56 KiB
| title | TARGET DECK | FILE TAGS | tags | |||
|---|---|---|---|---|---|---|
| Floating Point | Obsidian::STEM | binary::float ieee |
|
Overview
The IEEE floating-point standard defines an encoding used to represent numbers of form (-1)^s \times M \times 2^E$$
where s denotes the sign bit, M the significand, and E the exponent. The binary representation of floating point numbers are segmented into three fields: the sign bit, the exponent field, and the fraction field. Furthermore, there are three classes these fields are interpreted with respect to:
- Normalized Form
- Here the exponent field is neither all
0s nor all1s. - The significand is
1 + f, wherefdenotes the fractional part. E = e - Biaswhereeis the unsigned interpretation of the exponent field.
- Here the exponent field is neither all
- Denormalized Form
- Here the exponent field is all
0s. - The significand is
f, wherefdenotes the fractional part. E = 1 - Bias, defined for smooth transition between normalized and denormalized values.
- Here the exponent field is all
- Special Values
- Here the exponent field is all
1s. - If the fraction field is all
0s, we have an\inftyvalue. - If the fraction field is not all
0s, we haveNaN.
- Here the exponent field is all
The Bias in the first two forms is set to 2^{k - 1} - 1 where k denotes the number of bits that make up the exponent field. In C, fields have the following widths:
| Declaration | Sign Bit | Exponent Field | Fractional Field |
|---|---|---|---|
float |
1 |
8 |
23 |
double |
1 |
11 |
52 |
The precision of a floating-point type refers to the number of bits found in the fractional field.
%%ANKI
Basic
In base-10 scientific notation, what form do nonzero numbers take on?
Back: m \times 10^n
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
What radix is implicitly specified in scientific notation form m \times 10^n?
Back: 10
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
In base-10 scientific notation, what numbers does m take on in form m \times 10^n?
Back: A nonzero real number.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
In base-10 scientific notation, what numbers does n take on in m \times 10^n?
Back: An integer.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
What term refers to m in scientific notation m \times 10^n?
Back: The significand.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
What term refers to n in scientific notation m \times 10^n?
Back: The exponent.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
What does it mean for m \times 10^n to be in normalized form?
Back: That 1 \leq |m| < 10.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
In base-2 scientific notation, what form do nonzero numbers take on?
Back: m \times 2^n
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
What radix is implicitly specified in scientific notation form m \times 2^n?
Back: 2
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
In base-2 scientific notation, what numbers does m take on in form m \times 2^n?
Back: A nonzero real number.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
In base-2 scientific notation, what numbers does n take on in m \times 2^n?
Back: An integer.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
What term refers to m in scientific notation m \times 2^n?
Back: The significand.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
What term refers to n in scientific notation m \times 2^n?
Back: The exponent.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI
Basic
What does it mean for scientific notation m \times 2^n to be in normalized form?
Back: That 1 \leq |m| < 2.
Reference: “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.
END%%
%%ANKI Basic How is IEEE pronounced? Back: "eye-triple-ee" 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 IEEE an acronym for? Back: Institute of Electrical and Electronics Engineers. 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 IEEE standard (number) describes floating point operations? Back: 754 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 alternative name does IEEE Standard 754 go by? Back: IEEE floating-point 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 floating point encoding is guaranteed by the C standard? Back: N/A Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: c17
END%%
%%ANKI Basic What floating point encoding is used in most C implementations? Back: IEEE Standard 754 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 are digits left of a decimal point weighted?
Back: As a nonnegative power of 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
How are digits right of a decimal point weighted?
Back: As negative powers of 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
How are digits left of a binary point weighted?
Back: As a nonnegative power of 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 are digits right of a binary point weighted?
Back: As a negative power of 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 binary 10.11_2?
Back: 2^1 + 2^{-1} + 2^{-2} = 2.75
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 decimal value does 0.1111_2 evaluate to?
Back: \frac{15}{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
What decimal value does 0.11_2 evaluate to?
Back: \frac{3}{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
What decimal value does 0.11\cdots1_2 evaluate to?
Back: Given n 1's, 1 - 2^{-n}.
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 visualization explains why 0.11\cdots1_2 = 1 - 2^{-n}?
Back: Each additional 1 adds half of the remaining interval to a running total.
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 result of shifting the decimal point of d_m \cdots d_1 d_0 . d_{-1} d_{-2} \cdots d_{-n} to the left?
Back: Division by 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 is the result of shifting the decimal point of d_m \cdots d_1 d_0 . d_{-1} d_{-2} \cdots d_{-n} to the right?
Back: Multiplication by 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 is the result of shifting the binary point of b_m \cdots b_1 b_0 . b_{-1} b_{-2} \cdots b_{-n} to the right?
Back: Multiplication by 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 result of shifting the binary point of b_m \cdots b_1 b_0 . b_{-1} b_{-2} \cdots b_{-n} to the left?
Back: Division by 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 binary pattern does 1 - \epsilon denote?
Back: 0.11\cdots1.
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 compact notation is used to denote 0.11\cdots1_2?
Back: 1 - \epsilon
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 compact notation is used to denote 1.11\cdots1_2?
Back: 2 - \epsilon
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 name is given to the . in decimal number d_m \cdots d_1 d_0 . d_{-1} d_{-2} \cdots d_{-n}?
Back: The decimal point.
END%%
%%ANKI
Basic
What name is given to the . in binary number b_m \cdots b_1 b_0 . b_{-1} b_{-2} \cdots b_{-n}?
Back: The binary point.
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 IEEE floating-point standard represents numbers in form {1:(-1)^s} \times {1:M} \times {1:2^E}.
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 term is used to refer to s in IEEE floating-point (-1)^s \times M \times 2^E?
Back: The sign.
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 term is used to refer to M in IEEE floating-point (-1)^s \times M \times 2^E?
Back: The significand.
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 range of values does the significand M take on in IEEE floating-point?
Back: Between 0 and 2 - \epsilon.
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 term is used to refer to E in IEEE floating-point (-1)^s \times M \times 2^E?
Back: The exponent.
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 The bit representation of a floating-point number is divided into what three fields? Back: The sign, exponent, and fraction. 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 many bits make up the sign field of a float?
Back: 1
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
How many bits make up the exponent field of a float?
Back: 8
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
How many bits make up the fraction field of a float?
Back: 23
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
How many bits make up the sign field of a double?
Back: 1
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
How many bits make up the exponent field of a double?
Back: 11
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
How many bits make up the fraction field of a double?
Back: 52
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Cloze
The exponent field of a float has {8} bits and a double has {11} bits.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Cloze
The fraction field of a float has {23} bits and a double has {52} bits.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
Which IEEE floating-point fields have the same width in floats and doubles?
Back: The sign bit field.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
Which IEEE floating-point fields have different widths in floats and doubles?
Back: The exponent and fraction fields.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
When is a floating-point number considered normalized?
Back: When the exponent field is neither all 0s nor all 1s.
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 distinguishes the exponent field from the exponent value? Back: The latter refers to the value after biasing the unsigned interpretation of the former. 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 bias refer to? Back: The number used to adjust the interpreted value of the exponent field. 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 value of the bias?
Back: Given k bits in the exponent field, 2^{k-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 binary representation of a float's bias?
Back: 01111111
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the binary representation of a double's bias?
Back: 01111111111
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
How do you determine the exponent value in normalized form?
Back: e - Bias where e is the unsigned interpretation of the exponent field.
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 do you determine the significand value in normalized form?
Back: It equals 1 plus the fraction field.
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
A sign bit value of {1:0} is positive and {1:1} is negative.
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 Which floating-point field is the bias relevant to? Back: The exponent field. 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 do you determine the sign of a normalized floating-point?
Back: A sign bit of 0 is positive, a sign bit of 1 is negative.
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
For which floating-point form is "implied leading 1" relevant?
Back: Normalized form.
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
Which floating-point form is depicted in the following?
!
Back: Normalized form.
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 is a floating-point number considered denormalized?
Back: When the exponent field is all 0s.
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 do you determine the exponent value in denormalized form?
Back: 1 - Bias
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 do you determine the significand value in denormalized form? Back: It equals the fraction field. 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
Is value 0 representable in normalized form?
Back: No.
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
Is value 0 representable in denormalized form?
Back: Yes.
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
Which floating-point form corresponds to very large numbers (|V| \gg 0)?
Back: Normalized form.
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
Which floating-point form corresponds to near 0 numbers (|V| \ll 1)?
Back: Denormalized form.
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:|V| \ll 1} is to {2:denormalized} form whereas {2:|V| \gg 0} is to {1:normalized} form.
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
Significand range {[0, 1 - \epsilon]} is to denormalized whereas {2:[1, 2 - \epsilon]} is to normalized.
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 can't normalized floating-point encode 0?
Back: Because of the implied leading 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
Which number can be encoded in two different ways?
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
In what two ways can 0 be encoded?
Back: As -0.0 or +0.0.
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 is the actual bit encoding of floating-point number +0.0?
Back: All 0s.
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 actual bit encoding of floating-point number -0.0?
Back: A sign bit 1 followed by all 0s.
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
Which floating-point form is depicted in the following?
!
Back: Denormalized form.
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 actual bit encoding of floating-point number +\infty?
Back: Sign bit 0, exponent field of all 1s, a fractional field of all 0s.
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 actual bit encoding of floating-point number -\infty?
Back: Sign bit 1, exponent field of all 1s, a fractional field of all 0s.
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 actual bit encoding of floating-point number NaN?
Back: An exponent field of all 1s and a nonzero fractional field.
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 value is encoded in the following image?
!
Back: Infinity.
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 value is encoded in the following image?
!
Back: Not-a-number.
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:e - Bias} is to {2:normalized} form whereas {2:1 - Bias} is to {1:denormalized} form.
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
Which form corresponds to exponent value e - Bias, where e is the unsigned interpretation of the exponent field?
Back: Normalized form.
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
In normalized form's exponent value e - Bias, what does e refer to?
Back: The unsigned interpretation of the exponent field.
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
Which form corresponds to exponent value 1 - Bias?
Back: Denormalized form.
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 denormalized form's exponent value defined as 1 - Bias?
Back: It provides a smooth transition between values in normalized and denormalized form.
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 first integer value not exactly representable by a float?
Back: 2^{24} + 1
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the first integer value not exactly representable by a double?
Back: 2^{53} + 1
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the first integer value not exactly representable by an IEEE floating-point number?
Back: Given n > 0 fractional bits, 2^{n + 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
Given n > 0 fractional bits, why is 2^{n+1} + 1 the first integer value not exactly representable?
Back: There exists a maximum of n + 1 significant digits in the significand.
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 bit representation of the largest normalized positive float?
Back: Sign bit 0, exponent field 11 \cdots 10_2, fraction field all 1s.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the bit representation of the smallest positive float?
Back: Sign bit 0, exponent field 0s, fraction field 00 \cdots 01_2.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the bit representation of the smallest normalized positive float?
Back: Sign bit 0, exponent field 00 \cdots 01_2, fraction field all 0s.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
Let float x = 1.0. What is the bit representation of x's exponent field?
Back: 01111111
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
Let double x = 1.0. What is the bit representation of x's exponent field?
Back: 01111111111
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the bit representation of the largest normalized positive double?
Back: Sign bit 0, exponent field 11 \cdots 10_2, fraction field all 1s.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the bit representation of the smallest normalized positive double?
Back: Sign bit 0, exponent field 00 \cdots 01_2, fraction field all 0s.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the bit representation of the smallest positive double?
Back: Sign bit 0, exponent field all 0s, fraction field 00 \cdots 01_2.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the largest unsigned decimal value a normalized float's exponent field can be?
Back: 2^8 - 2
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the smallest positive float that can be exactly represented?
Back: 2^{-23}
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the largest unsigned decimal value a normalized double's exponent field can be?
Back: 2^{11} - 2
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the smallest positive double that can be exactly represented?
Back: 2^{-52}
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
What is the smallest positive IEEE floating-point number that can be exactly represented?
Back: Given n fractional bits, 2^{-n}.
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 range does the exponent value take on in normalized form?
Back: Integer values in closed interval [1 - Bias, Bias].
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 range does the exponent value take on in denormalized form?
Back: The exponent always evaluates to 1 - Bias.
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 signficance of term 1 in "the smallest normalized exponent value is 1 - Bias"?
Back: The smallest unsigned interpretation of a normalized exponent field is 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 does the unsigned interpretation of the largest normalized exponent field relate to the Bias?
Back: The largest unsigned interpretation is 2 \cdot Bias.
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 the largest normalized exponent value relate to the Bias?
Back: It equals Bias.
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 the smallest normalized exponent value relate to the Bias?
Back: It equals 1 - Bias.
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 three forms can an IEEE floating-point number take on? Back: Normalized, denormalized, and special value. 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 is a floating-point number considered a special value?
Back: When the exponent field is all 1s.
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 special values can a floating-point number take on?
Back: \infty and NaN
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
Representable floating-point numbers are denser around what?
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 IEEE floating-point was designed to allow efficiently sorting using what? Back: An integer sorting routine. 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 can IEEE floating-point values be sorted using an integer sorting routine? Back: The unsigned interpretation of ascending floating-point numbers is also ascending. 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 complication exists in integer sorting routines applied to IEEE floating-point values? Back: The unsigned interpretation of negative floating-point numbers is in descending order. 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 precision of a floating-point number refer to? Back: The number of bits found in its fractional field. Reference: Jens Gustedt, Modern C (Shelter Island, NY: Manning Publications Co, 2020).
END%%
Rounding
Because floating-point arithmetic can't represent every real number, it must round results to the "nearest" representable number, however "nearest" is defined. The IEEE floating-point standard defines four rounding modes to influence this behavior:
- Round-to-even rounds numbers to the closest representable value. In the case of values equally between two representations, it rounds to the number with an even least significant digit.
- Round-toward-zero rounds downward for positive values and upward for negative values.
- Round-down always rounds downward.
- Round-up always rounds upward.
%%ANKI Basic What are the four rounding modes supported in the IEEE floating-point standard? Back: Round-to-even, round-toward-zero, round-down, and round-up. 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:Round-toward-zero} is to {2:integer} division whereas {2:round-down} is to {1:floor} division. 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:Round-up} is to {2:ceiling} division whereas {2:round-toward-zero} is to {1:integer} division. 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 default IEEE floating-point standard rounding mode? Back: Round-to-even. 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 alternative name does round-to-even go by? Back: Round-to-nearest. 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 floating-point 1.40 rounded to an integer in round-to-even mode?
Back: 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 floating-point 1.50 rounded to an integer in round-to-even mode?
Back: 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 floating-point 1.60 rounded to an integer in round-to-even mode?
Back: 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 floating-point -1.50 rounded to an integer in round-to-even mode?
Back: -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 floating-point 1.40 rounded to an integer in round-to-zero mode?
Back: 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 floating-point 1.50 rounded to an integer in round-to-zero mode?
Back: 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 floating-point -1.50 rounded to an integer in round-to-zero mode?
Back: -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 floating-point 1.40 rounded to an integer in round-down mode?
Back: 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 floating-point 1.50 rounded to an integer in round-down mode?
Back: 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 floating-point -1.50 rounded to an integer in round-down mode?
Back: -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 floating-point 1.40 rounded to an integer in round-up mode?
Back: 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 floating-point 1.50 rounded to an integer in round-up mode?
Back: 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 floating-point -1.50 rounded to an integer in round-up mode?
Back: -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 does round-to-even prefer even over odd numbers? Back: This is an arbitrary choice. 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 does round-to-even prefer even over always rounding down? Back: The former more reliably avoids potential statistical biases. 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
In round-to-even rounding, what bit is considered even?
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
In round-to-even rounding, what bit is considered odd?
Back: 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 does the IEEE floating-point standard define 1/-0?
Back: -\infty
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 the IEEE floating-point standard define 1/+0?
Back: +\infty
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 value(s) do IEEE floating-point numbers take on in the case of overflow?
Back: \pm\infty
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 value(s) do IEEE floating-point numbers take on in the case of underflow?
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%%
Arithmetic
%%ANKI
Basic
What does +^f denote?
Back: Floating-point addition.
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 result of x +^f y?
Back: Round(x + y) where Round refers to the current rounding-mode.
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
Is +^f commutative?
Back: No.
Reference: Jens Gustedt, Modern C (Shelter Island, NY: Manning Publications Co, 2020).
END%%
%%ANKI
Basic
Is +^f associative?
Back: No.
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
Which IEEE floating-point values do not have an additive inverse?
Back: \pm\infty and NaN
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
Let f be a normalized floating-point value. What is its additive inverse?
Back: -f
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
Let f be a denormalized floating-point value. What is its additive inverse?
Back: -f
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
Let f be a special floating-point value. What is its additive inverse?
Back: N/A.
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 most important group quality +^f is lacking?
Back: Associativity.
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 *^f denote?
Back: Floating-point multiplication.
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 result of x *^f y?
Back: Round(x * y) where Round refers to the current rounding-mode.
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
Is *^f commutative?
Back: Yes.
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
Is *^f associative?
Back: No.
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 multiplicative identity of *^f?
Back: 1.0
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
Does *^f distribute over +^f?
Back: No.
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 property of floating-point values prevents it behaving like "real math"? Back: It represents a finite number of values and rounds results if need be. 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 precision affected when casting from float to double?
Back: It isn't.
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 precision affected when casting from double to float?
Back: Rounding may occur.
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 might rounding occur when casting from double to float?
Back: floats have less precision.
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 overflow values might result when casting from float to double?
Back: N/A
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 overflow values might result when casting from double to float?
Back: \pm\infty
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 might overflow occur when casting from double to float?
Back: floats have smaller range.
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
Assuming no overflow, what is the result of casting a double to an int?
Back: The double's value rounded toward 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
Assuming overflow, what is the result of casting a double to an int?
Back: The result is implementation-specific.
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
Assuming no overflow, what is the result of casting a float to an int?
Back: The float's value rounded toward 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 is the result of (int) (double) 1.5?
Back: 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 result of (int) (double) -1.5?
Back: -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
Assuming overflow, what is the result of casting a float to an int?
Back: The result is implementation-specific.
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
Bibliography
- Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
- “Scientific Notation.” In Wikipedia, March 6, 2024. https://en.wikipedia.org/w/index.php?title=Scientific_notation&oldid=1212169750.