173 lines
6.4 KiB
Markdown
173 lines
6.4 KiB
Markdown
---
|
|
title: Hexadecimal
|
|
TARGET DECK: Obsidian::STEM
|
|
FILE TAGS: binary::hex
|
|
tags:
|
|
- binary
|
|
- hexadecimal
|
|
---
|
|
|
|
## Overview
|
|
|
|
Hexadecimal encoding refers to the 16-base representation of binary numbers. Distinguish potentially ambiguous values like $32$ with the base as a subscript, e.g. $32_{10}$ vs $32_{16}$.
|
|
|
|
%%ANKI
|
|
Cloze
|
|
A byte consists of {2} hexadecimal digits.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641563-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
A nibble consists of {1} hexadecimal digits.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
Hexadecimal digits are represented by what characters?
|
|
Back: `a` to `f`, `A` to `F`, and `0` to `9`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641565-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How does C denote a hexadecimal numeric constant?
|
|
Back: With `0x` or `0X`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641567-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
What is the decimal equivalent of hex `A`, `C`, and `F`?
|
|
Back: `10`, `12`, and `15` respectively.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641568-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
What is the hexadecimal equivalent of decimal `11`, `12`, and `14`?
|
|
Back: `B`, `C`, and `E` respectively.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641570-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
*When* should padding be introduced in binary to hexadecimal conversion?
|
|
Back: When the number of bits is not a multiple of `4`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641571-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
*Where* is padding introduced in binary to hexadecimal conversion?
|
|
Back: To the left of the binary sequence.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641573-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
What are the possible hex values the first digit of $2^n$ can take on?
|
|
Back: `1`, `2`, `4`, and `8`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641579-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
What are the possible values in binary that the first nibble of $2^n$ can take on?
|
|
Back: `0001`, `0010`, `0100`, and `1000`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641580-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is $j$ interpreted in the hex representation of $2^{i + 4j}$?
|
|
Back: As the number of `0`s in the encoding.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641582-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is the $0$ in $2^{0 + 4j}$ translated to hex?
|
|
Back: As hex digit `1`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641583-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is the $1$ in $2^{1 + 4j}$ translated to hex?
|
|
Back: As hex digit `2`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641585-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is the $2$ (power) in $2^{2 + 4j}$ translated to hex?
|
|
Back: As hex digit `4`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641586-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is the $3$ in $2^{3 + 4j}$ translated to hex?
|
|
Back: As hex digit `8`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641587-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is $n$ in $2^n$ factored to quickly write the decimal value's hex representation?
|
|
Back: $n = i + 4j$ where $0 \leq i \leq 3$.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641589-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is the *remainder* of e.g. `158 / 16` managed in decimal to hex conversion?
|
|
Back: As the next least significant bit of our conversion.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641594-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is the *quotient* of e.g. `158 / 16` managed in decimal to hex conversion?
|
|
Back: As the next value to divide by `16`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641595-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
When does repeated division in decimal to hex conversion end?
|
|
Back: When the quotient (*not* the remainder) is `0`.
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707919792632-->
|
|
END%%
|
|
|
|
%%ANKI
|
|
Basic
|
|
How is e.g. `0xAC32` expressed as a sum of decimal values?
|
|
Back: $(16^3 \times 10) + (16^2 \times 12) + (16^1 \times 3) + (16^0 \times 2)$
|
|
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
|
<!--ID: 1707432641596-->
|
|
END%%
|
|
|
|
## References
|
|
|
|
* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|