Left Shift Right Shift Calculator

Bit Shift Formulas:

\[ \text{Left Shift} = x \ll n = x \times 2^n \] \[ \text{Right Shift} = x \gg n = \left\lfloor\frac{x}{2^n}\right\rfloor \]

Result:

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1. What Are Bit Shifts?

Bit shifting is a fundamental operation in computer programming that moves the bits of a binary number left or right. Left shifts multiply a number by powers of two, while right shifts divide by powers of two (with truncation).

2. How Bit Shifting Works

The calculator uses these formulas:

\[ \text{Left Shift} = x \ll n = x \times 2^n \] \[ \text{Right Shift} = x \gg n = \left\lfloor\frac{x}{2^n}\right\rfloor \]

Where:

\( x \) — Integer value to be shifted
\( n \) — Number of bits to shift (0 to 64)
\( \ll \) — Left shift operator
\( \gg \) — Right shift operator

Explanation: Each left shift doubles the value (equivalent to multiplying by 2), while each right shift halves the value (equivalent to integer division by 2).

3. Practical Applications

Details: Bit shifting is used in low-level programming for efficient multiplication/division, packing data, cryptography, and graphics programming. It's much faster than regular arithmetic operations at the hardware level.

4. Using the Calculator

Tips: Enter any integer value and the number of bits to shift (0-64). Select left shift (multiplication) or right shift (division). Negative numbers are handled using two's complement representation.

5. Frequently Asked Questions (FAQ)

Q1: What happens when bits are shifted out?
A: In left shift, bits that overflow are discarded. In right shift, bits shifted out are lost (truncated division).

Q2: How does shifting negative numbers work?
A: Negative numbers use two's complement representation. Right shift preserves the sign (arithmetic shift), while left shift may change the sign.

Q3: What's the difference between logical and arithmetic right shift?
A: Arithmetic shift (>>) preserves the sign bit, while logical shift (>>> in some languages) fills with zeros. This calculator uses arithmetic shift.

Q4: Are there limits to how many bits I can shift?
A: This calculator limits shifts to 64 bits (size of a 64-bit integer). Shifting beyond the bit width of a number is undefined behavior in many languages.

Q5: Why use bit shifts instead of regular arithmetic?
A: Bit shifts are extremely fast operations at the processor level and are often used in performance-critical code or low-level programming.