Bitwise Calculator

About Bitwise Calculator

Welcome to the Bit Shift Calculator, a specialized tool for performing left shift, right shift, and bitwise NOT operations with visual bit diagrams. This calculator helps programmers, students, and engineers understand how bits move during shift operations and how the NOT operation inverts all bits.

Bit Shift Operations

Left Shift (<<)

The left shift operation moves all bits to the left by a specified number of positions. New bits filled in on the right are always zeros. Each left shift by 1 position is equivalent to multiplying the number by 2.

Example: 5 << 2

• 5 in binary: 0101
• Shift left by 2: 010100
• Result: 20 (which is 5 multiplied by 4)

Formula: n << k = n multiplied by 2 to the power of k

Right Shift (>>)

The right shift operation moves all bits to the right by a specified number of positions. Bits that shift off the right end are discarded. Each right shift by 1 position is equivalent to integer division by 2.

Example: 20 >> 2

• 20 in binary: 10100
• Shift right by 2: 00101
• Result: 5 (which is 20 divided by 4)

Formula: n >> k = n divided by 2 to the power of k (integer division)

Bitwise NOT (~)

The NOT operation inverts every bit: 0 becomes 1 and 1 becomes 0. The result depends on the bit width being used.

Example: NOT 5 (8-bit)

• 5 in binary (8-bit): 00000101
• NOT operation: 11111010
• Result: 250

Common Use Cases

Fast Multiplication and Division

• Multiply by 2: n << 1
• Multiply by 4: n << 2
• Multiply by 8: n << 3
• Divide by 2: n >> 1
• Divide by 4: n >> 2

Creating Bit Masks

• Mask for bit k: 1 << k
• Mask for lower n bits: (1 << n) - 1

Setting and Clearing Bits

• Set bit k: n | (1 << k)
• Clear bit k: n & ~(1 << k)
• Toggle bit k: n ^ (1 << k)

How to Use This Calculator

1. Select input format: Choose Binary, Decimal, or Hexadecimal.
2. Enter your number: Type the number you want to shift.
3. Enter shift amount: Specify how many positions to shift (1-64).
4. Choose bit width: Select a specific width or leave on Auto.
5. Select operation: Click Shift Left, Shift Right, or Calculate All.
6. Analyze results: View the visual bit diagram showing how bits moved.

Frequently Asked Questions

What is a left bit shift operation?

Left shift (<<) moves all bits to the left by a specified number of positions, filling the right side with zeros. Each left shift by 1 effectively multiplies the number by 2. For example, 5 << 2 shifts 0101 to 10100, which equals 20 (5 multiplied by 4).

What is a right bit shift operation?

Right shift (>>) moves all bits to the right by a specified number of positions, discarding bits that shift off the right end. Each right shift by 1 effectively divides the number by 2 (integer division). For example, 20 >> 2 shifts 10100 to 00101, which equals 5.

What is the bitwise NOT operation?

Bitwise NOT (~) inverts every bit: 0 becomes 1 and 1 becomes 0. The result depends on the bit width used. For an 8-bit number, NOT 5 (00000101) equals 250 (11111010). This operation is also known as ones complement.

Why use bit shifting instead of multiplication?

Bit shifting is often faster than multiplication because it is a simpler CPU operation. Left shift by n is equivalent to multiplying by 2^n, and right shift by n is equivalent to dividing by 2^n. This technique is commonly used in performance-critical code.

Related Operations

For bitwise AND, OR, and XOR operations, visit our Bitwise Calculator.