1. What is Binary Left Shift?

The binary left shift operation moves all bits in a binary number to the left by a specified number of positions, filling the new rightmost bits with zeros. This operation is equivalent to multiplying the number by 2ⁿ where n is the number of shift positions.

2. How Left Shift Works

The left shift operation follows these rules:

Example: 1011 (11 in decimal) shifted left by 2 positions:

• Original: 1011
• Shifted: 101100 (44 in decimal)
• Calculation: 11 × 2² = 11 × 4 = 44

3. Mathematical Explanation

Details: Each left shift position multiplies the number by 2. This works because in binary, each position represents a higher power of 2.

4. Using the Calculator

Tips: Enter a valid binary string (only 0s and 1s) and the number of positions to shift. The calculator will show the result and the step-by-step solution.

5. Frequently Asked Questions (FAQ)

Q1: What happens if I shift more bits than the binary length?
A: The operation still works - it just adds more zeros to the right. For example, 1 shifted left by 5 becomes 100000.

Q2: Is left shift the same as multiplication?
A: For unsigned integers, yes. Left shift by n positions is equivalent to multiplying by 2ⁿ.

Q3: What about negative numbers?
A: This calculator works with binary strings. For signed numbers, the behavior depends on the representation (two's complement, etc.).

Q4: What's the maximum number of shifts I can do?
A: Technically unlimited, but practical limits depend on your system and the length of the binary string.

Q5: Can I shift fractional numbers?
A: This calculator works with integer binary numbers. Floating-point representation would require different handling.