update doc

papers/doc/1-intro/README.md

@@ -7,6 +7,17 @@ It has a music tracker interface. think of a piano roll, or a table that scrolls
 
 Another core feature of Furnace is its windowing system, similar to that of GEMS or Deflemask, but with a few more features.
 
+## Interface
+
+Furnace is built to have a user-friendly interface that is intentionally made so that it is quick and easy to get around when working in Furnace.
+However, we understand that the interface may not be the easiest to learn, depending on how you learn, so there is documentation on it as well.
+
+See [2-interface](https://github.com/tildearrow/furnace/tree/master/papers/doc/2-interface) and [3-pattern](https://github.com/tildearrow/furnace/tree/master/papers/doc/3-pattern) to view said documentation.
+
+## Hexadecimal
+
+Furnace uses hexadecimal (abbreviated as "hex") numbers frequently. see [hex.md](this guide) for a crash course.
+
 ## Sound generation
 
 Furnace generates sound from 3 different main types of sound sources.
@@ -19,9 +30,3 @@ Wavetables only work in the sequencer if you bind them to an instrument. See [4-
 To sequence a sample, you do not need to assign it to an instrument, however, to resample samples (change the speed of a sample), you need to bind it to a Sample instrument.
 See [6-sample](https://github.com/tildearrow/furnace/tree/master/papers/doc/6-sample) and [4-instrument](https://github.com/tildearrow/furnace/tree/master/papers/doc/4-instrument) for more details.
 
-## Interface/other
-
-Furnace is built to have a user-friendly interface that is intentionally made so that it is quick and easy to get around when working in Furnace.
-However, we understand that the interface may not be the easiest to learn, depending on how you learn, so there is documentation on it as well.
-
-See [2-interface](https://github.com/tildearrow/furnace/tree/master/papers/doc/2-interface) and [3-pattern](https://github.com/tildearrow/furnace/tree/master/papers/doc/3-pattern) to view said documentation.

papers/doc/1-intro/hex.md

@@ -0,0 +1,97 @@
+# hexadecimal
+
+the hexadecimal numeral system differs from the decimal system by having 16 digits rather than 10:
+
+```
+hex| decimal
+---|---------
+`0`| 0
+`1`| 1
+`2`| 2
+`3`| 3
+`4`| 4
+`5`| 5
+`6`| 6
+`7`| 7
+`8`| 8
+`9`| 9
+`A`| 10
+`B`| 11
+`C`| 12
+`D`| 13
+`E`| 14
+`F`| 15
+```
+
+when there is more than one digit, these are multiplied by 16, 256, 4096 and so on rather than 10, 100, 1000:
+
+```
+hex | decimal
+----|---------
+`00`| 0
+`04`| 4
+`08`| 8
+`0F`| 15
+`10`| 16
+`11`| 17
+`12`| 18
+`13`| 19
+`20`| 32
+`30`| 48
+`40`| 64
+```
+
+# hex to decimal
+
+for example, take hexadecimal number `AA`:
+
+```
+          2nd digit -\   /- 1st digit
+                     A   A
+ 16^1*10 = 16*10 = 160 + 10 = 170
+```
+
+now for hexadecimal number `4C5F`:
+
+```
+
+      3rd digit -\    /- 2nd digit
+ 4th digit -\    |    |    /- 1st digit
+            4    C    5    F
+            |    |    |    |
+            |    |    |    15 =        15 =    15 +
+            |    |    \16^1*5 =   16 * 5  =    80
+            |    \--- 16^2*12 =  256 * 12 =  3072
+            \--------- 16^3*4 = 4096 * 4  = 16384
+                                           -------
+                                          = 19551
+```
+
+# decimal to hex
+
+if it's less than 16, just memorize the table at the top of this document.
+
+otherwise find the power of 16 that is closest to the number you want to convert, but no larger than the number.
+then divide, and take the remainder.
+divide the remainder with the previous power of 16, until the divider is 1.
+
+for example, for the decimal number `220`:
+
+```
+220 ÷ 16 = 13 (r = 12)    D
+ 12 ÷  1 = 12 (stop here) C
+
+= DC
+```
+
+now for decimal number `69420`:
+
+```
+69420 ÷ 65536 =  1 (r = 3884)  1
+ 3884 ÷  4096 =  0 (r = 3884)  0
+ 3884 ÷   256 = 15 (r =   44)  F
+   44 ÷    16 =  2 (r =   12)  2
+   12 ÷     1 = 12 (stop here) C
+
+= 10F2C
+```