1. Introduction to Computers

2. What does it mean to be digital?
Wikipedia defines digital as the use of discrete values to represent something
The opposite term analog is a representation scheme that uses a continuous stream of values
A clock with hands is an analog representation
Shows a gradual progression to the next minute
A clock with numbers is a digital representation
Shows an instantaneous transition to the next minute every 60 seconds

3. More examples Lights Moving from the first to the second floor A stove
A switch is on or off (digital)
A dimmer allows any intensity (analog)
Moving from the first to the second floor
Stairs ascend in given increments (digital)
A ramp lets you be any distance above the floor
A stove
A digital display usually allows oven temperature to be set at increments of 5 or 10 degrees
A knob lets you set the oven at any temp (analog)

4. The world is going digital
Think about devices in your home…
Which are analog and which are digital?
Be careful to look at the main function of the device
A digital clock does not make your car a digital device
How many used to be analog and are now digital?
Record players and cassette tapes versus CDs
VCRs versus DVDs
Other examples?
Human senses function on an analog basis
But devices are gradually becoming digital

5. Digital electronics
Move to electronic digital devices has largely been brought about by computer technology
Digital electronics use only two states, on or off
Can also be thought of as 1 or 0, high or low
Analog devices use on and off plus the entire range of signal intensities found between on and off
Every scrap of electronic data is represented using these two states, on and off
Why is this better?

6. The Digital Advantage Light switch easier to interpret than a dimmer
With a switch, the question is “on or off?”
With a dimmer, the question is “how bright?”
The “on or off?” question can be answered simply
The “how bright?” question requires interpretation
Try to create the exact same lighting every day
Very hard to exactly recreate lighting with a dimmer
Instead try it with an 8 by 8 grid of tiny light bulbs
Put all 64 switches in a previous configuration to perfectly recreate a particular level of lighting

7. Bits
The basic unit of digital data storage is a single on/off switch, referred to as a bit or binary digit
Bit is a contraction of binary digit
Bit is used far more often than binary digit
A small “b” is used to refer to a bit
Computers represent much more complex data by grouping bits together in different ways

8. Representing numbers with bits
We express numbers using the decimal system
Uses 10 digits, zero through nine
We count beyond nine by carrying a 1 to the next place to the left
Computers use the binary system for numbers
Uses 2 digits, zero and one
Fits well with the on/off nature of computer bits
In order to count beyond one, must carry a 1 to the next place to the left, just as in the decimal system

9. Counting using the binary system
The example to the right illustrates both the decimal and binary number systems
Counting in the Decimal System
To count beyond nine, carry a 1 to the next place to the left
This 1 counts as ten since it’s in the 10’s place
To count beyond 99, carry a 1 to the next place to the left
This 1 counts as a hundred since it’s in the 100’s place
Counting in the Binary System
To count beyond one, carry a 1 to the next place to the left
This 1 counts as two since it’s in the 2’s place
To count beyond 3, carry a 1 to the next place to the left
This 1 counts as four since it’s in the 4’s place

10. Counting in binary… another view
Add the place values (1s, 2s, 4s, etc.) for all “on” light bulbs
Note all place values are powers of 2
1’s place = 20
2’s place = 21
4’s place = 22
8’s place = 23
= 0
= 1
= 2
= 3
= 4

11. Decimal places vs. binary places
The binary system looks odd, but it follows the same basic rules as the decimal system
Main difference is number of digits and value of each place
Each decimal place is worth 10place (103, 102, 101, 100)
So the value of 3042 in decimal is: (3 x 103) (0 x 102) (4 x 101) (2 x 100) 3 thousands + 0 hundreds tens ones
Each binary place is worth 2place (23, 22, 21, 20)
So the value of 1101 in binary is: (1 x 23) (1 x 22) (0 x 21) (1 x 100) = 13

12. Convert Binary to Decimal
What values are represented by the “on” bulbs?
Binary
100
111
101101
128s s s 16s s s s s
Decimal
= 4
= 7
= 45
= 102
= 255

13. Convert decimal to binary
Determine the highest binary place value less than the remaining number
Put 1 in that place value
Subtract place value to get a new remaining number
If remaining number not zero, return to step 1
Start with 75
Put 1 in 64’s place binary with 11 left
Put 1 in 8’s place binary with 3 left
Put 1 in 2’s place binary with 1 left
Put 1 in 1’s place binary with 0 left
75 in binary is:
64s 32s 16s s s s s

14. Convert Decimal to Binary
Convert these decimal values to binary
Decimal 4 11 54 97
252
128s s s 16s s s s s
Binary
= 100
= 1011 = = =

15. Binary addition
Use the normal rules for addition
Binary has no digit beyond 1
So carry a 1 for any result greater than 1
1’s place
1 + 1 = 10
Write 0 in 1’s place, carry a 1 to the 2’s place
2’s place
1 carried from 1’s place = 10
Write 0 in 2’s place, carry a 1 to the 4’s place
4’s place
1 carried from 2’s place = 10
Write 0 in 4’s place, carry a 1 to the 8’s place
8’s place
1 carried from 4’s place = 1
Write 1 in 8’s place
Binary Addition Example
place value
Decimal Equivalent
1 5
2 8

16. A little techie humor
100 in binary = 4 in decimal

17. Representing characters with bits
Data representation schemes allow complex data to be encoded as simple 1s & 0s
Morse Code a good example of a data representation scheme
Created more than 150 years ago for the telegraph
Represents characters as a series of dots and dashes
Dots and dashes represent two states, just like digital 1s and 0s

18. Bits and Bytes
Computers represent characters such as letters and punctuation using groups of 8 bits
Each of these 8 bit groups is called a byte
Each byte represents a single character
A capital “B” indicates a value measured in bytes

19. Representation of character data
Initially used ASCII to represent characters
This is a 7 bit data representation scheme
Includes upper & lower case letters, punctuation, numerals, and special characters such as etc.
7 bits lets us represent up to 128 (27) characters
128 characters too limiting for many languages
We now use extended ASCII as the standard
An 8 bit scheme allowing for 256 (28) characters
Allows for umlaut, tilde, & other such symbols
8 bits equals one byte which equals one character

20. The extended ascii character set
Each character has a unique 8 bit setting
Extended ASCII character set

21. file and storage size prefixes
Computer terminology typically expresses file sizes & storage capacities with prefixes such as:
Kilo (K) – about a thousand (actually 210 or 1,024)
Mega (M) - about a million (220 to be exact)
Giga (G) - about a billion (230 to be exact)
Note the exact values are all powers of 2
This is typical with computers
The dual state, on/off nature of computer data means most everything is measured in powers of 2

22. file size and storage size examples
Using the prefixes from the previous slide tells us that:
A 56Kb internet connection transmits approximately per second
A 48KB file contains approximately
A 1.6MB file has approximately
An 80GB hard disk can hold more than
56,000 bits
48,000 bytes
1,600,000 bytes
80,000,000,000 bytes

23. Representing a picture with bits
A picture is broken down into many pixels
A pixel can be thought of as a single point of color
An entire picture can be digitized as a grid of pixels
Each pixel can be one of 256 possible colors
You can recreate the picture if you know:
The color of each pixel
The location of each pixel in the grid
Color of each pixel requires one byte of storage
Location of each pixel in a 250x250 grid needs 2 bytes, one for row location, one for column location

24. Storage requirements for a picture
A picture of size 250x250 pixels needs:
250 rows x 250 columns = 62,500 pixels
3 bytes of storage needed for each pixel
62,500 pixels x 3 bytes per pixel = 187,500 bytes
A picture of modest size requires 187KB
A paragraph of text is often less than 187 bytes
Imagine the storage needed for a video clip!
Requires a series of many still images

25. In conclusion Nearly any type of data can be represented digitally
Data is digitized by:
Breaking it down into a discrete set of points
Using a coding scheme to represent each point
Numbers and characters require little storage
More complex data such as pictures or music require significantly more storage