Introduction to Computers

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

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)

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

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?

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

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

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

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

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

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 + 4 tens + 2 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) 8 + 4 + 0 + 1 = 13

Convert Binary to Decimal What values are represented by the “on” bulbs? Binary 100 111 101101 1100110 11111111 128s 64s 32s 16s 8s 4s 2s 1s Decimal = 4 = 7 = 45 = 102 = 255

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 -64 1000000 binary with 11 left Put 1 in 8’s place - 8 1001000 binary with 3 left Put 1 in 2’s place - 2 1001010 binary with 1 left 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

Convert Decimal to Binary Convert these decimal values to binary Decimal 4 11 54 97 252 128s 64s 32s 16s 8s 4s 2s 1s Binary = 100 = 1011 = 110110 = 1100001 = 11111100

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 + 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 10 1000 2 1 place value 8 4 2 1 Decimal Equivalent 1 5 + 1 + 3 2 8

A little techie humor 100 in binary = 4 in decimal

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

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

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

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

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

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

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

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

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