--- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. END%% ## References * Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.