1. Unit 1 Digital Data Section D

2. Chapter 1, Slide 2Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 2 Wikipedia defines digital as the use of discrete values to represent somethingdigital 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. Chapter 1, Slide 3Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 3 Lights 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. Chapter 1, Slide 4Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 4 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. Chapter 1, Slide 5Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 5 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. Chapter 1, Slide 6Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 6 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 Can set all 64 switches in a previous configuration to perfectly recreate a particular level of lighting

7. Chapter 1, Slide 7Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 7 The basic unit of digital data storage is a single on/off switch, referred to as a bit or binary digitbitbinary 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. Chapter 1, Slide 8Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 8 We express numbers using the decimal systemdecimal 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 numbersbinary system 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. Chapter 1, Slide 9Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 9 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. Chapter 1, Slide 10Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 10 Add the place values (1s, 2s, 4s, etc.) for all “on” light bulbs Note all place values are powers of 2 1’s place = 2 0 2’s place = 2 1 4’s place = 2 2 8’s place = 2 3 = 0 = 1 = 2 = 3 = 4

11. Chapter 1, Slide 11Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 11 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 10 place (10 3, 10 2, 10 1, 10 0 ) So the value of 3042 in decimal is: (3 x 10 3 ) + (0 x 10 2 ) + (4 x 10 1 ) + (2 x 10 0 ) 3 thousands +0 hundreds + 4 tens +2 ones Each binary place is worth 2 place (2 3, 2 2, 2 1, 2 0 ) So the value of 1101 in binary is: (1 x 2 3 ) + (1 x 2 2 ) + (0 x 2 1 ) + (1 x 10 0 ) 8 + 4 + 0 + 1 = 13

12. Chapter 1, Slide 12Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 12 What values are represented by the “on” bulbs? Decimal 128s 64s 32s 16s 8s 4s 2s 1s Binary 100 111 101101 1100110 11111111

13. Chapter 1, Slide 13Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 13 1. Determine the highest binary place value less than the remaining number 2. Put 1 in that place value 3. Subtract place value to get a new remaining number 4. If remaining number not zero, return to step 1 1. Start with 75 2. Put 1 in 64’s place-64 1000000 binary with 11 left 3. Put 1 in 8’s place- 8 1001000 binary with 3 left 4. Put 1 in 2’s place- 2 1001010 binary with 1 left 5. Put 1 in 1’s place- 1 1001011 binary with 0 left 75 in binary is: 64s 32s 16s 8s 4s 2s 1s 1 0 0 1 0 1 1

14. Chapter 1, Slide 14Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 14 Convert these decimal values to binary Decimal 4 11 54 97 252 Binary

15. Chapter 1, Slide 15Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 15 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 + 0 + 1 = 10 Write 0 in 2’s place, carry a 1 to the 4’s place 4’s place 1 carried from 2’s place + 1 + 0 = 10 Write 0 in 4’s place, carry a 1 to the 8’s place 8’s place 1 carried from 4’s place + 0 + 0 = 1 Write 1 in 8’s place Binary Addition Example 1 101 +1+011 101000 2 1place value 8 4 2 1 Decimal Equivalent 15 +1 +3 28

16. Chapter 1, Slide 16Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 16 100 in binary = 4 in decimal

17. Chapter 1, Slide 17Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 17 Data representation schemes allow complex data to be encoded as simple 1’s & 0’s Morse CodeMorse 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. Chapter 1, Slide 18Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 18 Computers represent characters such as letters and punctuation using groups of 8 bits Each of these 8 bit groups is called a bytebyte Each byte represents a single character A capital “B” indicates a value measured in bytes

19. Chapter 1, Slide 19Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 19 Initially used ASCII to represent charactersASCII 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 (2 7 ) characters 128 characters too limiting for many languages We now use extended ASCII as the standardextended ASCII An 8 bit scheme allowing for 256 (2 8 ) characters Allows for umlaut, tilde, & other such symbols 8 bits equals one byte which is also one character

20. Chapter 1, Slide 20Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 20 Each character has a unique 8 bit setting Extended ASCII character set

21. Chapter 1, Slide 21Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 21 Computer terminology typically expresses file sizes & storage capacities with prefixes such as: Kilo (K) – about a thousand (actually 2 10 or 1,024) Mega (M) - about a million (2 20 to be exact) Giga (G) - about a billion (2 30 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. Chapter 1, Slide 22Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 22 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

23. Chapter 1, Slide 23Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 23 A picture is broken down into many pixelspixels 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. Chapter 1, Slide 24Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 24 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. Chapter 1, Slide 25Starting Out with Visual Basic 3 rd EditionIntroduction to ComputersUnit 1D – Digital DataSlide 25 Nearly any type of data can be represented digitally Data is digitized by:digitized 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