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76 lines
2.5 KiB
Markdown
76 lines
2.5 KiB
Markdown
# Section 1 / Hexadecimal
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Hex is only lightly covered here because there is a very good chance you
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are already familiar with the concept.
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The TL;DR is: Hex is base sixteen. Hex is useful because 16 is 2 raised
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to the power of 4. Each hex digit represents 4 bits. Just two hex digits
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completely specify the 8 bits in a byte. Hex digits run from 0 through 9
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and then A through F.
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Example: decimal 255 is hex FF.
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## Numbers in Base 10
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You already know that each digit in a base 10 number is multiplied by a
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power of 10. The least significant digit is multiplied by 10 to the 0.
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The next least significant digit is multiplied to 10 to the 1 and so on.
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Floating point numbers in decimal are multiplied by negative powers of
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10.
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The digits available to us are 0 through 9.
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## Numbers in Base 2
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Binary is the same thing except with powers of 2. The digits available
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to us are 0 and 1.
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The first (least significant) digit is multiplied by 2 to the 0. The
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second is multiplied by 2 to the 1 and so on.
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The digits of the fractional part of a floating point number are
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multiplied with negative powers of 2. See [Section
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2](../section_2/float/) for more detailed information.
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## Number in Base 16 - Hexadecimal
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In decimal there are 10 values available for each digit.
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In binary there are 2 values available for each digit.
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Hex numbers work the same way as binary and decimal except there are 16
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values for each digit. We draft the letters A through F to mean the
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values 10 through 15.
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Hex is a handy way of describing binary numbers with much less effort
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because each hex digit encodes 4 binary digits.
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## Octal - Numbers in Base 8
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Base 8, or octal, is used far less than hex in CS because base 8 doesn't
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naturally encode into a powers-of-two centric digital world. Two hex
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digits perfectly fit in a byte but two octal digits are 6 bits... too
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small. Three octal digits are 9 bits... too big.
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Goldilocks does not approve of octal.
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## Printing Hex
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With `printf()` use `%x`.
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With `iostream` use the modifier `hex` but note this is sticky. It will
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remain active until switched back to `dec`.
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## The REAL Reason We Love Hex
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You can spell stuff with hex.
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| Hex Value | Notes |
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| --------- | ----- |
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| DEADBEEF | Found frequently in MC68K code especially Amiga |
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| 8BADF00D | Found for similar reasons but on Apple products |
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| DEADDEAD | Associated with the Blue Screen of Death |
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| F003BA11 | Used by undergraduates everywhere |
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| C0EDBABE | Used by misogynists everywhere |
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| B16B00B5 | Used by misogynists at Microsoft |
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