Unit 3 Data Representation

output (1)

observable behaviors generated by the computer such as animation, sound, and text.

ASCII (4)

(American Standard Code for Information Interchange) - a table that outlines a common set of conventions established for converting between binary values and alphanumeric (represents 128 different characters). - Works for English only. - 7 bits.

DIGITIZING the real world... (2)

- ... is an example of abstraction. - The infinite details of a real hill are represented by a finite number of digital pieces.

bytes (2)

- 8 bit (used more commonly). - 0-255 total in integer values, but 256 including 0.

decimal (1,1)

- describes the base-10 number system. + The most commonly used number system.

analog (1,1)

- non-digital signals or information represented by a continuously variable physical quantity such as spatial position or voltage. + Continuous and natural.

list (2,1)

- A list is an ordered sequence of elements. + For example, [value1, value2, value3, ...] describes a list where value1 is the first element, value 2 is the second element, value 3 is the third element, and so on. - An abstraction.

AP pseudocode list (2)

- AP pseudocode the elements are indexed from 1 to the number of items on the list. - Trying to access item 0 or an index greater than the number of items would generate an error.

List Implementation in Different Languages (1,2):

- Almost all programming language contain lists/arrays of some kind. However, the details of implementation can differ between languages. + For example, in AP CSP pseudocode the first element on a list is indexed at position 1. + In the Java programming language the first item on a list is indexed at position 0.

digital representations (2)

- Although digital representations are discrete, the information represented can be either discrete, such as numbers or letters. - ... or continuous, such as sounds, images, and other measurements of continuous systems

What happens when a physical artifact is digitized? (2,2)

- An artifact is a visualization, a graphic, a program, or an audio recording created by a computer. - The state space (range of possibilities) perceived is broken into "chunks"--called QUANTA. + Each quantum is converted to a value using binary. + The binary representing the artifact depends on the algorithm or convention used (such as ASCII, Unicode, Base 2 numbers, etc.)--I.e. PNG, PDF..

Where do fixed-width encodings end? (1,3)

- Benefit of SEGMENTATION, SIZE, AND MAPPING: + Segmentation: allows us to know where a segment ends and begins. + Size: bits are used for the entire state space, so size of segment is known. + Mapping: easier to map button presses, since the physical number of wires/ circuits is fixed.

ASCII table (3)

- Compiler cannot read the Extended ASCII set (has to be plain). - Uppermost two rows in standard ASCII represent keys (I.e. bs = backspace). - Read from right column to uppermost row.

Fixed-point representation with decimals (3,1):

- Consider the following 32 bit representation: 11011111110001011101111111000101 3754287045 375428.7045 - This assumes that the number is always represented to the 1/10,000ths in precision, but this is arbitrary--could have chosen any different number of decimal places. - Would need to choose this number beforehand, and it would apply to any number encoded with this representation + = fixed-point representation because the decimal point is always in the same place.

The base of each exponential term is the base of the number system (2):

- Decimal: base 10. - Binary: base 2.

Where do variable-width encodings end? (4,1)

- I.e. What differentiates two 'E's in a row from one 'I'? + Uses DELIMETERS: - I.e. spreadsheet separates columns into commas (the commas are delimiters). - Good: it's easy to spot transitions between symbols. - Bad: delimiters add to the size of file for each symbol.

AP Exam: how to solve bytes to ASCII (2)

- Make an 7-8 bit. - Convert decimal to binary.

Floating-point numbers (2,1)

- Not only is the numeric value determined by the binary representation, but where the decimal point is located is encoded as well. + Note that moving the decimal point allows us to encode a much wider range of numbers than we could with fixed-point representation. - I.e. Using only 32 bits, encode positive values 3.40282 × 10^38... Note the number of zeroes in each. We can't encode all the values between these two numbers, just values to a certain degree of precision.

Limitations of using Bits to represent data (1):

- Programming languages are limited to a fixed number of bits to represent them > round-off or errors can occur. (I.e. 2/3 or .6666... = not enough bits to represent all values.)

variable-width encoding is used in... (2)

- Some forms of Unicode (because Unicode spans 8, 16, 32 bit representation). - A common form of compression called Huffman coding to save space.

fixed-width encoding is used in... (2)

- Standard ASCII (associates each symbol with 7 bits). - Extended ASCII (allocates 8 bits for each symbol).

digital copies (2)

- The fact that digital copies do not degrade is perhaps the most important component of the digital revolution... - ... and a drawback (that they are really just approximations of what they represent).

Purpose of bits (3)

- To represent something digitally. - Represent how information (or data) is stored, accessed, transformed and used by computers. - Heuristic method, to represent numbers, but not the extent of it (I.e. cannot demonstrate the largest number).

State space is not about numbers (3,3):

- Unlike the base10 system, each place value in binary (or base2) has only two possibilities (0 or 1). - The addition of each digit represents a doubling of the possible values represented: + If you have one binary digit ( _ ), you can encode two different numbers (0-1). + If you have two binary digits ( _ _ ), you can encode four different numbers (0-3)... - When asked what direction facing in a 1D space, can naively ask "is it right?" And "is it left?" + However, the state space of one binary question contains two possibilities, "is it right?" OR "is it left?"

Common misconception: Digital copies are "perfect." (2,1)

- Whereas the process of copying does not suffer degradation, the digital copies, like the original digital file, are still only approximations of the natural object. - What actually is copied perfectly in a digital file is the binary representation, including any flaws or loss through digitization. + This also assumes the process of copying is careful. If not, errors can be introduced causing an "imperfect" digital copy.

unicode (2)

- a binary encoding system that can represent much more of the world's text than ASCII can (represents 65,536 different characters—2^16). - Similar to ASCII, but add 8 bits in front with leading 0's.

multiset (1,1)

- a collection of items that may contain duplicates. + a set does not contain duplicate entries

index (1,3)

- a data structure to facilitate fast lookup of: + terms and clauses in a logic program. + deductive database. + automated theorem prover.

fixed-point numbers (2)

- numbers where the decimal point is always in the same place. - Not a practical method to demonstrate decimals (I.e. what if a bit is required after the decimal "byte"?).

discrete (1,1)

- separate or divided (digital). + I.e. computers v. nature (analog).

Base 10 (3,1)

- ten numbers to work with to create any number. - Our original number system. - 10^x where x is dependent on the bit placement (4th bit is 2^4). + I.e. 41 = 10^1 for the 4 + 10^0 for the 1.

join (1,1)

- the "join" block in Scratch concatenates, or links two values together. + Example: "hello" and "there" would result in "hellothere".

alphanumeric (2)

- the characters that consists of uppercase and lowercase letters in addition to numerals 0-9. - What texts consist of.

bits (2,1)

- the foundation for digital computing (the individual 1s and 0s) - short for binary digits. + The lowest-level component of an algorithm is bits. - When bits are grouped together they represent abstraction (I.e. 10100110 can represent a number, character or color).

scientific notation (2)

- the mathematical representation of a decimal number in floating-point form. - examples: 4 x 10³ for 4,000, 4.002 x 10³x 10 for 4,002 or 2.345E6 for 2,345,000.

exponential growth (2)

- the rate of growth that rapidly increases in proportion to the growing total number or size. - grows exponentially (I.e. 3-digit decimal and bit).

Base 2 (1,2)

- two numbers (0 and 1) to work with to create any number. + 2^x where x is dependent on the bit placement (4th bit is 2^4). + Don't need to show leading 0's.

continuous (1,1)

- unbroken, without interruption (analog). + I.e. nature v computers (digital).

variable-width encoding (2,1)

- using codes of different lengths (symbols) to encode a character set for representation (example: Morse Code). - Allocates a differing number of bits to each symbol. + Some symbol may require as few as 1 or 2 bits, where other require many more.

fixed-width encoding (4)

- using codes with a fixed width to encode a character set for representation (example: Baudot Code). - Allocates a specific number of bits to each symbol. - Most modern encodings are fixed-width encodings. - Longer than variable-width, due to empty space.

Boundary cases (3,3)

- when code is not intuitive. - Asking code to do something it can't do. - I.e. boundary cases of Scratch lists: + Cannot distinguish between capitalize/ lower cases. + Cannot add to list when the length of list is less than the assigned object placement. + Asking for an item in list that doesn't exist > will turn blank.

element (1)

An element is an individual value in a list that is assigned a unique index.

Lists in AP Pseudocode (1):

Can insert Booleans into lists as "true" or "false."

Lower/capitalized letters: (1)

Computers do not understand lower/capitalized letters, and need to be separated in binary.

Tip (1)

On the exam, check whether the number is a bit, a decimal, or a dexa.

real numbers (1)

numbers approximated by floating-point representations that do not necessarily have infinite precision.

floating-point numbers (1)

numbers where the decimal point can float because there is no fixed number of digits before and after the decimal point. (AKA: real numbers.)

Baudot Code (1)

a binary code invented by Emile Baudot in 1870 that uses crosses and dots in order to encode 2^5 or 32 characters.

Morse Code (1)

a code where letters are represented by combinations of long and short signals of light or sound.

procedure (1)

a group of blocks that are combined to perform a specific task.

string (1)

a linear sequence of characters, words, or other data.

linear search (1)

a method for finding a target value within a list (whether presorted or not) by checking each value until a match is found or until all the elements have been searched.

data structure (1)

a particular way of organizing and storing data such as an array, table, etc.

bit string (1)

a sequence of bits that can be used to represent sets or to manipulate binary data.

substring (1)

a subset of a string of alphanumeric fields or variables.

mapping (1)

associating each element of a given set with one or more elements of a second set.

data (1)

characters, symbols or quantities on which operations are performed, stored and/or transmitted by a computer.

binary code (1)

code represented with the two symbols of 1 and 0 (hence is dichotomous).

approximation (1)

digital copies are only approximations of the natural object.

data abstraction (1)

help manage complexity in programs by giving a collection of data a name without referencing the specific details of the representation.

digital (1)

how information is stored, accessed, transformed and used by computers.

dichotomous (1)

in which something can only be one thing or another (yes or no).

digital noise (1)

irrelevant or meaningless data that has found its way into otherwise meaningful code.

3-digit decimal (1)

the biggest value would be 999 (9 100's, 9 10's and 9 1's).

abstraction (1)

the process of removing or suppressing details to create a manageable level of complexity.

index value (1)

the representation of the location of each item in a list.

state space (1)

the space of potential possibilities