Topic 1: Digital Data

Transcription

1 Term paper: Judging the feasibility of a topic Is it a topic you are excited about? Is there enough existing research in this area to conduct a scholarly study? Topic 1: Digital Data ECS 15, Winter 2015 Lecture 3 Finding existing literature --- e.g., scholar.google.com, webofknowledge.com, pubmed.com (Note cited reference search see the follow-on work) What is my hypothesis? (What kind of interesting results can I expect to find?) How can I validate or invalidate my hypothesis? What are the implications of my conclusions? Some resources for research scholar.google.com Find articles on a particular topic Search through all follow-up work (i.e., papers that have hence cited the work of interest). apps.isiknowledge.com (Must be on ucdavis.edu network) (ISI Web of Knowledge/ Web of Science) (Like scholar.google.com only for scientific journal articles) UC Davis libraries (Thurs 1/22, Phoebe Ayers talk) Wikipedia (but look at page history to understand any controversies or debates) TED (Technology Entertainment and Design), Ideas worth spreading, Computer Science Theory of computation Software engineering Computer graphics Computer security and cryptography Computer networks Artificial intelligence Human-computer interface Bioinformatics Systems and architecture

2 Growth Mindset Test your mindset: Do you agree that intelligence is something about a person that he/she can t change very much? Strongly agree to strongly disagree Fixed mindset vs. growth mindset Can one learn to be good at computers? Yes, absolutely. And yes, absolutely worth your time and effort Google growth mindset for more information. Focus and concentration are skills! Practice distraction free hour Digital Data Binary and Hexadecimal numbers ASCII code and UNICODE Sampling and Quantitizing Example: sound Basic Concepts Binary and Hexadecimal numbers Number representation We are used to counting in base 10: ASCII code and UNICODE Example:.. thousands hundreds tens units Sampling and Quantitizing Example: sound x1000+7x100+3x10+2x1 = 1732 digits Terminology: most-significant digit / least-significant digit

3 Number representation Computers use a different system: base 2: Converting from base 2 to base 10 is simple. For instance: bits x1024+1x512+0x256+1x128+1x64+0x32+ 0x16+ 0x8 + 1x4 + 0x2 + 0x1 = 1732 Number representation Base 10 Base Facts about Binary Numbers Binary numbers, 8 bits = 1 byte - Each digit of a binary number (each 0 or 1) is called a bit - 1 byte = 8 bits - 1 KB = 1 kilobyte = 2 10 bytes = 1024 bytes ( 1 thousand bytes) - 1 MB = 1 Megabyte = 2 20 bytes = 1,048,580 bytes ( 1 million bytes) - 1 GB = 1 Gigabyte = 2 30 bytes = 1,073,741,824 bytes ( 1 billion bytes) - 1 TB = 1 Tetabyte = 2 40 bytes = 1,099,511,627,776 bytes ( 1 trillion bytes) - A byte can represent numbers up to 255: (base 2) = 255 (base 10) - The maximum number represented by a binary number of size N is 2 N The maximum number represented by a binary number of size N is 2 N = 63 = = A byte (8 bits) can represent numbers ranging from 0 up to = (base 2) = 255 (base 10)

4 Algorithms to convert from base10 to base2 (Recall base2 to base10 simple and direct) 1. The modulus algorithm, bottom-up (determine least significant bit first) Let m be a base 10 number. Convert m to a base 2 number: 1. The bottom-up modulus algorithm (determine least significant bit first). The operation a % b (said a mod b ) returns the remainder when a is divided by b. 2. The top-down recursive algorithm (determine most significant bit first). From base 10 to base 2: 1877 %2 = 938 Remainder %2 = 469 Remainder %2 = 234 Remainder %2 = 117 Remainder %2 = 58 Remainder 1 58 %2 = 29 Remainder 0 29 %2 = 14 Remainder 1 14 %2 = 7 Remainder 0 7 %2 = 3 Remainder 1 3 %2 = 1 Remainder 1 1 %2 = 0 Remainder 1 Read off number from last determined back to first (to get ordering from most significant to least) (base10) = (base 2) 2. The recursive algorithm, top-down (determine most significant bit first and repeat) Let m be a base 10 number. Convert m to a base 2 number: 1. Identify biggest n such that 2 n m. 2. Place a 1 in the slot corresponding to 2 n. (The n+1 slot!) 3. Subtract: m = m 2 n 4. Repeat steps 1 to 3 with m=m, continue until m =0. Base 10: Base 2: Digital data: Base 10, Base 2, Base 16: thousands hundreds tens units The digits are: e.g., m = Step 1: 1 in 11 th slot (2 10 =1024); m = = 29. Step 2: 1 in 5 th slot (2 4 =16); m = = 13. Step 3: 1 in 4 th slot (2 3 =8); m = 13-8 = 5. Step 4: 1 in 3 rd slot (2 2 =4); m = 5-4 = 1. Step 5: 1 in 1 st slot (2 0 =1); m =0. So 1053 in base 10 = in base The digits are: 0 1 Base 16: The digits are: A B C D E F

5 In class exercise, part I 1. Choose at random a base 2 number, of 8 digits in length, with four 1 s and four 0 s interspersed. Convert it to the corresponding base 10 number. Hexadecimal numbers While base 10 and base 2 are the most common bases used to represent numbers, others are also possible: base 16 is another popular one, corresponding to hexadecimal numbers Choose at random a 4-digit base 10 number (less than 2048 is good). Make sure it is not a simple power of 2. Convert it into the corresponding binary number The digits are: A B C D E F Example: 2 A F x * x1 = 687 Hexadecimal numbers Everything we have learned in base 10 should be studied again in other bases!! Example: multiplication table in base 16: Number representation Base 10 Base 2 Base A B C D E F

6 Conversion: From base 2 to base 16, and back This is in fact easy!! - From base 2 to base 16: Example: Step 1: break into groups of 4 (starting from the right): Step 2: pad left-most with 0, if needed: Step 3: convert each group of 4, using table: 6 C 4 Step 4: regroup: 6C (base 2) = 6C4 (base 16) Conversion: From base 2 to base 16, and back From base 16 to base 2: Example: 4FD Step 1: split: 4 F D Step 2: convert each digit, using table: Step 3: Remove leading 0, if needed Step 4: regroup: FD (base 16) = (base 2) In class exercise, part II 3. Convert this hexadecimal number to base 10: 2A3F Basic Concepts Binary and Hexadecimal numbers ASCII code and UNICODE Sampling and Quantitizing Example: sound

7 ASCII American Standard Code for Information Interchange So far, we have seen how computers can handle numbers. What about letters / characters? The ASCII code was designed for that: it assigns a number to each character: A-Z: a-z: : UNICODE ASCII only contains 127 characters (though an extended version exists with 257 characters). This is by far not enough as it is too restrictive to the English language. UNICODE was developed to alleviate this problem: the latest version, UNICODE contains more than 100,000 characters, covering most existing languages. For more information, see: Basic Concepts Binary and Hexadecimal numbers ASCII code and UNICODE Sampling and Quantitizing Example: sound

8 Digital Sound What is sound? Transverse and longitudinal waves Sound is produced by the vibration of a media like air or water. Audio refers to the sound within the range of human hearing. Naturally, a sound signal is analog, i.e. continuous in both time and amplitude. These are analog, continuous waves. To store and process sound information in a computer or to transmit it through a computer network, we must first convert the analog signal to digital form using an analog-to-digital converter ( ADC ); the conversion involves two steps: (1) sampling, and (2) quantization. Sampling Sampling is the process of examining the value of a continuous function at regular intervals. Sampling Note that choosing the sampling rate is not innocent (not without consequence): Sampling usually occurs at uniform intervals, which are referred to as sampling intervals. The reciprocal of sampling interval is referred to as the sampling frequency or sampling rate. If the sampling is done in time domain, the unit of sampling interval is second and the unit of sampling rate is Hz, which means cycles per second. How do we choose the sampling rate?

9 How do we choose the sampling rate? Quantization Quantization is the process of limiting the value of a sample of a continuous function to one of a predetermined number of allowed values, which can then be represented by a finite number of bits. A higher sampling rate usually allows for a better representation of the original sound wave. However, when the sampling rate is set to twice the highest frequency in the signal, the original sound wave can be reconstructed without loss from the samples. This is known as the Nyquist theorem. Quantization (The allowed amplitudes) The number of bits used to store each intensity defines the accuracy of the digital sound: Adding one bit makes the sample twice as accurate