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Move notes on integer encoding.

c-declarations
Joshua Potter 2024-02-21 13:33:59 -07:00
parent d93f0d3cb6
commit 2538533aee
2 changed files with 23 additions and 57 deletions
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2
notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
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@ -171,7 +171,7 @@
"algorithms/binary-search.md": "08cb6dc2dfb204a665d8e8333def20ca",
"_journal/2024-02-17.md": "7c37cb10515ed3d2f5388eaf02a67048",
"_journal/2024-02/2024-02-16.md": "e701902e369ec53098fc2deed4ec14fd",
"binary/integer-encoding.md": "fc9e88adabcbbf106c50718016e238c7",
"binary/integer-encoding.md": "193566bf1b9e88257002d32bb2bc0bf2",
"combinatorics/index.md": "f9de9671fdb6068ef2bb5e63051734be",
"_journal/2024-02-18.md": "67e36dbbb2cac699d4533b5a2eaeb629",
"_journal/2024-02/2024-02-17.md": "7c37cb10515ed3d2f5388eaf02a67048",

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notes/binary/integer-encoding.md
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@ -108,21 +108,9 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
<!--ID: 1708455064696-->
END%%
%%ANKI
Basic
What does $TMin_w$ evaluate to?
Back: $-2^{w-1}$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708545383252-->
END%%
### Unsigned Encoding
%%ANKI
Basic
What does $TMax_w$ evaluate to?
Back: $2^{w-1} - 1$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708545383255-->
END%%
Always represents nonnegative numbers. Given an integral type $\vec{x}$ of $w$ bits, we convert binary to its unsigned encoding with: $$B2U_w(\vec{x}) = \sum_{i=0}^{w-1} 2^ix_i$$
%%ANKI
Basic
@ -140,29 +128,9 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
<!--ID: 1708545383258-->
END%%
### Unsigned Encoding
Always represents nonnegative numbers. Given an integral type $\vec{x}$ of $w$ bits, we convert binary to its unsigned encoding with: $$B2U_w(\vec{x}) = \sum_{i=0}^{w-1} 2^ix_i$$
%%ANKI
Basic
What is the largest unsigned value an integral type of $w$ bits can encode?
Back: $2^w - 1$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708177246119-->
END%%
%%ANKI
Basic
What is the smallest unsigned value an integral type of $w$ bits can encode?
Back: $0$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708177246123-->
END%%
%%ANKI
Basic
What half-open interval represents the possible $w$-bit unsigned values?
What half-open interval represents the possible $w$-bit unsigned decimal values?
Back: $[0, 2^w)$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708177246128-->
@ -186,7 +154,7 @@ END%%
%%ANKI
Basic
What is the decimal expansion of unsigned type $1010_2$?
What is the decimal expansion of unsigned integer $1010_2$?
Back: $2^3 + 2^1 = 10$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708177246143-->
@ -302,23 +270,23 @@ Represents negative numbers along with nonnegative ones. Given an integral type
%%ANKI
Basic
What is the largest two's-complement value an integral type of $w$ bits can encode?
Back: $2^{w-1} - 1$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708179147807-->
END%%
%%ANKI
Basic
What is the smallest two's-complement value an integral type of $w$ bits can encode?
What does $TMin_w$ evaluate to?
Back: $-2^{w-1}$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708179147810-->
<!--ID: 1708545383252-->
END%%
%%ANKI
Basic
What half-open interval represents the possible $w$-bit two's-complement values?
What does $TMax_w$ evaluate to?
Back: $2^{w-1} - 1$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708545383255-->
END%%
%%ANKI
Basic
What half-open interval represents the possible $w$-bit two's-complement decimal values?
Back: $[-2^{w-1}, 2^{w-1})$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708177246128-->
@ -507,7 +475,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
<!--ID: 1708453398469-->
END%%
The "two's-complement" of an integer often refers to the binary representation of the integer's additive inverse. For example, $0110_2 = 6$ has two's-complement $1010_2 = -6$. In contrast, the "complement" of an integer is the other integer such that together add up to $2^{w-1}$. For example, $0110_2 = 6$ has complement $0010_2 = 2$ (with respect to $2^3 = 8$).
The "two's-complement" of an integer often refers to the binary representation of the integer's additive inverse. For example, $0110_2 = 6$ has two's-complement $1010_2 = -6$. In contrast, the "complement" of a nonnegative integer is the other nonnegative integer such that together add up to $2^{w-1}$. For example, $0110_2 = 6$ has complement $0010_2 = 2$ (with respect to $2^3 = 8$).
%%ANKI
Basic
@ -517,14 +485,6 @@ Reference: “Two’s-Complement.” In *Wikipedia*, January 9, 2024. [https://e
<!--ID: 1708545383262-->
END%%
%%ANKI
Basic
In two's-complement, how many negative values can be encoded compared to nonnegative values?
Back: The same amount.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708545383264-->
END%%
%%ANKI
Cloze
In two's-complement, the {sign bit} partitions the encoding range into two sets.
@ -556,6 +516,12 @@ Reference: “Two’s-Complement.” In *Wikipedia*, January 9, 2024. [https://e
<!--ID: 1708545383270-->
END%%
%%ANKI
Cloze
$TMin$ is called the "{weird number}" because {it is it's own two's-complement}.
Reference: “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).
END%%
%%ANKI
Basic
What is the result of applying the two's-complement operation on $TMin$?