Confusion
Strictly speaking, JIS X 0201 encoding as "half-width katakana" is incorrect, as the standard does not define character widths – it defines only the code representation of katakana characters. In the JIS X 0201 standard, katakana characters are printed in normal (full) width, not half-width.
Half-width characters were only used for display during the period when characters were displayed at half-width (and single-byte encodings were used), before full-width character displays (and associated double-byte encodings such as JIS X 0208) became widespread. However, in the Shift JIS standard, which combines the JIS X 0201 standard (whose characters – Latin and katakana – were displayed as half-width) and the JIS X 0208 standard (whose characters – katakana, hiragana, kanji, and Latin – were displayed as full-width), katakana and Latin characters are encoded twice, both in JIS X 0201 and JIS 0208, but displayed as half-width or full-width according to which section they are in (0201 or 0208) – thus the 0201 katakana block can be thought of as corresponding to "half-width kana", and the misunderstanding that the 0201 standard defines "half-width" characters is widespread.
Further, though JIS X 0201 is a single-byte encoding (and displayed at half-width) and JIS X 0208 is a double-byte encoding (and displayed at full-width), there is no connection between number of bytes and width (other than these corresponding in Shift JIS, as above) – for example, Unicode can be encoded with four bytes (UTF-32) to display both full-width and single-width characters.
Read more about this topic: Half-width Kana
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