notebook/notes/encoding/floating-point.md

title	TARGET DECK	FILE TAGS	tags
Floating Point	Obsidian::STEM	binary::float ieee	binary ieee float

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 all 1s.
  • The significand is 1 + f, where f denotes the fractional part.
  • E = e - Bias where e is the unsigned interpretation of the exponent field.
• Denormalized Form
  • Here the exponent field is all 0s.
  • The significand is f, where f denotes the fractional part.
  • E = 1 - Bias, defined for smooth transition between normalized and denormalized values.
• Special Values
  • Here the exponent field is all 1s.
  • If the fraction field is all 0s, we have an \infty value.
  • If the fraction field is not all 0s, we have NaN.

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

%%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.

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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: 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 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.