11 KiB
| title | TARGET DECK | FILE TAGS | tags | |
|---|---|---|---|---|
| Integer Encoding | Obsidian::STEM | binary |
|
Overview
Integers are typically encoded using either unsigned encoding or two's complement.
%%ANKI Basic What is a C integral type? Back: A type representing finite ranges of integers. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: c
END%%
%%ANKI Basic In what two ways are C integral types encoded? Back: Unsigned encoding or two's-complement. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: c
END%%
%%ANKI Basic What integer values does unsigned encoding represent? Back: Nonnegative values. 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 integer values does two's-complement represent? Back: Negative, zero, and positive values. 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 An integral value of 0 has what encoding? Back: Either unsigned or two's-complement. 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 An integral value of 100 has what encoding? Back: Either unsigned or two's-complement. 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 An integral value of -100 has what encoding? Back: Two's-complement. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
Unsigned Encoding
Always represents nonnegative numbers. Given an integral type \vec{x} of w bits, we convert binary to its unsigned encoding with: $B2U_w(\vec{x}) = \sum_{i=0}^{w-1} 2^ix_i$
%%ANKI
Basic
What is the largest unsigned value an integral type of w bits can encode?
Back: 2^w - 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
What is the smallest unsigned value an integral type of w bits can encode?
Back: 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
What half-open interval represents the possible w-bit unsigned values?
Back: [0, 2^w)
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 binary representation of the smallest 4-bit unsigned number?
Back: 0000_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
What is the binary representation of the largest 4-bit unsigned number?
Back: 1111_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
What is the decimal expansion of unsigned type 1010_2?
Back: 2^3 + 2^1 = 10
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 does the "uniqueness" of unsigned encoding refer to? Back: The function used to convert integral types to their unsigned encoding is a bijection. 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 Bryant et al. define B2U_w?
Back: B2U_w(\vec{x}) = \sum_{i=0}^{w-1} 2^ix_i
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 B2U_w an acronym for?
Back: Binary "to" unsigned.
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 does w in B2U_w represent?
Back: The number of bits in the integral type being interpreted.
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 domain of B2U_w?
Back: Bit vectors of size w.
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 range of B2U_w?
Back: [0, 2^w)
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
Why is "B2U" insufficient for use?
Back: We need to understand how many bits conversion is with respect to.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
Two's-Complement
Represents negative numbers along with nonnegative ones. Given an integral type \vec{x} of w bits, we convert binary to its twos'-complement encoding with: $B2T_w(\vec{x}) = -2^{w-1}x_{w-1} + \sum_{i=0}^{w-2} 2^ix_i$
%%ANKI
Basic
What is the largest two's-complement value an integral type of w bits can encode?
Back: 2^{w-1} - 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
What is the smallest two's-complement value an integral type of w bits can encode?
Back: -2^{w-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
What half-open interval represents the possible w-bit two's-complement values?
Back: [-2^{w-1}, 2^{w-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
Cloze
[{1:0}, {2:2^w}) is to unsigned as [{1:-2^{w-1}}, {2:2^{w-1}}) is to two's-complement.
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 binary representation of the smallest 4-bit two's-complement number?
Back: 1000_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
What is the binary representation of the largest 4-bit two's-complement number?
Back: 0111_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 Cloze The {sign bit} refers to the {most significant bit} in two's-complement. 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 weight of the sign bit in w-bit two's-complement?
Back: -2^{w-1}
The {sign bit} refers to the {most significant bit} in two's-complement.
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 does the "uniqueness" of two's-complement refer to? Back: The function used to convert integral types to two's-complement is a bijection. 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 Bryant et al. define B2T_w?
Back: B2T_w(\vec{x}) = -2^{w-1}x_{w-1} + \sum_{i=0}^{w-2} 2^ix_i
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 B2T_w an acronym for?
Back: Binary "to" two's-complement.
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 does w in B2T_w represent?
Back: The number of bits in the integral type being interpreted.
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 domain of B2T_w?
Back: Bit vectors of size w.
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 range of B2T_w?
Back: [-2^{w-1}, 2^{w-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
Why is "B2T" insufficient for use?
Back: We need to understand how many bits conversion is with respect to.
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.