CS-150 – Data Representation: Vocabulary Flashcards

Analog vs Digital

• Analog = continuous, Digital = discrete

• Digitise: convert analog signal to binary

• Discretise: map continuous space to finite set

Binary Basics

• Bit: 0/1; Byte = 8 bits; Word = machine’s native multiple

• Capacity: n\text{ bits}\;\Rightarrow\;2^n values

• Required bits: \lceil \log_2 t \rceil for t symbols

Integer Representation

• Unsigned: direct binary

• Sign-magnitude: MSB = sign; two zeros ⇒ rarely used

• Two’s complement (standard)

  • Range -2^{n-1}\dots2^{n-1}-1

  • Negate: invert bits + 1

  • Addition/subtraction as normal; overflow when result outside range

Fixed-Size Int Ranges (signed / unsigned)

• 8-bit: -128..127 / 0..255

• 16-bit: -32768..32767 / 0..65535

• 32-bit: -2\,147\,483\,648..2\,147\,483\,647 / 0..4\,294\,967\,295

• 64-bit: -9.22\times10^{18}..9.22\times10^{18} / 0..1.84\times10^{19}

Real Numbers & Floating Point

• Binary fractions use positions 2^{-1},2^{-2},\dots

• Floating-point form: \text{sign}\times\text{mantissa}\times\text{base}^{\text{exponent}}

• IEEE 754

  • Single (float): 1 sign, 8 biased exponent (bias 127), 23 fraction bits

  • Double: 1 sign, 11 exponent (bias 1023), 52 fraction bits

• Fixed-point: constant digits right of radix; used in accounting

• Conversion algorithms: repeated divide (integer part) / multiply (fractional part)

Scientific Notation

• Keeps one non-zero digit left of point; e.g. 1.2001\times10^4 \equiv 1.2001E4

Text Encoding

• Map characters → bit patterns

• Standards: ASCII (7-bit), EBCDIC, ISO-8859-1, Unicode (UTF-8/16/32, >143\,000 chars)

Colour Representation

• RGB triplet, usually 8 bits/channel (24-bit colour)

• Example brown: (150,75,0) \to #964B00

• Other models: HSV, CMY, CMYK

• Colour depth = bits per channel

Images

• Pixel = coloured dot; Resolution = pixel count

• Raster (BMP, GIF, JPEG, PNG, TIFF): store every pixel; scaling ⇒ pixelation

• Vector (SVG): store shapes; scale cleanly; small for line art

• JPEG: lossy; transform to frequency domain & discard high-frequency components

Audio

• Sound digitised by PCM: sample & quantise

• Nyquist: sample ≥ 2f_{max}; CD: 44\,100 Hz, 16-bit stereo

• Formats: Uncompressed (WAV, AIFF), Lossless (FLAC, ALAC), Lossy (MP3, AAC, Ogg)

Video

• Codec = encoder/decoder, usually lossy, uses temporal + spatial compression

• Formats: MPEG-2, MPEG-4, AVI, WebM, Matroska

Data Compression Fundamentals

• Compression ratio = \frac{\text{size(compressed)}}{\text{size(original)}} (smaller = better)

• Lossless vs Lossy (text → lossless; media often lossy)

Lossless Techniques

• Run-length: *c5 \Rightarrow ccccc

• Keyword: replace frequent words with single tokens

• Huffman coding: variable-length prefix codes built from symbol frequencies; optimal among prefix codes

Storage Example

• 24-bit RGB image 1920×1080: 2\,073\,600\times24 \approx 50\,\text{Mbits} \approx 6\,\text{MB} uncompressed → compression essential