mirror of https://github.com/dirtbags/moth.git
96 lines
2.7 KiB
Markdown
96 lines
2.7 KiB
Markdown
Decimal
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=======
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Decimal (Greek “deca-”, meaning “ten”), or base ten, is the counting
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system most people use regularly, consisting of ten digits:
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9
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To count past nine, one must use the “tens place”, starting by placing a
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1 in the “tens place”:
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10, 11, 12, 13, 14, 15, …
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The presence of a 1 in the “tens place” means “add ten one time”. 2 in
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the “tens place” would mean “add ten two times", and so on. The decimal
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number:
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372
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Reads “three times one hundred, plus seven times ten, plus two”.
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A “hundreds place” and “thousands place” can exist as well, and so on
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for any nth digit representing the place for ten times itself n times,
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or 10ⁿ.
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Octal
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=====
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Octal (Greek “okta-” meaning “eight”), or base eight, is a method of
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counting with only eight digits. In the interest of making it obvious
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when a number is octal, all octal numbers on this page will be preceded
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by the number “0”. The digits are thus:
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00, 01, 02, 03, 04, 05, 06, 07
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Octal features an “eights place”, a “sixty-fours place”, a “five hundred
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twelves place”, and so on. Counting from zero to ten in octal would
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therefore go like so:
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00, 01, 02, 03, 04, 05, 06, 07, 010, 011, 012
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Where “010” means “one times eight” (eight), “011” means “one times
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eight plus one” (nine), and “012” means “one times eight plus two”
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(ten).
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The octal number:
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0372
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Reads “three times sixty-four, plus seven times eight, plus two”, or two
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hundred thirty four.
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In general, the nth digit of an octal number represents the place for
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eight times itself n times, or 8ⁿ.
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Hexadecimal
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===========
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Hexadecimal (Greek “hexa-”, meaning “six”; plus “deca-”, meaning ten),
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or base sixteen, is a method of counting with sixteen digits (preceded
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by “0x” on this page):
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0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7,
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0x8, 0x9, 0xA, 0xB, 0xC, 0xD, 0xE, 0xF
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Hexadecimal (or “hex”) features a “sixteens place”, a “two hundred fifty
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sixes place”, and so on. Counting from zero to twenty in hex therefore
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would go like so:
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0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7,
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0x8, 0x9, 0xA, 0xB, 0xC, 0xD, 0xE, 0xF,
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0x10, 0x11, 0x12, 0x13, 0x14
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Where “0xA” means “ten”, “0xB” means “eleven”, “0xF” means “fifteen”, “0x10”
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means “one times sixteen”, “0x11” means “one times sixteen plus one”, et
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cetera.
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The hexadecimal number:
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0x372
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Reads “three times two hundred fifty six, plus seven times sixteen, plus
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two”, or eight hundred eighty-two.
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Question
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========
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The key for this page is the decimal representation of the following
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sum:
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12 + 072 + 0x5D
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