Data Representation and Storage

Data Storage Overview

• Data comes in various forms: numbers, text, audio, images, and video.
• Multimedia is the term used to describe information containing a combination of numbers, text, images, audio, and video.

Data Representation in Computers

• All data types are converted into a uniform bit pattern for storage and then transformed back to their original form upon retrieval.

Data Compression

• Data is typically compressed before storage to minimize memory space, as discussed in Chapter 15.

Error Detection and Correction

• Issues regarding error detection and correction during data transmission or storage are covered in Appendix H.

Storing Numbers

• Numbers are converted to the binary system before storage.
• Challenges include storing the sign of the number and indicating the decimal point.

Storing Integers

• Integers are whole numbers, lacking a fractional component.
• Fixed-point representation stores integers, where the decimal point position is fixed to the right of the least significant bit.
• The decimal point is assumed but not explicitly stored.

Unsigned Integer Representation

• Unsigned integers are non-negative.
• Stored by converting the integer to binary, then padding with zeros on the left if necessary to meet the required length.
• Example: Storing 7 in an 8-bit memory location involves converting 7 to binary (111) and adding five leading zeros, resulting in 00000111.

Overflow in Unsigned Integers

• Occurs when trying to store an integer larger than what a given memory location can hold
• Example: Storing an integer larger than 15 in a memory location that can only hold four bits (2^4 - 1 = 15)

Sign-and-Magnitude Representation

• The available range for integers is split into equal sub-ranges where the first half represents positive integers and the second half negative integers.
• The leftmost bit indicates the sign: 0 for positive, 1 for negative.
• +/- 28 can be stored in an 8-bit memory location. 0011100 & 1011100

Two's Complement Representation

• Almost all computers use two's complement
• It divides the range for an n-bit unsigned integer into two sub-ranges, which represent negative and non-negative integers.
• Determining the value uses the 0, the integer is positive / 1, the integer is negative principle

One's Complementing

• This reverses (flips) each bit to its inverse: A 0 becomes a 1 and a 1 becomes a 0.
• Applying this operation twice returns the original outcome

Two's Complementing

• Copy bits from the right until a 1 is copied, then flip the bits
• An alternative way to perform a two's complement is to do one's complement first and add 1 to the result.
• Example: storing +28 in an 8-bit location, it's transformation is decimal to binary and adding leading zeros.
• Negative 28 requires that we also perform the two's complement operation

Comparison of Integer Storage Systems

• Unsigned representation only stores positive value
• Sign & Magnitude and Two's Complement representations store negative numbers

Storing Real Numbers

• Real numbers have an integral and a fractional part.
• Recommended not be stored in fixed-point due to accuracy / precision
• Real numbers are stored using floating-point representation, which includes a sign, a shifter, and a fixed-point number.
• This method maintains accuracy or precision

Floating-Point Representation

• Includes a sign, shifter and fixed part number

Normalization

• Used make fixed parts of representation uniform
• both scientific and floating point methods use one non zero digit on the left of the decimal point
• In the decimal system this digit can be 1 to 9 and in binary it can only be 1.

Mantissa

• The mantissa is a fractional part that, put together with the sign, like an integer stored in sign-and-magnitude representation.

Binary System

• Both positive and negative integers store as unsigned integers in this system.
• A positive biases each number in order to shift them to the non-negative side e.g., Excess-7: biasing value is 7.

IEEE Standard

• The IEEE standard is used for floating-point representation, with single precision (32 bits) and double precision (64 bits) forms.

Exponent

• Is a power that shows how many bits the decimal point should be moved to the left or right, is a signed number.

Overflow and Underflow

• Occur in real number storage, alongside the means of storing Zero

Storing Text

• Text is stored as a sequence of symbols/characters.

Representing Text

• Text like "CATS" can be n-bit patterns where the pattern defines a single symbol
• Each bit pattern depends on the number of symbols
• Common codes include ASCII and Unicode

Storing Audio

• By nature audio digital data that are countable entities
• digital data differs from audio/ analog data

Sampling

• Selects only a finite number of points on the analog signal, measure their values, and record them
• We cannot record all the values in an audio sampling over an interval.

Quantization

• Approximates the value of each sample to the closest integer value.

Encoding

• Encodes quantized sample values as bit patterns.
• Bit depth (B) represents the number of bits per sample.

Bit Rate

• Number of samples per second (S) times the number of bits per sample, (B).
• For example, using 40,000 samples / second and 16 bits per sample gives a bit rate of 640,000 bits / second.

Standards for sound encoding

• MP3 (MPEG Layer 3) uses 44,100 samples / second and 16 bits / sample

Storing Images

• Stored using raster graphics and vector graphics.

Raster Graphics

• Also known as Bitmap graphics
• Suited for storing analog images of data that's intensity varies.
• Sampling is called scanning, with pixels being picture elements.

Resolution

• Density of pixels in an image or the scanning rate

Color Depth

• The number of bits used to represent a pixel
• Color perception is how eyes respond to a light beam
• RGB is the three primary colors red, green, and blue

True Color

• Uses 24 bits to encode a pixel
• Example: Some colors in True Color are Red (255,0,0), Green (0,255,0), and Blue (0,0,255).

Indexed Color

• Also known as Palette Color.
• It Uses only a portion of the colors

Image Encoding Standards

• JPEG uses the True-Color scheme combined with compression
• GIF images often utilize indexed color schemes

Vector Graphics

• Unlike raster graphics do not save bit patterns for each pixel meaning the file size is small
• Images are geometric shapes e.g., radius and equation of circle

Storing Videos

• Stored as frames over time
• Combination of stored images representing the video.
• Video compression methods are in chapter 15