11 KiB
title | TARGET DECK | FILE TAGS | tags | |
---|---|---|---|---|
Radices | Obsidian::STEM | algebra |
|
Overview
The radix is the number of unique digits used to represent numbers in a positional numeral system. Most commonly used systems tend to be binary (2
-base), octal (8
-base), decimal (10
-base), and #Hexadecimal (16
-base).
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Basic
What is the process of subtracting a larger digit from a smaller one in radix r
?
Back: Decrement the next nonzero and add r
to the smaller digit in question.
Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173.
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Basic
What does the process of "borrowing" in subtraction 100_2 - 10_2
look like?
Back:
2
000
- 10
-----
010
Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173.
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%%ANKI Basic In a positional numeral system, what does "radix" refer to? Back: The number of unique digits used to represent numbers. Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173.
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Basic
What is the radix of the decimal system?
Back: 10
Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173.
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Basic
What is the radix of the octal system?
Back: 8
Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173.
Tags: binary
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Basic
What is the radix of the hexadecimal system?
Back: 16
Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173.
Tags: binary::hex
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Basic
What is the radix of the binary system?
Back: 2
Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173.
Tags: binary
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Hexadecimal
Hexadecimal is a 16-base numeral system, usually represented with digits 0
to 9
and a
to f
or A
to F
.
%%ANKI Cloze A hexadecimal digit represents {4} bits. Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173. Tags: binary::hex
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%%ANKI Cloze An octal digit represents {3} bits. Reference: “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173. Tags: binary
END%%
%%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. Tags: binary::hex
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%%ANKI Cloze 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. Tags: binary::hex
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex c17
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
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. Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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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.
Tags: binary::hex
END%%
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Basic
Which hexadecimal digits encode binary with a leading 1
bit?
Back: 8
through F
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary::hex
END%%
%%ANKI
Basic
Which hexadecimal digits encode binary with a leading 0
bit?
Back: 0
through 7
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary::hex
END%%
References
- Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
- “Radix,” in Wikipedia, August 6, 2023, https://en.wikipedia.org/w/index.php?title=Radix&oldid=1169046173.