TeXipedia

Lsh

Represents a leftward shift operation commonly used in mathematical logic, computing contexts, and formal specifications.

Overview

Serves as a specialized operator in formal mathematics and computer science, particularly valuable for expressing transformations and operations that move or modify elements toward the left.

  • Essential in bitwise operations and digital logic specifications
  • Used in formal proofs and mathematical reasoning to denote leftward transformations
  • Appears in algorithmic notation and program semantics
  • Helpful in expressing state transitions and rotational operations in discrete mathematics

Examples

Bitwise left shift operation in computational notation

xk shifts bits of x left by k positionsx \Lsh k \text{ shifts bits of } x \text{ left by } k \text{ positions}
x \Lsh k \text{ shifts bits of } x \text{ left by } k \text{ positions}

Formal specification of a state transition system

S1S2    P(S2)S_1 \Lsh S_2 \implies P(S_2)
S_1 \Lsh S_2 \implies P(S_2)

Binary operation showing multiple left shifts

101022=10100021010_2 \Lsh 2 = 101000_2
1010_2 \Lsh 2 = 101000_2