37 KiB
| title | TARGET DECK | FILE TAGS | tags | |||
|---|---|---|---|---|---|---|
| Float Encoding | 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 two forms 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 either all
0s or all1s. - 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 either all
The Bias in both 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 |
%%ANKI
Basic
In base-10 scientific notation, what form do non-zero 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 non-zero 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 non-zero 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 non-zero 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 m has value 1.
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 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 halves the remaining interval.
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 1 and 2 - \epsilon or between 0 and 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 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
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 either all 0s or 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
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 non-zero 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
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%%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
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%%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 interpretation of a float's exponent field?
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 interpretation of a double's exponent field?
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 largest unsigned interpretation of the exponent field relate to the Bias?
Back: The largest unsigned interpretation is 2 \times 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 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 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%%
References
- 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.