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computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
, a logical shift is a
bitwise operation In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operatio ...
that shifts all the bits of its operand. The two base variants are the logical left shift and the logical right shift. This is further modulated by the number of bit positions a given value shall be shifted, such as ''shift left by 1'' or ''shift right by n''. Unlike an arithmetic shift, a logical shift does not preserve a number's sign bit or distinguish a number's exponent from its significand (mantissa); every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled, usually with zeros, and possibly ones (contrast with a circular shift). A logical shift is often used when its operand is being treated as a
sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is cal ...
of bits instead of as a number. Logical shifts can be useful as efficient ways to perform multiplication or division of unsigned
integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
s by powers of two. Shifting left by ''n'' bits on a signed or unsigned binary number has the effect of multiplying it by 2''n''. Shifting right by ''n'' bits on an ''unsigned'' binary number has the effect of dividing it by 2''n'' (rounding towards 0). Logical right shift differs from arithmetic right shift. Thus, many languages have different operators for them. For example, in
Java Java is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea (a part of Pacific Ocean) to the north. With a population of 156.9 million people (including Madura) in mid 2024, proje ...
and
JavaScript JavaScript (), often abbreviated as JS, is a programming language and core technology of the World Wide Web, alongside HTML and CSS. Ninety-nine percent of websites use JavaScript on the client side for webpage behavior. Web browsers have ...
, the logical right shift operator is , but the arithmetic right shift operator is . (Java has only one left shift operator (), because left shift via logic and arithmetic have the same effect.) The
programming language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...
s C, C++, and Go, however, have only one right shift operator, . Most C and C++ implementations, and Go, choose which right shift to perform depending on the type of integer being shifted: signed integers are shifted using the arithmetic shift, and unsigned integers are shifted using the logical shift. In particular, C++ uses its logical shift operators as part of the syntax of its input and output functions, called "cin" and "cout" respectively. All currently relevant C standards (ISO/IEC 9899:1999 to 2011) leave a definition gap for cases where the number of shifts is equal to or bigger than the number of bits in the operands in a way that the result is undefined. This helps allow C compilers to emit efficient code for various platforms by allowing direct use of the native shift instructions which have differing behavior. For example, shift-left-word in
PowerPC PowerPC (with the backronym Performance Optimization With Enhanced RISC – Performance Computing, sometimes abbreviated as PPC) is a reduced instruction set computer (RISC) instruction set architecture (ISA) created by the 1991 Apple Inc., App ...
chooses the more-intuitive behavior where shifting by the bit width or above gives zero, whereas SHL in
x86 x86 (also known as 80x86 or the 8086 family) is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel, based on the 8086 microprocessor and its 8-bit-external-bus variant, the 8088. Th ...
chooses to mask the shift amount to the lower bits ''to reduce the maximum execution time of the instructions'', and as such a shift by the bit width doesn't change the value. Some languages, such as the .NET Framework and
LLVM LLVM, also called LLVM Core, is a target-independent optimizer and code generator. It can be used to develop a Compiler#Front end, frontend for any programming language and a Compiler#Back end, backend for any instruction set architecture. LLVM i ...
, also leave shifting by the bit width and above ''unspecified'' (.NET) or ''undefined'' (LLVM). Others choose to specify the behavior of their most common target platforms, such as C# which specifies the x86 behavior.


Example

If the bit sequence 0001 0111 (decimal 23) is logically shifted by one bit position, then: Note: MSB = Most Significant Bit, LSB = Least Significant Bit


References

{{DEFAULTSORT:Logical shift Binary arithmetic Operators (programming) zh:位操作#逻辑移位