Bits, Bytes and Files

Bits, Bytes and Files CS 1 Introduction to Computers and Computer Technology Rick Graziani Spring 2007

Digitization • Digitize – To represent information with digits or symbols. • Digitization does not require any digits, any set of symbols will to. • We use digits 0 through 9, do digitize a phone number: • (Area code) Prefix – Number • (aaa) ppp – nnnn • We use numbers, but we could have chosen any group of symbols. Rick Graziani graziani@cabrillo.edu

Digitization • The advantage of using digits instead symbols is they can be listed in numerical order. • Symbols can have an order to them, known as collating sequence, such as player encoding for DVD and VCR players. Rick Graziani graziani@cabrillo.edu

Other Collating Sequences? Rick Graziani graziani@cabrillo.edu

Encoding with Dice • Because information can be digitized using any symbols, consider a representation based on using dice. • Encoding - The process of putting information into a specific format (usually digital format). • A die has 6 unique patterns on it. • If we used a single die we could encode, represent, 6 pieces of information. • This would not be enough to represent the entire alphabet. A B C D E F Rick Graziani graziani@cabrillo.edu

Encoding with Dice • Two dice patterns together produce 6 x 6 = 36 different pattern sequences, because each die can be paired with each of 6 different patterns of the other die. • Three dice would produce 6 x 6 x 6 = 216 different pattern sequences. Pairing two dice patterns results in 36 = 6  6 possible pattern sequences. Rick Graziani graziani@cabrillo.edu

Encoding with Dice • If we used two dice to encode information… A B C D … F E G Rick Graziani graziani@cabrillo.edu

Encoding with Dice • Two dice patterns together produce 6 x 6 = 36 different pattern sequences. • Notice that only 26 of the 36 unique pattern sequences are needed for the 26 letters in the alphabet. Rick Graziani graziani@cabrillo.edu

Encoding with Dice • Encode the phrase CABRILLO COLLEGE using two dice. • Choose a sequence for the space. __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ Rick Graziani graziani@cabrillo.edu

C A B R I L L space O O L L E C G E space Rick Graziani graziani@cabrillo.edu

Encoding with Dice • The other 10 combinations could be used for numbers 0 through 9. • Or • It could be used for punctuation including an Escape Character or a Shift Key. space Rick Graziani graziani@cabrillo.edu

Encoding with Dice • Using one of the keys as a special character key, like the Shift Key, can double the number of possibilities for all other keys. • Using combinations of two keys, can triple the possible combinations, i.e. Control-Shift-Delete A a b c d e f g h i j k l Shift a m n o p q r s t u v w x y z Shift Rick Graziani graziani@cabrillo.edu

Moving to Bits… • Most fundamental form of information is the presence or absence of a physical phenomenon: • Is something there, or not? • Is light detected, or not? • Is it magnetized, or not? • PandA is the name we use for the fundamental patterns of digital information based on the presence or absence of a physical phenomenon. Rick Graziani graziani@cabrillo.edu

BIT – BInary digiT • In computer technology, the PandA unit is known as a bit. • Bit (Binary Digit) = Basic unit of information, representing one of two discrete states. The smallest unit of information within the computer. • The only thing a computer understands. • Abbreviation: b • Bit has one of two values: 1 (ON) or 0 (OFF) ON OFF Rick Graziani graziani@cabrillo.edu

Bits • Two patterns are known as the state of the bit. • For example, magnetic encoding of information on tapes, floppy disks, and hard disks are done with positive or negative polarity. The boxes illustrate a position where magnetism may be set and sensed; pluses (red) indicate magnetism of positive polarity (1 bit), interpreted as “present” and minuses (blue) (0 bit). 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 Rick Graziani graziani@cabrillo.edu

Bits Analogy: Sidewalk Memory • Memory (temporary or permanent) analogy is like a strip of concrete. • Stone on the sidewalk represents a 1 bit, absence of a stone represents a 0 bit. Sidewalk sections as a sequence of bits (1010 0010). Rick Graziani graziani@cabrillo.edu

Combining Bit Patterns • Using a single bit, with two discrete states, gives only two options (ON or OFF). • Like using multiple dice, combining two or more bits gives us more options. (Bits only have 2 unique patterns, whereas the die had 6). • 1 bit, 2unique patterns: 0 or 1 • 2 bits, 4unique patterns: 00, 01, 10 or 11 • 4 bits, 16unique patterns: 0000, 0001, 0010, 0010, …1111 • 8 bits, 256unique patterns: 00000000, 00000001, 00000010, … 11111111 bit OFF ON die Rick Graziani graziani@cabrillo.edu

Binary Math • Why does 7 bits give you 128 unique bytes? • Why does 8 bits give you 256 unique bytes? Starting with all “off’s” or 0’s 0 0 0 0 0 0 0 0 Add 1 until you get all 1’s (on’s) 1 1 1 1 1 1 1 1 You get 256 unique combinations of 0’s and 1’s Rick Graziani graziani@cabrillo.edu

Binary Math www.thinkgeek.com Rick Graziani graziani@cabrillo.edu

Binary Math 0 0 1 10 11 100 101 +0 +1 +1 +1 +1 + 1 + 1 0 1 10 11 100 101 110 Decimal 0 1 2 3 4 5 5 111 00000000 11111110 + 1 + 0 -> + 1 1000 …… 00000000 11111111 Rick Graziani graziani@cabrillo.edu

Base 10 (Decimal) Number System Digits (10): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Number of: 104 103 102 101 100 10,000’s1,000’s100’s10’s1’s 1 2 3 9 1 0 9 9 1 0 0 Rick Graziani graziani@cabrillo.edu

Base 10 (Decimal) Number System Digits (10): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Number of: 104 103 102 101 100 10,000’s1,000’s100’s10’s1’s 4 1 0 8 3 8 2 1 0 0 0 9 1 0 0 1 0 Rick Graziani graziani@cabrillo.edu

Rick’s Number System Rules • All digits start with 0 • A Base-n number system has n number of digits: • Decimal: Base-10 has 10 digits • Binary: Base-2 has 2 digits • Hexadecimal: Base-16 has 16 digits • The first column is always the number of 1’s • Each of the following columns is n times the previous column (n = Base-n) • Base 10: 10,000 1,000 100 10 1 • Base 2: 16 8 4 2 1 • Base 16: 65,536 4,096 256 16 1 Rick Graziani graziani@cabrillo.edu

Base 2 (Binary) Number System Digits (2): 0, 1 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 2 1 0 10 1 0 1 0 17 70 130 255 Rick Graziani graziani@cabrillo.edu

Base 2 (Binary) Number System Digits (2): 0, 1 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 2 1 0 10 1 0 1 0 17 1 0 0 0 1 70 1 0 0 0 1 1 0 130 1 0 0 0 0 0 1 0 255 1 1 1 1 1 1 1 1 Rick Graziani graziani@cabrillo.edu

Converting between Decimal and Binary Digits (2): 0, 1 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 172 192 Rick Graziani graziani@cabrillo.edu

Converting between Decimal and Binary Digits (2): 0, 1 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 70 1 0 0 0 1 1 0 40 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 128 1 0 0 0 0 0 0 0 172 1 0 1 0 1 1 0 0 192 1 1 0 0 0 0 0 0 Rick Graziani graziani@cabrillo.edu

Computers do Binary 0 1 • Bits have two values: OFF and ON • The Binary number system (Base-2) can represent OFF and ON very well since it has two values, 0 and 1 • 0 = OFF • 1 = ON • Understanding Binary to Decimal conversion is critical in networking. • Although we use decimal numbers in networking to display information such as IP addresses (LATER), they are transmitted as OFF’s and ON’s that we represent in binary. Rick Graziani graziani@cabrillo.edu

Rick’s Program Rick Graziani graziani@cabrillo.edu

Binary Math Why does 7 bits give you 128 unique bytes? Starting with all “off’s” or 0’s 0 0 0 0 0 0 0 (decimal 0) Add 1 until you get all 1’s (on’s) 1 1 1 1 1 1 1 (decimal 127) You get 128 unique combinations of 0’s and 1’s With 7 combinations of 2 bits,27 = 128 Number of: 26 25 24 23 22 21 20 64’s32’s16’s8’s4’s2’s1’s Dec. 0 0 0 0 0 0 0 0 127 1 1 1 1 1 1 1 Rick Graziani graziani@cabrillo.edu

Binary Math Why does 8 bits give you 256 unique bytes? Starting with all “off’s” or 0’s 0 0 0 0 0 0 0 0 (decimal 0) Add 1 until you get all 1’s (on’s) 1 1 1 1 1 1 1 1 (decimal 255) You get 256 unique combinations of 0’s and 1’s With 8 combinations of 2 bits,28 = 256 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 0 0 0 0 0 0 0 0 0 255 1 1 1 1 1 1 1 1 Rick Graziani graziani@cabrillo.edu

Digitizing Text • Earliest uses of PandA was to digitize text (keyboard characters). • We will look at digitizing images and video later. • Assigning Symbols in United States: • 26 upper case letters • 26 lower case letters • 10 numerals • 20 punctuation characters • 10 typical arithmetic characters • 3 non-printable characters (enter, tab, backspace) • 95 symbols needed Rick Graziani graziani@cabrillo.edu

ASCII-7 • In the early days, a 7 bit code was used, with 128 combinations of 0’s and 1’s, enough for a typical keyboard. • The standard was developed by ASCII (American Standard Code for Information Interchange) • Each group of 7 bits was mapped to a single keyboard character. 0 = 0000000 1 = 0000001 2 = 0000010 3 = 0000011 … 127 = 1111111 Rick Graziani graziani@cabrillo.edu

Byte Byte = A collection of bits (usually 7 or 8 bits) which represents a character, a number, or other information. • More common: 8 bits = 1 byte • Abbreviation: B Rick Graziani graziani@cabrillo.edu

Bytes 1 byte (B) Kilobyte (KB) = 1,024 bytes (210) • “one thousand bytes” 1,024 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 Megabyte (MB) = 1,048,576 bytes (220) • “one million bytes” Gigabyte (GB) = 1,073,741,824 bytes (230) • “one billion bytes” Rick Graziani graziani@cabrillo.edu

ASCII-8 • IBM later extended the standard, using 8 bits per byte. • This was known as Extended ASCII or ASCII-8 • This gave 256 unique combinations of 0’s and 1’s. 0 = 00000000 1 = 00000001 2 = 00000010 3 = 00000011 … 255 = 11111111 Rick Graziani graziani@cabrillo.edu

ASCII-8 Rick Graziani graziani@cabrillo.edu

Remember the Dice… 256 possible combinations 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 or shown as 16 x 16 = 256 36 possible combinations 6 x 6 = 36 Rick Graziani graziani@cabrillo.edu

Try it! • Write out Cabrillo College (Upper and Lower case) in bits (binary) using the chart above. 0100 0010 0110 0001 … C a Rick Graziani graziani@cabrillo.edu

The answer! 0100 0010 0110 0001 0110 0010 0111 0010 0110 1001 0110 1100 C a b r i l 0110 1100 0110 1111 0010 0000 0100 0010 0110 1111 0110 1100 l o space C o l 0110 1100 0110 0101 0110 0111 0110 0101 l e g e Rick Graziani graziani@cabrillo.edu

Unicode • Although ASCII works fine for English, many other languages need more than 256 characters, including numbers and punctuation. • Unicode uses a 16 bit representation, with 65,536 possible symbols. • Unicode can handle all languages. • www.unicode.org Rick Graziani graziani@cabrillo.edu

Non-text Files: Representing Images and Sound

RGB Colors and Binary Representation • A monitors screen is divided into a grid of small unit called picture elements or pixels. (See reading from Chapter 1). • The more pixels per inch the better the resolution, the sharper the image. • All colors on the screen are a combination of red, green and blue (RGB), just at various intensities. Rick Graziani graziani@cabrillo.edu

Each Color intensity of red, green and bluerepresented as a quantity from 0 through 255. • Higher the number the more intense the color. • Black has no intensity or no color and has the value (0, 0, 0) • White is full intensity and has the value (255, 255, 255) • Between these extremes is a whole range of colors and intensities. • Grey is somewhere in between (127, 127, 127) Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation • You can use your favorite program that allows you to choose colors to view these various red, green and blue values. Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation • Let’s convert these colors from Decimal to Binary! RedGreenBlue Purple: 172 73 185 Gold:253 249 88 Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation RedGreenBlue Purple: 172 73 185 Gold:253 249 88 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 172 73 185 253 249 88 Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation RedGreenBlue Purple: 172 73 185 Gold:253 249 88 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 172 1 0 1 0 1 1 0 0 73 0 1 0 0 1 0 0 1 185 1 0 1 0 1 1 1 1 253 1 1 1 1 1 1 0 1 249 1 1 1 1 1 0 0 1 88 0 1 0 1 1 0 0 0 Rick Graziani graziani@cabrillo.edu

Bits, Bytes and Files

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