytes, zetabytes, and yottabytes.

7. Representing Text and Symbols
To represent a text document in digital form, we simply need to be able to represent every possible character that may appear.
There are finite number of characters to represent. So the general approach for representing characters is to list them all and assign each a number (represented in binary).
An encoding scheme is simply a list of characters and the codes used to represent each one.
To represent symbols, computers must use a standard encoding scheme, so that the same symbols have the same codes across different computers.
Discussion question: How many possible different characters can Unicode represent and how is that derived?
Answer: 2 to the 16th power=65,526 character combinations

8. ASCII Encoding Scheme
ASCII stands for American Standard Code for Information Interchange. The ASCII character set originally uses 8 bits to represent each character, allowing for 256 (or 28) unique characters.
Discussion question: How many possible different characters can Unicode represent and how is that derived?
Answer: 2 to the 16th power=65,526 character combinations

9. Representing Text and Symbols
ASCII - the binary code most widely used with microcomputers
EBCDIC - used with large computers
Unicode - uses two bytes for each character rather than one
Discussion question: How many possible different characters can Unicode represent and how is that derived?
Answer: 2 to the 16th power=65,526 character combinations

10. The Parity Bit
Parity bit - an extra bit attached to the end of a byte for purposes of checking for accuracy
Even parity - sum of bits must come out even
Ex: given code , the extended code is:
Ex: given code , the extended code is:
Odd parity - sum of bits must come out odd
Even parity scheme

11. Representing Numbers The binary number system
Decimal is base 10: 0,1,2,3,4,5,6,7,8,9
Binary is base 2: 0,1
Any decimal number can be converted to binary by doing base conversion from base 10 to base 2.
Any binary number can be converted to decimal by doing base conversion from base 2 to base 10.

12. Number base 10 - decimal The Decimal Number 101 102 101 100
100’s 10’s 1’s
x 1 =
x =
x =
101

13. Number base 2 - binary The Binary Number 101 22 21 20 4’s 2’s 1’s
4’s 2’s 1’s
x 1 =
x =
x = 5

14. Binary Conversion - Examples
= 45 25 24 23 22 21 20 32 16 8 4 2 1

15. Binary Conversion - Examples
= 86 64 32 16 8 4 2 1
Easier way to remember:
Just add the values for each position where there is a 1
128 64 32 16 8 4 2 1 1
= 181

16. Hexadecimal Representation
Hexadecimal (Hex) = Base 16
Hex digits: 0, 1, 2, …, 9, A, B, C, D, E, F
Decimal
Hex
Binary
0000 1
0001 2
0010 3
0011 4
0100 5
0101 6
0110 7
0111
Decimal
Hex
Binary 8
1000 9
1001 10 A
1010 11 B
1011 12 C
1100 13 D
1101 14 E
1110 15 F
1111

17. Hexadecimal Representation
Hex can be used as a short hand for long binary strings
Use one Hex digit to represent every group of 4 bits
Start from the right and an go left grouping 4 bit sequences
Add leading 0’s if the last group has less then 4 bits A D 6 5 B

18. Hexadecimal Representation
What is Hex 4C8F in binary?
4 C F
0100
1100
1000
1111

19. Representing Images as Bit maps
Image is collection of dots (pixels)
Pixel = “picture element”
Black & white: one bit per pixel
Color: each pixel represented by combination of green, red, blue in varying intensity, to form all colors. Three bytes per pixel: one byte (8 bits) for each color intensity, value
Usually each byte is represented in Hex
D4 7F 59  red (D4), green (7F), blue (59)
For example, D4 is binary which is decimal value 212
Bit maps are not efficient
3 byte/pixel, for 1280 x 1024 pixels = several megabytes
Image cannot be enlarged, since pixels get bigger and image gets grainy or “blocky”
.GIF and .JPEG formats compress images

20. Image Formats GIF JPEG (JPG) Graphics Interchange Format
Developed by Compuserve (ISP)
Stores only 256 colors
Loses some picture quality but is simple and fast
Common in computer action games
JPEG (JPG)
Joint Photographic Experts Group
Stores differences between adjacent pixels, not absolute values
Uses variable-length data (values take a minimum number of bits to store), uses only 5% of the space of bitmaps

21. Image Formats Vector Images Pixels are not mapped
Equations for the lines and curves making up the image are stored
Image is stored as the instructions for drawing the image
Images are easily scaled
Modern type fonts are vector images
Used in computer aided design (CAD) systems for “blueprint” drawings
Good for three-dimensional drawings
Windows metafile (.wmf) or Visio (.vsd)
Cannot produce photographic images