Final answer:
Calculating the power of a number using bitwise operators involves using exponentiation by squaring and simulating multiplication with repeated addition or bitwise shifts. It doesn't directly apply to non-integer exponents as these operations are typically not suitable for such calculations.
Step-by-step explanation:
Calculating the power of a number using bitwise operators is a common operation in computers and technology. To calculate a power, say a to the power of n (an), where n is an integer, you essentially multiply a by itself n times. However, since you're not allowed to use multiplication or division operators, you'd have to approach it differently.
One method is to employ the concept of exponentiation by squaring, which can utilize bitwise operations. The idea is to decompose the exponent into a sum of powers of 2 (which you can do by examining the bits of the exponent), then compute the powers by successive squaring, and finally multiply the required terms. As an example:
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- Find the binary representation of the exponent n.
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- For each bit set in the binary representation, square the base a that many times, using bit shifting for squaring.
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- Combine results by simulating multiplication with bitwise operations or repeated addition.
To handle decimal exponents like 31.7, bitwise operations are not typically used. Instead, the calculation is often performed by functions like pow in programming or by calculators that implement floating-point arithmetic. If you're limited to integer exponents and cannot use multiplication or division, bitwise operator techniques apply primarily to those scenarios.