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
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%%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
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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
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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
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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
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%%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
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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
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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
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Basic
How is j interpreted in the hex representation of 2^{i + 4j}?
Back: As the number of 0s 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
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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
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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
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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
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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
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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
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Basic
How is the remainder of e.g. 158 / 16 managed in decimal to hex conversion?
Back: Assuming big-endian, as the next most 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
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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
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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
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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
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Basic
Which hexadecimal digits are encoded in 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
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Basic
Which hexadecimal digits are encoded in 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
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Bibliography
- 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.