Data storage and compression · ⁨数据存储与压缩⁩

Squeezing files smaller

• Data storage is measured in units that each step up by 1024.
• We can calculate the size of an image or sound file.
• Compression 压缩 then makes files smaller.

Measuring storage

• bit (one 0/1) · nibble (4 bits) · byte (8 bits).
• Then each unit is 1024× the one before (because $1024 = 2^{10}$): kibibyte 二进制千字节 (KiB) = 1024 bytes, mebibyte (MiB) = 1024 KiB, gibibyte (GiB) = 1024 MiB, tebibyte (TiB) = 1024 GiB.
• Always divide by 1024 (not 1000) to step up a unit.

Computers represent all data as binary — long strings of 0s and 1s.

Calculating file size

• Image (bits) $=$ width × height × colour depth.
• Sound (bits) $=$ sample rate × sample resolution × seconds.
• Divide by 8 for bytes, then by 1024 for KiB, again for MiB.
• e.g. $1024 \times 1024$ at 16 bpp $= 16\,777\,216$ bits $= 2$ MiB.

Compression

• Lossless 无损 compression makes a file smaller with no permanent loss — the original can be rebuilt exactly. Run-length encoding 行程编码 (RLE) stores a run of repeats once (e.g. WWWWWWWW → "8 W").
• Lossy 有损 compression makes it much smaller by permanently removing data (lower resolution/sample rate).
• Use lossless for text and program files; lossy for photos, music and video.

Run-length encoding stores a run of repeats once, as a (count, value) pair: 8 W, then 4 R.

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