diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
index e45481d..52f18ec 100644
--- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
+++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
@@ -337,7 +337,7 @@
     "filesystems/cas.md": "d41c0d2e943adecbadd10a03fd1e4274",
     "git/objects.md": "887ebb42a6fb7c0ff448dd482ba53922",
     "git/index.md": "ca842957bda479dfa1170ae85f2f37b8",
-    "encoding/integer.md": "54130a02e1fc0a6033ce6ab7a781b0ae",
+    "encoding/integer.md": "f98ca0221b24c16b80aea45d01fcbfd7",
     "_journal/2024-02-29.md": "f610f3caed659c1de3eed5f226cab508",
     "_journal/2024-02/2024-02-28.md": "7489377c014a2ff3c535d581961b5b82",
     "_journal/2024-03-01.md": "a532486279190b0c12954966cbf8c3fe",
@@ -382,7 +382,7 @@
     "_journal/2024-03/2024-03-15.md": "e54b2513beac5f46313b4c37622adf39",
     "_journal/2024-03-17.md": "72e99c7630085aee2c7f340a06b5ada7",
     "_journal/2024-03/2024-03-16.md": "ab7629c24ebe70838072cf6acec47cb0",
-    "encoding/floating-point.md": "88e305245e5115b6f9b6593b59364225",
+    "encoding/floating-point.md": "90c36f4b93312e28e5cfec3e2a8231f4",
     "_journal/2024-03-18.md": "8479f07f63136a4e16c9cd07dbf2f27f",
     "_journal/2024-03/2024-03-17.md": "23f9672f5c93a6de52099b1b86834e8b",
     "set/directed-graph.md": "b4b8ad1be634a0a808af125fe8577a53",
@@ -783,11 +783,11 @@
     "c17/enums.md": "9414fb67aa256a0a11b7240534c67bf6",
     "c17/derived-types.md": "6fb8f23a2423f05d5bdccb6672a32e38",
     "c17/basic-types.md": "7c6653bf6dc24c2f2aa72fc95c4f7875",
-    "c17/types/simple.md": "0fab7afc623e441cd17ae23497f6babe",
+    "c17/types/simple.md": "0edbd5da2138aa46669135a03b935db9",
     "c17/types/enumerated.md": "e1f70a30677c776b7b44ac3e0ff4e76d",
     "c17/types/derived.md": "aff0d2b6d218fb67af3cc92ead924de3",
     "c17/types/basic.md": "5064e21e683c0218890058882e06b6f3",
-    "c17/types/index.md": "7f8541016f9ac91cc6477fe864fdccd3",
+    "c17/types/index.md": "14b651bcfc8b2d62ffd200a74a9a2a6b",
     "_journal/2024-08-25.md": "e73a8edbd027d0f1a39289540eb512f2",
     "_journal/2024-08/2024-08-24.md": "563fad24740e44734a87d7c3ec46cec4",
     "algebra/abs-val.md": "a47bc08db62304eb526d15ede3e300cf",
@@ -844,7 +844,10 @@
     "_journal/2024-09/2024-09-25.md": "c8a3414e27c8ce635fe995c2dfbf6019",
     "c17/macros.md": "f7bade849d2cf714cd2ff79c4ed003d4",
     "_journal/2024-09-27.md": "dd82b2c5c5389b6a35c4c2fcf857417c",
-    "_journal/2024-09/2024-09-26.md": "2d3e8325e7ab63168c460f18e7aa1afc"
+    "_journal/2024-09/2024-09-26.md": "2d3e8325e7ab63168c460f18e7aa1afc",
+    "_journal/2024-09-28.md": "7726baed125a2561def07dcaf48bf5a0",
+    "_journal/2024-09/2024-09-27.md": "d788fa04c029009f42387317c549d93e",
+    "encoding/binary.md": "0b9beb6913906aa2523d8ab193c67f67"
   },
   "fields_dict": {
     "Basic": [
diff --git a/notes/_journal/2024-09-28.md b/notes/_journal/2024-09-28.md
index f76ae29..81b862f 100644
--- a/notes/_journal/2024-09-28.md
+++ b/notes/_journal/2024-09-28.md
@@ -4,6 +4,10 @@ title: "2024-09-28"
 
 - [ ] Anki Flashcards
 - [x] KoL
-- [ ] OGS
+- [x] OGS
 - [ ] Sheet Music (10 min.)
-- [ ] Korean (Read 1 Story)
\ No newline at end of file
+- [ ] Korean (Read 1 Story)
+
+* Walked through the proof of the recursion theorem on $\omega$.
+* Additional notes on [[simple#Exact-Width Integer Types|exact-width integer types]].
+* Severy more notes on C types/limits/etc.
\ No newline at end of file
diff --git a/notes/binary/index.md b/notes/binary/index.md
deleted file mode 100644
index 98cb4eb..0000000
--- a/notes/binary/index.md
+++ /dev/null
@@ -1,84 +0,0 @@
----
-title: Binary
-TARGET DECK: Obsidian::STEM
-FILE TAGS: binary
-tags:
-  - binary
----
-
-## Overview
-
-A binary digit or **bit** is a `0` or `1` character. A **bit string** is then a contiguous sequence of bits. It's **weight** is a reference to the number of `1`s in the bit string. Compare the below operation to the method for converting from one numerical base to another (e.g. [[radices#Hexadecimal|hexadecimal]]).
-
-```c
-unsigned int bit_weight(int64_t n) {
-  unsigned int count = 0;
-  while (n) {
-    count += (n % 2 == 0) ? 0 : 1;
-    n /= 2;
-  }
-  return count;
-}
-```
-
-%%ANKI
-Basic
-Why is a "bit" named the way it is?
-Back: It is short for **b**inary dig**it**.
-Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1707432641557-->
-END%%
-
-%%ANKI
-Basic
-What does the weight of a bit string refer to?
-Back: The number of `1`s in the string.
-Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708366788645-->
-END%%
-
-%%ANKI
-Basic
-How might you use C to find the weight of a bit string?
-Back: Repeatedly divide by `2`, counting all remainders of `1`.
-Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-Tags: c17
-<!--ID: 1708366788648-->
-END%%
-
-%%ANKI
-Cloze
-A byte consists of {8} bits.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1707432641557-->
-END%%
-
-%%ANKI
-Cloze
-A byte consists of {2} nibbles.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1707432641560-->
-END%%
-
-%%ANKI
-Cloze
-A nibble consists of {4} bits.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1707432641562-->
-END%%
-
-%%ANKI
-Basic
-What process is used to convert from e.g. decimal to another base?
-Back: Divide repeatedly by the base. Maintain remainders right to left.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1707432641591-->
-END%%
-
-%%ANKI
-Basic
-Why does converting from e.g. decimal to another base involve repeated division?
-Back: The position of a digit corresponds to the base raised to that position.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1707432641592-->
-END%%
\ No newline at end of file
diff --git a/notes/c17/types/index.md b/notes/c17/types/index.md
index 71d09b3..55f13df 100644
--- a/notes/c17/types/index.md
+++ b/notes/c17/types/index.md
@@ -312,6 +312,20 @@ Reference: “ISO: Programming Languages - C,” April 12, 2011, [https://port70
 <!--ID: 1724543977383-->
 END%%
 
+%%ANKI
+Cloze
+Integer types are to {1:$\mathbb{N}$} and {2:$\mathbb{Z}$}.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341581-->
+END%%
+
+%%ANKI
+Cloze
+Floating-point types are to {1:$\mathbb{R}$} and {2:$\mathbb{C}$}.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341582-->
+END%%
+
 %%ANKI
 Cloze
 The {real} types contrast the {complex} types.
diff --git a/notes/c17/types/simple.md b/notes/c17/types/simple.md
index 37c77e8..1b6809e 100644
--- a/notes/c17/types/simple.md
+++ b/notes/c17/types/simple.md
@@ -61,28 +61,26 @@ END%%
 
 %%ANKI
 Basic
-What does the "width" of an integer type refer to?
-Back: The number of bits used to represent its value.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1707835869737-->
-END%%
-
-%%ANKI
 What two variants does a C integral type declaration have?
 Back: Signed and unsigned.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1727551341544-->
 END%%
 
 %%ANKI
+Basic
 What does it mean for an integer to be "signed"?
 Back: It can represent negative, zero, and positive values.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1727551341545-->
 END%%
 
 %%ANKI
+Basic
 What does it mean for an integer to be "unsigned"?
 Back: It can only represent nonnegative values.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1727551341546-->
 END%%
 
 %%ANKI
@@ -206,7 +204,7 @@ END%%
 
 %%ANKI
 Cloze
-{1:`float`} has {2:4} byte precision whereas {2:`double`} has {1:8} byte precision.
+{1:`float`} has {2:4} byte width whereas {2:`double`} has {1:8} byte width.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 <!--ID: 1707493017242-->
 END%%
@@ -265,19 +263,17 @@ Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co
 <!--ID: 1723859121972-->
 END%%
 
-### Unsigned
+### Unsigned Integers
 
-These correspond to nonnegative integer values.
-
-| Name                 | Narrow | Rank |
-| -------------------- | ------ | ---- |
-| `bool`               | Yes    | 0    |
-| `char` (maybe)       | Yes    | 1    |
-| `unsigned char`      | Yes    | 1    |
-| `unsighed short`     | Yes    | 2    |
-| `unsigned int`       | No     | 3    |
-| `unsigned long`      | No     | 4    |
-| `unsigned long long` | No     | 5    |
+| Name                 | Narrow | Rank | Minimum Width |
+| -------------------- | ------ | ---- | ------------- |
+| `bool`               | Yes    | 0    | 1             |
+| `char` (maybe)       | Yes    | 1    | -             |
+| `unsigned char`      | Yes    | 1    | 8             |
+| `unsighed short`     | Yes    | 2    | 16            |
+| `unsigned int`       | No     | 3    | 16            |
+| `unsigned long`      | No     | 4    | 32            |
+| `unsigned long long` | No     | 5    | 64            |
 
 %%ANKI
 Basic
@@ -351,21 +347,154 @@ Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co
 <!--ID: 1723859122023-->
 END%%
 
-### Signed
+%%ANKI
+Basic
+What is the minimum width of a `bool`?
+Back: $1$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341547-->
+END%%
 
-These correspond to possibly negative integer values.
+%%ANKI
+Basic
+What is the minimum precision of a `bool`?
+Back: $1$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341548-->
+END%%
 
-| Name                 | Narrow | Rank |
-| -------------------- | ------ | ---- |
-| `char` (maybe)       | Yes    | 1    |
-| `signed char`        | Yes    | 1    |
-| `signed short`       | Yes    | 2    |
-| `signed int`         | No     | 3    |
-| `signed long`        | No     | 4    |
-| `signed long long`   | No     | 5    |
-| `float`              | -      | -    |
-| `double`             | -      | -    |
-| `long double`        | -      | -    |
+%%ANKI
+Basic
+What is the minimum width of an `unsigned char`?
+Back: $8$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341549-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of an `unsigned char`?
+Back: $8$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341550-->
+END%%
+
+%%ANKI
+Basic
+What is the maximum precision of an `unsigned char`?
+Back: N/A. C does not define maximum precisions.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341551-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum width of an `unsigned short`?
+Back: $16$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341552-->
+END%%
+
+%%ANKI
+Basic
+What is the underlying binary representation used to encode an `unsigned short`?
+Back: Unsigned encoding.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341553-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of an `unsigned short`?
+Back: $16$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341554-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum width of an `unsigned int`?
+Back: $16$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341555-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of an `unsigned int`?
+Back: $16$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341556-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum width of an `unsigned long`?
+Back: $32$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341557-->
+END%%
+
+%%ANKI
+Basic
+What is the underlying binary representation used to encode an `unsigned long`?
+Back: Unsigned encoding.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341558-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of an `unsigned long`?
+Back: $32$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341559-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum width of an `unsigned long`?
+Back: $32$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of an `unsigned long long`?
+Back: $32$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341560-->
+END%%
+
+%%ANKI
+Basic
+How do we portably compute the smallest possible `unsigned long long`?
+Back: As `0`.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157085-->
+END%%
+
+%%ANKI
+Basic
+How do we portably compute the largest possible `unsigned long long`?
+Back: As `ULLONG_MAX`.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157086-->
+END%%
+
+### Signed Integers
+
+| Name               | Narrow | Rank | Minimum Width |
+| ------------------ | ------ | ---- | ------------- |
+| `char` (maybe)     | Yes    | 1    | -             |
+| `signed char`      | Yes    | 1    | 8             |
+| `signed short`     | Yes    | 2    | 16            |
+| `signed int`       | No     | 3    | 16            |
+| `signed long`      | No     | 4    | 32            |
+| `signed long long` | No     | 5    | 64            |
+| `float`            | -      | -    | -             |
+| `double`           | -      | -    | -             |
+| `long double`      | -      | -    | -             |
 
 %%ANKI
 Basic
@@ -431,6 +560,117 @@ Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co
 <!--ID: 1723859122080-->
 END%%
 
+%%ANKI
+Basic
+What is the minimum width of a `signed char`?
+Back: $8$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341561-->
+END%%
+
+%%ANKI
+Basic
+What is the underlying binary representation used to encode a `signed char`?
+Back: N/A. This is implementation specific.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341562-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of a `signed char`?
+Back: $7$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341563-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum width of a `signed short`?
+Back: $16$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341564-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of a `signed short`?
+Back: $15$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341565-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum width of a `signed int`?
+Back: $16$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341566-->
+END%%
+
+%%ANKI
+Basic
+What is the underlying binary representation used to encode a `signed char`?
+Back: N/A. This is implementation specific.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of a `signed int`?
+Back: $15$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341567-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum width of a `signed long`?
+Back: $32$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341568-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of a `signed long`?
+Back: $31$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341569-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum width of a `signed long long`?
+Back: $64$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341570-->
+END%%
+
+%%ANKI
+Basic
+What is the minimum precision of a `signed long long`?
+Back: $63$
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341571-->
+END%%
+
+%%ANKI
+Basic
+How do we portably compute the smallest possible `signed int`?
+Back: As `INT_MIN`.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157087-->
+END%%
+
+%%ANKI
+Basic
+How do we portably compute the largest possible `signed int`?
+Back: As `INT_MAX`.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157088-->
+END%%
+
 ### Literals
 
 Negative integer literals are typed in a counterintuitive way. When the compiler sees a number of form `-X`, the type of `X` is determined *before* being negated. Promotion follows the **first fit rule** described as follows:
@@ -675,7 +915,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1714677608769-->
 END%%
 
-Integer constants can be forced to be unsigned or to be a type with minimal width by using the following suffixes:
+Integer constants can be made a certain signedness or type by using the following suffixes:
 
 | Suffix | Type                 |
 | ------ | -------------------- |
@@ -826,7 +1066,7 @@ END%%
 
 ### Literals
 
-Floating-point constants can be forced to be a type with minimal width by using the following suffixes:
+Floating-point constants can be made a certain type by using the following suffixes:
 
 | Suffix | Type          |
 | ------ | ------------- |
@@ -905,6 +1145,117 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1723938382436-->
 END%%
 
+%%ANKI
+Cloze
+`INT_MAX` is to {`<limits.h>`} whereas `DBL_MAX` is to {`<float.h>`}.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157090-->
+END%%
+
+%%ANKI
+Basic
+What does `DBL_MIN` refer to?
+Back: The smallest `double` strictly greater than 0.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157091-->
+END%%
+
+%%ANKI
+Basic
+How do we portably compute the smallest possible `double`?
+Back: As `-DBL_MAX`.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157092-->
+END%%
+
+%%ANKI
+Basic
+How do we portably compute the largest possible `double`?
+Back: As `DBL_MAX`.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157093-->
+END%%
+
+## Exact-Width Integer Types
+
+The `stdint.h` library contains **exact-width integer types**. These are aliases to types that represent an exact width and sign representation:
+
+* If the type `uintN_t` is provided, it is an unsigned integer type with exactly $N$ bits of width and precision.
+* If the type `intN_t` is provided, is is signed, with two's complement representation, has a width of exactly $N$ bits and a precision of $N - 1$.
+
+The C standard says these `typedef`s *must* be defined if they can be satisfied. Otherwise they may not exist.
+
+%%ANKI
+Cloze
+The {`<stdint.h>`} library contains {exact-width integer types}.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341572-->
+END%%
+
+%%ANKI
+Basic
+Suppose `uintN_t` exists. What is its width?
+Back: `N` bits.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341573-->
+END%%
+
+%%ANKI
+Basic
+Suppose `uintN_t` exists. What is its precision?
+Back: `N`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341574-->
+END%%
+
+%%ANKI
+Basic
+Suppose `uintN_t` exists. It is encoded using what binary representation?
+Back: Unsigned encoding.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341575-->
+END%%
+
+%%ANKI
+Basic
+Suppose `intN_t` exists. What is its width?
+Back: `N` bits.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341576-->
+END%%
+
+%%ANKI
+Basic
+Suppose `intN_t` exists. What is its precision?
+Back: `N - 1`
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341577-->
+END%%
+
+%%ANKI
+Basic
+Suppose `intN_t` exists. It is encoded using what binary representation?
+Back: Two's-complement encoding.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341578-->
+END%%
+
+%%ANKI
+Basic
+Suppose a platform has a 32-bit signed integer type. Why might `int32_t` not be defined?
+Back: The platform may not use two's-complement encoding.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341579-->
+END%%
+
+%%ANKI
+Basic
+Suppose a platform has a 32-bit signed two's-complement integer type. Why might `int32_t` not be defined?
+Back: N/A. The C standard states `int32_t` *must* be defined.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341580-->
+END%%
+
 ## Enumerated Types
 
 An `enum` is a mapping of identifiers with integer values. They have general form:
diff --git a/notes/binary/endianness.md b/notes/encoding/binary.md
similarity index 58%
rename from notes/binary/endianness.md
rename to notes/encoding/binary.md
index f0360c4..bf557a7 100644
--- a/notes/binary/endianness.md
+++ b/notes/encoding/binary.md
@@ -1,14 +1,90 @@
 ---
-title: Endianness
-TARGET DECK: Obsidian::STEM
-FILE TAGS: binary::endian
+title: Binary
+TARGET DECK: Obsidian::H&SS
+FILE TAGS: binary
 tags:
   - binary
-  - endian
 ---
 
 ## Overview
 
+A binary digit or **bit** is a `0` or `1` character. A **bit string** is then a contiguous sequence of bits. It's **weight** is a reference to the number of `1`s in the bit string. Compare the below operation to the method for converting from one numerical base to another (e.g. [[radices#Hexadecimal|hexadecimal]]).
+
+```c
+unsigned int bit_weight(int64_t n) {
+  unsigned int count = 0;
+  while (n) {
+    count += (n % 2 == 0) ? 0 : 1;
+    n /= 2;
+  }
+  return count;
+}
+```
+
+%%ANKI
+Basic
+Why is a "bit" named the way it is?
+Back: It is short for **b**inary dig**it**.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1707432641557-->
+END%%
+
+%%ANKI
+Basic
+What does the weight of a bit string refer to?
+Back: The number of `1`s in the string.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708366788645-->
+END%%
+
+%%ANKI
+Basic
+How might you use C to find the weight of a bit string?
+Back: Repeatedly divide by `2`, counting all remainders of `1`.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+Tags: c17
+<!--ID: 1708366788648-->
+END%%
+
+%%ANKI
+Cloze
+A byte consists of {8} bits.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1707432641557-->
+END%%
+
+%%ANKI
+Cloze
+A byte consists of {2} nibbles.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1707432641560-->
+END%%
+
+%%ANKI
+Cloze
+A nibble consists of {4} bits.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1707432641562-->
+END%%
+
+%%ANKI
+Basic
+What process is used to convert from e.g. decimal to another base?
+Back: Divide repeatedly by the base. Maintain remainders right to left.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1707432641591-->
+END%%
+
+%%ANKI
+Basic
+Why does converting from e.g. decimal to another base involve repeated division?
+Back: The position of a digit corresponds to the base raised to that position.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1707432641592-->
+END%%
+
+## Endianness
+
 Platforms with multi-byte objects must establish the object's address and byte ordering. Objects are typically addressed by the smallest address of the bytes used. Bytes are ordered either in **big-endian** or **little-endian**. In big-endian, the most significant byte is listed first. In little-endian, the least significant byte is ordered first.
 
 %%ANKI
diff --git a/notes/encoding/floating-point.md b/notes/encoding/floating-point.md
index b2b48b1..bd97674 100644
--- a/notes/encoding/floating-point.md
+++ b/notes/encoding/floating-point.md
@@ -33,6 +33,8 @@ Declaration | Sign Bit | Exponent Field | Fractional Field
 `float`     | `1`      | `8`            | `23`
 `double`    | `1`      | `11`           | `52`
 
+The **precision** of a floating-point type refers to the number of bits found in the fractional field.
+
 %%ANKI
 Basic
 In base-10 scientific notation, what form do nonzero numbers take on?
@@ -1032,6 +1034,14 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1710672470805-->
 END%%
 
+%%ANKI
+Basic
+What does the precision of a floating-point number refer to?
+Back: The number of bits found in its fractional field.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727552157081-->
+END%%
+
 ## Rounding
 
 Because floating-point arithmetic can't represent every real number, it must round results to the "nearest" representable number, however "nearest" is defined. The IEEE floating-point standard defines four **rounding modes** to influence this behavior:
@@ -1268,8 +1278,8 @@ END%%
 %%ANKI
 Basic
 Is $+^f$ commutative?
-Back: Yes.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Back: No.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
 <!--ID: 1710680824810-->
 END%%
 
diff --git a/notes/encoding/integer.md b/notes/encoding/integer.md
index b2dceb7..1922559 100644
--- a/notes/encoding/integer.md
+++ b/notes/encoding/integer.md
@@ -11,13 +11,38 @@ tags:
 
 Integers are typically encoded using either **unsigned encoding** or **two's-complement**. The following table highlights how the min and max of these encodings behave:
 
-Value    | $w = 8$ | $w = 16$ | $w = 32$
--------- | ------- | -------- | ------------
-$UMin_w$ | `0x00`  | `0x0000` | `0x00000000`
-$UMax_w$ | `0xFF`  | `0xFFFF` | `0xFFFFFFFF`
-$TMin_w$ | `0x80`  | `0x8000` | `0x80000000`
-$TMax_w$ | `0x7F`  | `0x7FFF` | `0x7FFFFFFF`
+| Value    | $w = 8$ | $w = 16$ | $w = 32$     |
+| -------- | ------- | -------- | ------------ |
+| $UMin_w$ | `0x00`  | `0x0000` | `0x00000000` |
+| $UMax_w$ | `0xFF`  | `0xFFFF` | `0xFFFFFFFF` |
+| $TMin_w$ | `0x80`  | `0x8000` | `0x80000000` |
+| $TMax_w$ | `0x7F`  | `0x7FFF` | `0x7FFFFFFF` |
 
+The **width** of an integer type refers to the number of bits used in the type's binary representation. It's **precision** refers to the number of bits used in the type's binary representation, excluding those used for signedness.
+
+%%ANKI
+Basic
+What does the "width" of an integer type refer to?
+Back: The number of bits used to represent its value.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1707835869737-->
+END%%
+
+%%ANKI
+Basic
+What does the "precision" of an integer type refer to?
+Back: The number of bits used to represent its value, excluding bits used for sign representations.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341542-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes the "width" from the "precision" of an integer type?
+Back: The latter does not consider bits used for sign representations.
+Reference: Jens Gustedt, _Modern C_ (Shelter Island, NY: Manning Publications Co, 2020).
+<!--ID: 1727551341543-->
+END%%
 
 %%ANKI
 Basic
@@ -2180,4 +2205,4 @@ END%%
 * Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 * Finley, Thomas. “Two’s Complement,” April 2000. [https://www.cs.cornell.edu/~tomf/notes/cps104/twoscomp.html](https://www.cs.cornell.edu/~tomf/notes/cps104/twoscomp.html).
 * Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
-* “Two’s-Complement.” In *Wikipedia*, January 9, 2024. [https://en.wikipedia.org/w/index.php?title=Two%27s_complement&oldid=1194543561](https://en.wikipedia.org/w/index.php?title=Two%27s_complement&oldid=1194543561).
\ No newline at end of file
+* “Two’s-Complement.” In *Wikipedia*, January 9, 2024. [https://en.wikipedia.org/w/index.php?title=Two%27s_complement&oldid=1194543561](https://en.wikipedia.org/w/index.php?title=Two%27s_complement&oldid=1194543561).