[301] Bits and Memory. Tyler Caraza-Harter
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1 [301] Bits and Memory Tyler Caraza-Harter
2 Ones and Zeros Computers speak ones and zeros (called bits)
3 Ones and Zeros what about Computers speak ones and zeros (called bits)
4 Ones and Zeros what about text Computers speak ones and zeros (called bits) hello, world
5 Ones and Zeros what about text numbers Computers speak ones and zeros (called bits) hello, world
6 Ones and Zeros what about text images numbers Computers speak ones and zeros (called bits) hello, world
7 Ones and Zeros what about text images numbers video Computers speak ones and zeros (called bits) hello, world
8 Ones and Zeros what about text music images numbers video Computers speak ones and zeros (called bits) hello, world
9 Ones and Zeros what about text Intuitively, people used to believe all of these different types of information were music images fundamentally different numbers video Computers speak ones and zeros (called bits) hello, world
10 Information Theory Claud Shannon invented information theory in 1948, with bits as basic unit of information. Before Shannon, there was precious little sense of information as an idea, a measurable quantity, an object fitted out for hard science. Before Shannon, information was a telegram, a photograph, a paragraph, a song. After Shannon, information was entirely abstracted into bits. The sender no longer mattered, the intent no longer mattered, the medium no longer mattered, not even the meaning mattered: a phone conversation, a snatch of Morse telegraph, a page from a detective story, were all brought under a common code. ~ A Mind at Play, by Jimmy Soni and Rob Goodman
11 Learning Objectives What is a bit? A byte? How to quantify them? How can we use simple bits to represent everything? How are bits stored in memory? How can we store instructions in memory?
12 Today's Topics Binary Bits, bytes Quantifying bytes Memory Organization Data representation
13 What is a bit? A bit is just a 0 or a 1
14 Why the name bit? In the decimal number system, with have ten digits 0, 1, 2, 3, 5, 6, 7, 8, 9
15 Why the name bit? In the decimal number system, with have ten digits 0, 1, 2, 3, 5, 6, 7, 8, 9 In a binary system Two possibilities: 0 or 1
16 Why the name bit? In the decimal number system, with have ten digits 0, 1, 2, 3, 5, 6, 7, 8, 9 In a binary system Two possibilities: 0 or 1 Binary is general word beyond scope of computing Binary Start System
17 Why the name bit? In the decimal number system, with have ten digits 0, 1, 2, 3, 5, 6, 7, 8, 9 In a binary system Two possibilities: 0 or 1 Binary is general word beyond scope of computing A bit is short for binary digit Binary Start System
18 Why use bits in computing? Why not decimal? (make it easier for humans) Or something else, like 12? (divisible by many things)
19 Why use bits in computing? Why not decimal? (make it easier for humans) Or something else, like 12? (divisible by many things) Reason 1: elegance 2 different symbols in the minimum possible
20 Why use bits in computing? Why not decimal? (make it easier for humans) Or something else, like 12? (divisible by many things) Reason 1: elegance 2 different symbols in the minimum possible Reason 2: electronics computers are built from transistors and capacitors 0/1 maps nicely to on/off, open/closed, charged/uncharged
21 What if you want more than 2 values? Use more bits! 1 bit gives 2 values: 0, 1 2 bits gives 4 values: 00, 01, 10, 11 3 bits gives 8 values: 000, 001, 010, 011, 100, 101, 110, 111 N bits gives 2 N values
22 What is a byte? A byte is just 8 bits
23 What is a byte? A byte is just 8 bits For example:
24 What is a byte? A byte is just 8 bits For example: How many different byte values are there?
25 Today's Topics Binary Bits, bytes Quantifying bytes Memory Organization Data representation
26 Computers can process large numbers of bytes! Metric system commonly used Just like a kilogram is 1000 grams, a kilobyte is 1000 bytes Abbreviate: kb (kilobyte, thousand), MB (megabyte, million), GB (gigabyte, billion), TB (terabyte, trillion)
27 Computers can process large numbers of bytes! Metric system commonly used Just like a kilogram is 1000 grams, a kilobyte is 1000 bytes Abbreviate: kb (kilobyte, thousand), MB (megabyte, million), GB (gigabyte, billion), TB (terabyte, trillion) These metrics are used for speed and space Capacity: my hard drive can store 500 GB of data Throughput: I can save 100 MB of data per second to by hard drive
28 Computers can process large numbers of bytes! Metric system commonly used Just like a kilogram is 1000 grams, a kilobyte is 1000 bytes Abbreviate: kb (kilobyte, thousand), MB (megabyte, million), GB (gigabyte, billion), TB (terabyte, trillion) These metrics are used for speed and space Capacity: my hard drive can store 500 GB of data Throughput: I can save 100 MB of data per second to by hard drive (sometimes written MB/s or MBps)
29 Computers can process large numbers of bytes! Metric system commonly used Just like a kilogram is 1000 grams, a kilobyte is 1000 bytes Abbreviate: kb (kilobyte, thousand), MB (megabyte, million), GB (gigabyte, billion), TB (terabyte, trillion) These metrics are used for speed and space Capacity: my hard drive can store 500 GB of data Throughput: I can save 100 MB of data per second to by hard drive (sometimes written MB/s or MBps) What is the fastest you could fill up this hard drive, if it starts empty?
30 Gotcha 1: powers of 2 In computing, we often use 1024 instead of is a round number in binary, because it is 2 10 Just like 1000 is round in decimal because it is 10
31 Gotcha 1: powers of 2 In computing, we often use 1024 instead of is a round number in binary, because it is 2 10 Just like 1000 is round in decimal because it is 10 For example So a kilobyte might mean 1024 bytes instead of 1000 bytes A megabyte might mean 1,048,576 bytes (instead of 1,000,000)
32 Gotcha 1: powers of 2 In computing, we often use 1024 instead of is a round number in binary, because it is 2 10 Just like 1000 is round in decimal because it is 10 For example So a kilobyte might mean 1024 bytes instead of 1000 bytes A megabyte might mean 1,048,576 bytes (instead of 1,000,000) Note: the difference in interpretations is relatively small
33 Gotcha 2: b vs B What is faster, 80 Mbps, or 20 MBps? A little b means bits A capital B means bytes
34 Gotcha 2: b vs B What is faster, 80 Mbps, or 20 MBps? A little b means bits A capital B means bytes 1 byte = 8 bits, so 80 Mbps is actually 10 MBps
35 Gotcha 2: b vs B What is faster, 80 Mbps, or 20 MBps? A little b means bits A capital B means bytes 1 byte = 8 bits, so 80 Mbps is actually 10 MBps Bits are often used for networking, and bytes for storage This suggests you could download 12.5 MB of data per second. Example ad from
36 Today's Topics Binary Memory Organization Data representation Numbers Colors and images Text
37 RAM: Random Access Memory Memory cell circuit that stores 1 bit of information often based on capacitors low voltage is 0, high voltage is 1
38 RAM: Random Access Memory Memory cell circuit that stores 1 bit of information often based on capacitors low voltage is 0, high voltage is 1 Memory a lot of memory cells! Typically billions (for gigabytes of memory) lots of tiny capacitors these are built in, and don t actually look like this in the chip
39 RAM: Random Access Memory Memory cell circuit that stores 1 bit of information often based on capacitors low voltage is 0, high voltage is 1 Memory a lot of memory cells! Typically billions (for gigabytes of memory) How to find the right bits you need to access?
40 RAM: Random Access Memory Memory cell circuit that stores 1 bit of information often based on capacitors low voltage is 0, high voltage is 1 Memory a lot of memory cells! Typically billions (for gigabytes of memory) How to find the right bits you need to access? give groups of bits/bytes addresses
41 Addresses bits in memory voltage low low low low high high high high low high low high low high low high
42 Addresses addresses bits in memory voltage low low low low high high high high low high low high low high low high
43 Addresses addresses request bits at address 150 bits in memory voltage low low low low high high high high low high low high low high low high
44 Addresses addresses request bits at address 150 get back bits in memory voltage low low low low high high high high low high low high low high low high
45 Today's Topics Binary Memory Organization Data representation Numbers Colors and images Text Instructions
46 Data representation Challenge How can we use ones and zeros (many of them) to represent a wide variety of data?
47 Today's Topics Binary Memory Organization Data representation Numbers Colors and images Text Instructions
48 Types of numbers imaginary numbers whole numbers integers real other other
49 Types of numbers imaginary numbers real integers whole numbers 0, 1, 2, 3, 4, other other
50 Base ten vs two example digits (decimal): 0301
51 Base ten vs two example thousand s place hundred s place ten s place one s place digits (decimal): 0301
52 Base ten vs two example thousand s place hundred s place ten s place one s place digits (decimal): 0301 = 0x x x10 + 1x1
53 Base ten vs two example thousand s place hundred s place ten s place one s place Step up by factors of ten because we have ten digits digits (decimal): 0301 = 0x x x10 + 1x1
54 Base ten vs two example thousand s place hundred s place ten s place one s place Step up by factors of ten because we have ten digits digits (decimal): 0301 = 0x x x10 + 1x1 bits (binary): 1011 Number only uses 0 s and 1 s (NOT thousand and eleven)
55 Base ten vs two example thousand s place hundred s place ten s place one s place Step up by factors of ten because we have ten digits digits (decimal): 0301 = 0x x x10 + 1x1 bits (binary): 1011 eight s place four s place two s place one s place
56 Base ten vs two example thousand s place hundred s place ten s place one s place Step up by factors of ten because we have ten digits digits (decimal): 0301 = 0x x x10 + 1x1 eight s place four s place two s place one s place Step up by factors of two because we have two digits bits (binary): 1011
57 Base ten vs two example thousand s place hundred s place ten s place one s place Step up by factors of ten because we have ten digits digits (decimal): 0301 = 0x x x10 + 1x1 eight s place four s place two s place one s place Step up by factors of two because we have two digits bits (binary): 1011 = 1x8 + 0x2 + 1x2 + 1x1
58 Base ten vs two example thousand s place hundred s place ten s place one s place Step up by factors of ten because we have ten digits digits (decimal): 0301 = 0x x x10 + 1x1 eight s place four s place two s place one s place Step up by factors of two because we have two digits bits (binary): 1011 = 1x8 + 0x2 + 1x2 + 1x1 = eleven
59 Base ten vs two example thousand s place hundred s place ten s place one s place Step up by factors of ten because we have ten digits digits (decimal): 0301 = 0x x x10 + 1x1 eight s place four s place two s place one s place Step up by factors of two because we have two digits bits (binary): 1011 = 1x8 + 0x2 + 1x2 + 1x1 = eleven What decimal number is represented by these bits? 11001
60 Types of numbers imaginary How to handle negatives? numbers integers whole numbers 0, 1, 2, 3, 4, real other other
61 Types of numbers imaginary numbers real integers, -3, -2, -1, 0, 1, 2, 3, other
62 Negative binary numbers eleven: 1011
63 Negative binary numbers eleven: 1011 negative eleven: -1011
64 Negative binary numbers eleven: 1011 negative eleven: Problem: computers know 0 and 1 What is this - thing?
65 Negative binary numbers eleven: 1011 negative eleven: Problem: computers know 0 and 1 What is this - thing? Discuss approaches to representing negative integers with only 0 s and 1 s with your neighbor
66 One representation scheme is eleven is negative eleven
67 One representation scheme is eleven is negative eleven main number
68 One representation scheme is eleven is negative eleven 0: positive 1: negative main number
69 One representation scheme is eleven is negative eleven 0: positive 1: negative main number One oddity: and are two different ways to say the same number, zero. In practice, most computers use a slightly more complicated representation.
70 Today's Topics Binary Memory Organization Data representation Numbers Colors and images Text Instructions
71 Representing color All colors of light are a combination of red, green, and blue Of varying intensities Sometimes abbreviated RGB Maximum intensity of all three is white
72 Representing color All colors of light are a combination of red, green, and blue Of varying intensities Sometimes abbreviated RGB Maximum intensity of all three is white How to represent intensity of one of these primary colors?
73 Red intensity Strategy Strategy: use whole numbers (already know how to represent these as bits) Small number: less red Big number: more red
74 Back to colors Strategy Encode final color as mix of three intensities =????
75 Back to colors Strategy Encode final color as mix of three intensities red green blue =????
76 Back to colors Strategy Encode final color as mix of three intensities red green blue result = orange
77 Back to colors Strategy Encode final color as mix of three intensities We can represent many colors with 12 bits now red green blue result = orange
78 What about images? Strategy Break into a bunch of small squares, called pixels Record color of each pixel
79 What about images? pixel 1 Strategy Break into a bunch of small squares, called pixels Record color of each pixel
80 What about images? pixel 2 Strategy Break into a bunch of small squares, called pixels Record color of each pixel
81 What about images? pixel 3 Strategy Break into a bunch of small squares, called pixels Record color of each pixel
82 What about images? Strategy Break into a bunch of small squares, called pixels Record color of each pixel
83 A note on breaking down problems Problem: how to represent images as 1 s and 0 s? Can we make it simpler?
84 A note on breaking down problems Problem: how to represent images as 1 s and 0 s? Can we make it simpler? We can represent images as a bunch of color values We can represent a color value as a three integers We can represent an integer as a bunch of bits
85 A note on breaking down problems Problem: how to represent images as 1 s and 0 s? Can we make it simpler? We can represent images as a bunch of color values We can represent a color value as a three integers We can represent an integer as a bunch of bits Chain these representations together to represent images as bits!
86 Today's Topics Binary Memory Organization Data representation Numbers Colors and images Text Instructions
87 How can we encode text, like Hello World, using just bytes?
88 Morse Code
89 Morse Code H E L L O
90 Morse Code H E L L O We can represent text as dots and dashes. Any ideas on how we can further encode dots and dashes as bits?
91 Morse Code H E L L O
92 Morse Code H E L L O What s wrong with this?
93 Morse Code H E L L O is this H or EEEE?
94 Morse Code H E L L O is this H or EEEE? Morse code depends on spaces, which aren t bits! (similar to problem we encountered with - )
95 A popular encoding: ASCII American Standard Code for Information Interchange We know how to encode integers as bits
96 A popular encoding: ASCII American Standard Code for Information Interchange We know how to encode integers as bits Assign every English letter (upper and lower case), digit, and various other symbols a number between 0 and 127 To save text as bits, convert each character to a number, then convert that number to bits
97
98 A popular encoding: ASCII American Standard Code for Information Interchange We know how to encode integers as bits Assign every English letter (upper and lower case), digit, and various other symbols a number between 0 and 127 To save text as bits, convert each character to a number, then convert that number to bits Problem: to be generally useful for text in many languages, 127 is not nearly enough. We need more characters!
99 Unicode A numbered set of characters for many languages The number assigned a character is its code point Has 137,439 characters Supports 146 different scripts (a script is the set of characters used in a language; different languages may share the same script) Many of the changes from Python 2 to Python 3 are related to making unicode the default
100 Unicode A numbered set of characters for many languages The number assigned a character is its code point Has 137,439 characters Supports 146 different scripts (a script is the set of characters used in a language; different languages may share the same script) Many of the changes from Python 2 to Python 3 are related to making unicode the default n has code point 110 ñ has code point 241
101 Code points to bits Unicode has multiple ways to convert code points to bits Useful for compatibility/efficiency Character Code Point Bits n 110 utf ñ 241 utf utf-32 is a way to convert code points to bits. If you use the same number of bits for every code point, you need lots of bits (because there are many code points)
102 Code points to bits Unicode has multiple ways to convert code points to bits Useful for compatibility/efficiency Character Code Point Bits utf n 110 utf utf ñ 241 utf utf-8 uses shorter sequences of bits for some characters and longer sequences for others. Depending on what characters you use, this may save bits.
103 Today's Topics Binary Memory Organization Data representation Numbers Colors and images Text Instructions
104 Storing code in memory Programs are also represented in memory A program is just a bunch of instructions Instructions are things like add, subtract, multiply, compare
105 Storing code in memory Programs are also represented in memory A program is just a bunch of instructions Instructions are things like add, subtract, multiply, compare Encoding strategy Give each instruction a number, for example: 1: add 2: multiply 3: compare
106 Storing code in memory Programs are also represented in memory A program is just a bunch of instructions Instructions are things like add, subtract, multiply, compare Encoding strategy Give each instruction a number, for example: 1: add 2: multiply 3: compare We already know how to represent numbers as bits, so we can also represent the instructions that make up a program as bits
107 Conclusion Today we learned about Binary numbers How RAM stores binary numbers Units for expressing capacity and throughput All information can be represented with bits! Encoding strategies for numbers, images, text, and programs - the details don t matter for this class. Just get a sense how to break down the problem of converting different types of data to ones and zeros
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