notebook/notes/algebra/radices.md

11 KiB

title TARGET DECK FILE TAGS tags
Radices Obsidian::STEM algebra
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).

%%ANKI 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.

END%%

%%ANKI 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.

END%%

%%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.

END%%

%%ANKI 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.

END%%

%%ANKI 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

END%%

%%ANKI 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

END%%

%%ANKI 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

END%%

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

END%%

%%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

END%%

%%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

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. Tags: binary::hex

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. Tags: binary::hex c17

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. Tags: binary::hex

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. Tags: binary::hex

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. 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%%

%%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. Tags: binary::hex

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. Tags: binary::hex

END%%

%%ANKI 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

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. Tags: binary::hex

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. Tags: binary::hex

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. Tags: binary::hex

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. Tags: binary::hex

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. Tags: binary::hex

END%%

%%ANKI 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

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. Tags: binary::hex

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. Tags: binary::hex

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. Tags: binary::hex

END%%

%%ANKI 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

END%%

%%ANKI 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

END%%

Bibliography