<P> In multiple - precision shift operations, the order of operand fragment processing depends on the shift direction . In left - shift operations, fragments are processed LS first because the LS bit of each partial--which is conveyed via the stored carry bit--must be obtained from the MS bit of the previously left - shifted, less - significant operand . Conversely, operands are processed MS first in right - shift operations because the MS bit of each partial must be obtained from the LS bit of the previously right - shifted, more - significant operand . </P> <P> In bitwise logical operations (e.g., logical AND, logical OR), the operand fragments may be processed in any arbitrary order because each partial depends only on the corresponding operand fragments (the stored carry bit from the previous ALU operation is ignored). </P> <P> Although an ALU can be designed to perform complex functions, the resulting higher circuit complexity, cost, power consumption and larger size makes this impractical in many cases . Consequently, ALUs are often limited to simple functions that can be executed at very high speeds (i.e., very short propagation delays), and the external processor circuitry is responsible for performing complex functions by orchestrating a sequence of simpler ALU operations . </P> <P> For example, computing the square root of a number might be implemented in various ways, depending on ALU complexity: </P>

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