Data Representation - Computers and Scientific Thinking - Lecture Slides, Slides of Computer Science

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Data Representation

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Analog vs. Digital

• there are two ways data can be stored electronically 1. analog signals represent data in a way that is analogous to real life  signals can vary continuously across an infinite range of values  e.g., frequencies on an old-fashioned radio with a dial 2. digital signals utilize only a finite set of values  e.g., frequencies on a modern radio with digital display
• the major tradeoff between analog and digital is variability vs. reproducibility
  • analog allows for a (potentially) infinite number of unique signals, but they are harder to reproduce
    • good for storing data that is highly variable but does not need to be reproduced exactly
  • digital signals limit the number of representable signals, but they are easily remembered and reproduced - good for storing data when reproducibility is paramount

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Decimal  Binary

• algorithm for converting from decimal (D) to binary (B):

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Representing Integers

• when an integer value must be saved on a computer, its binary equivalent can be encoded as a

bit pattern and stored digitally

• usually, a fixed size (e.g., 32 bits) is used for each integer so that the computer knows where

one integer ends and another begins

• the initial bit in each pattern acts as the sign bit (0=positive, 1=negative)
• negative numbers are represented in two’s complement notation
  • the "largest" bit pattern corresponds to the smallest absolute value (-1)

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Representing Characters

• characters have no natural

correspondence to binary numbers

• computer scientists devised an arbitrary system for representing characters as bit patterns
• ASCII (American Standard Code for Information Interchange) - maps each character to a specific 8- bit pattern - note that all digits are contiguous, as are all lower-case and all upper-case letters

'0' < '1' < … < '9' 'A' < 'B' < … < 'Z' 'a' < 'b' < … < 'z'

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Representing Text

• strings can be represented as sequences of ASCII codes, one for each character in the string

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specific programs may store additional information along with the ASCII

codes

 e.g. programming languages will often store the number of characters along with the ASCII codes  e.g., word processing programs will insert special character symbols to denote formatting (analogous to HTML tags in a Web page)

Representing Sounds (cont.)

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when analog recordings are repeatedly duplicated, small errors that were

originally unnoticed begin to propagate

digital recordings can be reproduced exactly without any deterioration

in sound quality

 analog waveforms must be converted to a sequence of discrete values  digital sampling is the process in which the amplitude of a wave is measured at regular intervals, and stored as discrete measurements

 frequent measurements must be taken to ensure high quality (e.g., 44,100 readings per second for a CD)  this results in massive amounts of storage  techniques are used to compress the data and reduce file sizes (e.g., MP3, WAV)

Representing Images

• EXAMPLE: representing images
  • images are stored using a variety of formats and compression techniques
  • the simplest representation is a bitmap
  • bitmaps partition an image into a grid of picture elements, called pixels , and then convert each pixel into a bit pattern

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resolution refers to the sharpness or

clarity of an image

 bitmaps that are divided into smaller pixels will yield higher resolution images  the left image is stored using 96 pixels per square inch, and the right image is stored using 48 pixels per square inch  the left image appears sharp, but has twice the storage requirements

Distinguishing Data Types

• how does a computer know what type of value is stored in a particular piece of memory?
  • short answer: it doesn't
  • when a program stores data in memory, it must store additional information as to what type of data the bit pattern represents
  • thus, the same bit pattern might represent different values in different contexts

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