mirror of
https://github.com/pkivolowitz/asm_book.git
synced 2026-06-21 04:06:48 +08:00
76 lines
2.5 KiB
Markdown
76 lines
2.5 KiB
Markdown
# Section 1 / Hexadecimal
|
|
|
|
Hex is only lightly covered here because there is a very good chance you
|
|
are already familiar with the concept.
|
|
|
|
The TL;DR is: Hex is base sixteen. Hex is useful because 16 is 2 raised
|
|
to the power of 4. Each hex digit represents 4 bits. Just two hex digits
|
|
completely specify the 8 bits in a byte. Hex digits run from 0 through 9
|
|
and then A through F.
|
|
|
|
Example: decimal 255 is hex FF.
|
|
|
|
## Numbers in Base 10
|
|
|
|
You already know that each digit in a base 10 number is multiplied by a
|
|
power of 10. The least significant digit is multiplied by 10 to the 0.
|
|
The next least significant digit is multiplied to 10 to the 1 and so on.
|
|
|
|
Floating point numbers in decimal are multiplied by negative powers of
|
|
10.
|
|
|
|
The digits available to us are 0 through 9.
|
|
|
|
## Numbers in Base 2
|
|
|
|
Binary is the same thing except with powers of 2. The digits available
|
|
to us are 0 and 1.
|
|
|
|
The first (least significant) digit is multiplied by 2 to the 0. The
|
|
second is multiplied by 2 to the 1 and so on.
|
|
|
|
The digits of the fractional part of a floating point number are
|
|
multiplied with negative powers of 2. See [Section
|
|
2](../section_2/float/) for more detailed information.
|
|
|
|
## Number in Base 16 - Hexadecimal
|
|
|
|
In decimal there are 10 values available for each digit.
|
|
|
|
In binary there are 2 values available for each digit.
|
|
|
|
Hex numbers work the same way as binary and decimal except there are 16
|
|
values for each digit. We draft the letters A through F to mean the
|
|
values 10 through 15.
|
|
|
|
Hex is a handy way of describing binary numbers with much less effort
|
|
because each hex digit encodes 4 binary digits.
|
|
|
|
## Octal - Numbers in Base 8
|
|
|
|
Base 8, or octal, is used far less than hex in CS because base 8 doesn't
|
|
naturally encode into a powers-of-two centric digital world. Two hex
|
|
digits perfectly fit in a byte but two octal digits are 6 bits... too
|
|
small. Three octal digits are 9 bits... too big.
|
|
|
|
Goldilocks does not approve of octal.
|
|
|
|
## Printing Hex
|
|
|
|
With `printf()` use `%x`.
|
|
|
|
With `iostream` use the modifier `hex` but note this is sticky. It will
|
|
remain active until switched back to `dec`.
|
|
|
|
## The REAL Reason We Love Hex
|
|
|
|
You can spell stuff with hex.
|
|
|
|
| Hex Value | Notes |
|
|
| --------- | ----- |
|
|
| DEADBEEF | Found frequently in MC68K code especially Amiga |
|
|
| 8BADF00D | Found for similar reasons but on Apple products |
|
|
| DEADDEAD | Associated with the Blue Screen of Death |
|
|
| F003BA11 | Used by undergraduates everywhere |
|
|
| C0EDBABE | Used by misogynists everywhere |
|
|
| B16B00B5 | Used by misogynists at Microsoft |
|