notebook/notes/binary/shifts.md

title	TARGET DECK	FILE TAGS	tags
Shifts	Obsidian::STEM	binary	binary

Overview

Left shift operations (<<) drop the k most significant bits and fills the right end of the result with k zeros. Right shift operations (>>) are classified in two ways:

• Logical
  • Drops the k least significant bits and fills the left end of the result with k zeros.
  • This mode is always used when calling >> on unsigned data.
  • Sometimes denoted as >>> to disambiguate from arithmetic right shifts.
• Arithmetic
  • Drops the k least significant bits and fills the left end of the result with k copies of the most significant bit.
  • This mode is usually used when calling >> on signed data.

%%ANKI Basic How is decimal value 2^n written in binary? Back: As 1 followed by n zeros. 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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%%ANKI Basic What kinds of left shift operations are there? Back: Just logical. 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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%%ANKI Basic What kinds of right shift operations are there? Back: Logical and arithmetic 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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%%ANKI Basic What is a logical right shift operation? Back: One that fills the left end of the result with k zeros. 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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%%ANKI Basic What is an arithmetic right shift operation? Back: One that fills the left end of the result with k copies of the most significant bit. 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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%%ANKI Basic What kind of right shift operation is usually applied to signed numbers? Back: Arithmetic. 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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%%ANKI Basic What kind of right shift operation is applied to unsigned numbers? Back: Logical. 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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%%ANKI Basic What portability issue do shift operations introduce? Back: There is no standard on whether right shifts of signed numbers are logical or arithmetic. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: c

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%%ANKI Cloze {1:Arithmetic} right shifts are to {1:signed} numbers whereas {2:logical} right shifts are to {2:unsigned} numbers. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: c

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In C, it is undefined behavior to shift by more than the width w of an integral type. Typically though, only the last w bits are considered in the computation. For example, given int32_t x, (x << 32) = (x << 0).

%%ANKI Basic Ignoring UB, what typically happens when shifting an int32_t by k ≥ 32 bits? Back: The shift value is interpreted as k mod 32. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: c

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%%ANKI Basic How is x \bmod 2^k equivalently written as a bit mask? Back: x & (k - 1) Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016. Tags: c

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References

• Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
• Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, Concrete Mathematics: A Foundation for Computer Science, 2nd ed (Reading, Mass: Addison-Wesley, 1994).