Comprehensive Study Guide to Informatics, Data Encoding, Graphics, and Audio Digitization

Fundamentals of Informatics, Information, and Data

• Informatics (Informatika): The scientific discipline dedicated to the study of algorithms and automated information processing using computers and software programs.

• Algorithm (Algoritmus): A well-defined, step-by-step procedure or set of operational instructions designed to accomplish a specific task or solve a particular problem.

• Information (Informácia): The structured accumulation of facts, experiences, knowledge, and observations that human society collects, systematically records, preserves, and communicates across individuals and generations.

• Data (Údaje): Facts, concepts, or knowledge that have been explicitly captured, recorded, and represented in a formalized format suitable for processing, communication, or storage.

• Core Activities with Information:

  • Acquisition (Získavanie): Gathering raw information through observation, active reading, and mediated transmission from third-party individuals or media sources (e.g., books, magazines, newspapers, television broadcasts, radio broadcasts, and the internet).
  • Storage (Uchovávanie): Preserving information onto dedicated physical and digital storage media (pamäťové médiá), including paper documents, analog photographs, optical discs (such as DVDs), USB flash storage drives, and magnetic/solid-state disks.
  • Processing (Spracovávanie): Executing computational, mathematical, or logical operations on known input data to derive structured outputs and actionable results.
  • Transmission (Prenos): Propagating information across distances via diverse physical and technological transmission channels, including postal services, printed media, internet networks, acoustic signals, optical fiber cables, satellite uplinks, facsimiles (fax), and telecommunication networks.

• Primary Classifications of Information:

  • Numerical (Číselná): Data expressed in numeric quantities, metrics, and positional notations.
  • Textual (Textová): Information represented through characters, words, sentences, and typographic sequences.
  • Graphical (Grafická): Visual representations, including two-dimensional illustrations, drawings, charts, and digital imagery.
  • Sound/Audio (Zvuková): Acoustic information conveyed through analog or digital waveforms, speech, and musical compositions.
  • Audiovisual (Audiovizuálna): Integrated multimedia formats combining synchronized acoustic and moving visual media.

Units of Information and Storage Capacity

• Binary Digit / Bit ($b$):

  • Represents a single digit within the binary numeral system, holding a discrete state of either $0$ or $1$.
  • Serves as the elementary, indivisible fundamental unit of digital information.

• Byte ($B$):

  • A contiguous group of $8\text{ bits}$.
  • Functions as the baseline architectural unit used to quantify computer file sizes, operational memory capacity (RAM), and secondary storage medium capacity.

• Decimal Storage Units (Powers of $10$):

  • Kilobyte ($\text{kB}$): $1\,\text{kB} = 1000\,\text{B} = 10^3\,\text{B}$
  • Megabyte ($\text{MB}$): $1\,\text{MB} = 1000\,\text{kB} = 10^6\,\text{B}$
  • Gigabyte ($\text{GB}$): $1\,\text{GB} = 1000\,\text{MB} = 10^9\,\text{B}$
  • Terabyte ($\text{TB}$): $1\,\text{TB} = 1000\,\text{GB} = 10^{12}\,\text{B}$
  • Petabyte ($\text{PB}$): $1\,\text{PB} = 1000\,\text{TB} = 10^{15}\,\text{B}$
  • Exabyte ($\text{EB}$): $1\,\text{EB} = 1000\,\text{PB} = 10^{18}\,\text{B}$
  • Zettabyte ($\text{ZB}$): $1\,\text{ZB} = 1000\,\text{EB} = 10^{21}\,\text{B}$
  • Yottabyte ($\text{YB}$): $1\,\text{YB} = 1000\,\text{ZB} = 10^{24}\,\text{B}$

• Binary Storage Units (IEC Binary Prefixes / Powers of $2$):

  • Kibibyte ($\text{KiB}$): $1\,\text{KiB} = 2^{10}\,\text{B} = 1024\,\text{B}$
  • Mebibyte ($\text{MiB}$): $1\,\text{MiB} = 2^{10}\,\text{KiB} = 2^{20}\,\text{B}$
  • Gibibyte ($\text{GiB}$): $1\,\text{GiB} = 2^{10}\,\text{MiB} = 2^{30}\,\text{B}$
  • Tebibyte ($\text{TiB}$): $1\,\text{TiB} = 2^{10}\,\text{GiB} = 2^{40}\,\text{B}$
  • Pebibyte ($\text{PiB}$): $1\,\text{PiB} = 2^{10}\,\text{TiB} = 2^{50}\,\text{B}$
  • Exbibyte ($\text{EiB}$): $1\,\text{EiB} = 2^{10}\,\text{PiB} = 2^{60}\,\text{B}$
  • Zebibyte ($\text{ZiB}$): $1\,\text{ZiB} = 2^{10}\,\text{EiB} = 2^{70}\,\text{B}$
  • Yobibyte ($\text{YiB}$): $1\,\text{YiB} = 2^{10}\,\text{ZiB} = 2^{80}\,\text{B}$

Data Compression Principles and Categories

• Definition and Purpose:

  • Compression involves diminishing the raw volume of data (measured in bytes) through the application of specialized mathematical algorithms.
  • Principally deployed to reduce bandwidth consumption during data transmission and to optimize long-term storage consumption on physical media.

• Classification of Compression Techniques:

  • Lossless Compression (Bezstratová kompresia): Reversibly condenses data without eliminating any original information. Upon decompression, the restored file is bit-for-bit identical to the source data.
  • Lossy Compression (Stratová kompresia): Permanently removes redundant, peripheral, or imperceptible data elements to achieve substantially smaller file sizes. Decompressed data is not mathematically identical to the original input.

Numerical Information Representation and Base Conversion

• Positional Number Systems:

  • Decimal System: Base-$10$ positional numbering system utilizing the ten standard digits: $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$.
  • Binary System: Base-$2$ positional numbering system utilizing two binary digits: $0, 1$.

• Decimal-to-Binary Conversion Algorithm:

  • The base-$10$ integer is repeatedly divided by the base factor $2$.
  • The integer quotient is retained for subsequent division, while the remainder ($0$ or $1$) is noted at each step.
  • The division process terminates when the quotient reaches $0$.
  • The resulting binary sequence is constructed by reading the sequence of recorded remainders in reverse order (from the final division remainder to the first).

• Binary-to-Decimal Decoding Process:

  • Employs the expanded positional notation of the binary number ($\text{rozvinutý zápis čísla}$).
  • Each binary digit is multiplied by its positional weight ($2^k$, where $k$ is the zero-indexed position from right to left), and the resulting terms are summed to compute the equivalent decimal integer.

Text Information Encoding Standards

• Foundational Principles:

  • Every typographic character within an alphabet or symbol set is mapped to an assigned integer value.
  • The systematic mapping between characters and numerical values is designated as a code table (kódová tabuľka).
  • Encoded text files consist of sequential series of binary codes representing consecutive characters.
  • Formatted Text Encoding: Visual typography and document layout properties (such as font weights, styles, and alignment) are encoded through specialized embedded control characters (riadiace znaky).

• ASCII (American Standard Code for Information Interchange):

  • Encodes individual characters using a fixed length of $1\,\text{Byte}$ ($8\,\text{bits}$).
  • Accommodates a capacity of $256$ distinct character representations ($2^8 = 256$).
  • Standard Allocation ($0$ to $127$): Universally designated for standardized worldwide characters, including standard Latin uppercase and lowercase letters, Arabic numerals, punctuation symbols, and system control codes.
  • Extended Allocation ($128$ to $255$): Reserved for national character sets (národné znakové sady), regional linguistic variations, diacritics, and specialized graphical glyphs.

• Unicode Standard:

  • Universal, unified character encoding designed to encompass every character, script, and symbol across all historical and contemporary written languages worldwide.
  • Standard implementation allocates $2\,\text{Bytes}$ ($16\,\text{bits}$) per character.
  • Provides direct encoding capacity for $65\,536$ discrete characters ($2^{16} = 65\,536$).
  • Maintains structural backward compatibility: the initial $128$ code indices correspond directly to the established ASCII standard.

• Worked Character Encoding Example:

  • Selected Character: J
  • Decimal calculation: $J = 64 + 10 = 74$
  • Eight-digit binary encoding: $01001010$

Graphical Information and Image Representation

• Core Digital Image Paradigms:

  • Graphical information is processed and stored under two distinct structural architectures: raster (bitmap) graphics and vector graphics.

• Raster Image Architecture:

  • Raster (Bitmap Grid): A regular geometric grid of tiny squares superimposed across the image area, subdividing the visual field into discrete picture elements.
  • Pixel (Obrazový bod): The atomic, foundational building block of a raster image. At any given instance, an individual pixel is assigned exactly one uniform color value.
  • Image Dimensions: Expressed strictly as the total count of horizontal pixel columns and vertical pixel rows comprising the grid matrix.
  • Raster Code Components: A comprehensive raster file incorporates information defining the color palette, the dimensional resolution (width and height), and the sequential matrix of color codes mapped to individual grid coordinates.

• Color Depth (Farebná hĺbka):

  • Quantifies the total number of bits allocated to store the specific color value of an individual pixel.
  • A bit allocation of $n\,\text{bits}$ enables the simultaneous representation of $2^n$ distinct colors.
  • To encode an image containing $X$ discrete colors, the required color depth $n$ must satisfy the mathematical boundary inequality:

$2^{n-1} < X \le 2^n$

• Standard Color Depth Categories:

  • Monochrome / Two-Color ($2\text{-color}$): $1\,\text{bit per pixel}$ ($2^1 = 2\,\text{colors}$
  • $16\text{-Color}$ Depth: $4\,\text{bits per pixel}$ ($2^4 = 16\,\text{colors}$
  • $256\text{-Color}$ Depth: $8\,\text{bits per pixel}$ ($2^8 = 256\,\text{colors}$
  • High Color: $16\,\text{bits per pixel}$ ($2^{16} = 65\,536\,\text{colors}$
  • True Color: $24\,\text{bits per pixel}$ ($2^{24} = 16\,777\,216\,\text{colors}$, the standard format for photorealistic rendering)
  • Deep Color: $48\,\text{bits per pixel}$ ($2^{48}\,\text{colors}$

• Mathematical Determination of Color Depth Example:

  • Target: Determine the bit depth required for an image containing $X = 26\,\text{colors}$.
  • Evaluating powers of two: $2^1 = 2$, $2^2 = 4$, $2^3 = 8$, $2^4 = 16$, $2^5 = 32$.
  • Applying the boundary condition: $16 = 2^{5-1} < 26 \le 2^5 = 32$.
  • Conclusion: The required minimum color depth is $n = 5\,\text{bits}$.

Raster Image File Formats

• File Format (Formát): A concrete, standardized organizational protocol for structuring and encoding digital data for persistent storage within a computer filesystem.

• BMP (Bitmap Image):

  • A direct raster implementation storing the palette header, spatial dimensions, and raw sequential color codes of every pixel without algorithmic compression.

• GIF (Graphics Interchange Format):

  • Employs lossless data compression algorithms.
  • Optimal for rendering graphic illustrations containing broad single-color fields, diagrams, or sharp geometric borders.
  • Highly effective for network distribution and web environments.
  • Native capabilities include simple multi-frame animation and binary single-color transparency.
  • Architectural limitation: Palettes are strictly constrained to an indexed maximum of $256\,\text{colors}$ ($8\,\text{bits}$).

• PNG (Portable Network Graphics):

  • Operates via lossless raster compression, developed as an architectural improvement over GIF.
  • Core advantages: Supports full, multi-color palettes (including $24\text{-bit}$ True Color depths) and multi-level alpha-channel transparency.
  • Functional distinction from GIF: Does not natively support animation.

• JPG / JPEG (Joint Photographic Experts Group):

  • Operates via lossy raster compression.
  • Algorithmic mechanics: Selectively discards high-frequency visual information; the compressed image is mathematically non-identical to the original uncompressed source.
  • Visual threshold: Exploits the biological limitations of the human visual system, which cannot discern minute color differences across smooth, subtle tonal gradations and natural photographic transitions.
  • Target application: Ideal for photographic imagery, rich continuous-tone graphics, and web publication where reduced file transfer weight takes precedence over mathematical precision.

Vector Graphics and Metaformats

• Vector Image Fundamentals:

  • Depicts an image through an assemblage of independent geometric shapes and mathematical primitives (e.g., points, lines, curves, polygons) defined by coordinate-based attributes and mathematical parameters.
  • Independent of pixel grid resolution, permitting arbitrary scaling, enlargement, and reduction without degradation of image quality or edge sharpness.

• Standard Vector Formats:

  • CDR: Proprietary vector format of CorelDRAW.
  • ZMF: Proprietary vector graphics format of Zoner Callisto.
  • AI: Proprietary format of Adobe Illustrator.
  • EPS (Encapsulated PostScript): Cross-platform standard vector format used in graphic layout and digital printing.
  • SVG / SWF (Scalable Vector Graphics): An open standard vector file format engineered specifically for vector graphic representation, scalability, and interactivity on the internet.

• Metaformats (Metaformáty):

  • Hybrid container formats capable of simultaneously encapsulating multiple diverse information structures within a unified document architecture, including embedded bitmap graphics, vector graphics, and formatted typographic text.
  • WMF (Windows Metafile): Native graphics metafile format utilized across Microsoft Windows operating environments.
  • PDF (Portable Document Format): Hardware- and software-independent universal document format designed for layout preservation, integrating text, vector art, raster photographs, and form elements.

Sound Digitization and Audio Encoding Formats

• Acoustic Wave Physics:

  • Sound travels through physical media in the form of a continuous mechanical pressure wave (an analog signal).
  • Wave Amplitude (Výška zvukovej vlny): The height/peak of the acoustic wave governs the perceived physical loudness/volume (hlasitosť).
  • Wavelength ($x$): The physical distance measured between two consecutive wave peaks determines the frequency and perceived pitch of the acoustic tone (výška tónu).

• Sound Sampling and Digitization (Samplovanie):

  • Analog sound signals are digitized by measuring the instantaneous wave amplitude at continuous, strictly regular time intervals.
  • Sampling Frequency (Vzorkovacia frekvencia): The measurement rate or temporal density of amplitude readings recorded per second.
  • Standard Operational Range: Typically sampled between $8000$ and $48\,000\,\text{times per second}$.
  • CD Standard Reference: Audio compact disc fidelity utilizes a sampling frequency of $44\,100\,\text{Hz}$.
  • The resulting digitized audio data forms an ordered, discrete numerical sequence of measured values.

• Audio File Formats:

  • WAV: Standard uncompressed or lossless pulse-code modulation audio format delivering complete waveform fidelity at large file sizes.
  • MP3: Utilizes psychoacoustic lossy compression to discard inaudible acoustic frequencies, reducing audio data footprints to approximately $\frac{1}{11}$ of an equivalent uncompressed WAV audio file.
  • MIDI (Musical Instrument Digital Interface):
  • Does not store digitized acoustic audio waveforms or voice recordings.
  • Comprises a structured stream of symbolic performance instructions defining how an electronic musical synthesizer or sound card must render the piece.
  • Encoded instructional parameters include: instrument identification (which synthesized instrument to trigger), specific musical note/pitch, exact note duration, and expressive velocity/volume of the tone.