do not write while sleeping

section_1/hex.md

@@ -3,49 +3,57 @@
 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 being base 16,
-each hex digit represents 4 bits and just two hex digits completely
-indicates the 8 bits in a byte. Hex digits run from 0 through 9 and then
-A through F. Example: decimal 255 is hex FF.
+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 added to a power
-of 10. The first digit is added to 10 to the 0. The second digit is
-added to 10 to the 1 and so on.
+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
 
-### Integers
+Binary is the same thing except with powers of 2. The digits available
+to us are 0 and 1.
 
-Binary is the same thing except with powers of 2.
+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 first (least significant) digit is added to 2 to the 0. The second
-is added to 2 to the 1 and so on.
-
-### Floats
-
-Floats are more complicated but in rough terms the digits are raised to
-negative powers of 2. See [Section 2](../section_2/float/) for more
-detailed information.
+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
 
-Hex numbers work the same way as binary and decimal except there are
-more than 10 values for each digit. We draft the letter A through F to
-mean the values 10 through 15.
+In decimal there are 10 values available for each digit.
 
-Hex is a handy way of describing binary numbers with much less effort.
+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
 
-We don't speak of such things.
+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. 
 
-More seriously, base 8, or octal, is used far less than hex (permission
-bits in Linux is one place where it is used) in CS because it doesn't
-naturally encode into a single byte. Two hex digits perfectly since in a
-byte but two octal digits is 6 bits... too small and three octal digits
-is 9 bits... too big. Goldilocks does not approve.
+Goldilocks does not approve of octal.
 
 ## Printing Hex
 
@@ -64,5 +72,5 @@ You can spell stuff with hex.
 | 8BADFOOD | Found for similar reasons but on Apple products |
 | DEADDEAD | Associated with the Blue Screen of Death |
 | F003BA11 | Used by undergraduates everywhere |
-| COEDBABE | Used by misogynists everywhere |
+| C0EDBABE | Used by misogynists everywhere |
 | B16B00B5 | Used by misogynists at Microsoft |