The Arithmetic Right Shift Calculator is a specialized tool that shifts the bits of a binary number to the right while preserving the sign of the number. Unlike a logical right shift, which fills the leftmost bits with zeros, an arithmetic right shift retains the sign bit (most significant bit) to ensure the number’s sign remains unchanged. This feature is particularly important when dealing with signed binary numbers, as it prevents incorrect results in arithmetic operations.
Formula of Arithmetic Right Shift Calculator
An arithmetic right shift is a bitwise operation that shifts the bits of a binary number to the right. It differs from a logical right shift because it maintains the sign of the number by copying the sign bit (most significant bit) into the new positions.
Formula for Arithmetic Right Shift
The formula to calculate the arithmetic right shift of a number NNN by kkk positions is as follows:
- Convert the number NNN to its binary representation.
- Perform the right shift operation:
- Shift all bits of NNN to the right by kkk positions.
- Fill the leftmost kkk bits with the original sign bit (most significant bit).
- Convert the resulting binary number back to its decimal form.
This process ensures that the sign of the number is preserved during the shift operation, which is crucial for accurate arithmetic computations.
General Terms and Conversion Table
Common Terms
- Bitwise Operation: An operation that acts on individual bits of a binary number.
- Binary Number: A number expressed in the base-2 numeral system, using only 0 and 1.
- Sign Bit: The most significant bit in a binary number, indicating its sign (0 for positive, 1 for negative).
Conversion Table
This table provides a quick reference for common arithmetic right shifts without the need for manual calculation.
| Decimal Number | Binary Representation | Right Shift by 1 | Right Shift by 2 | Right Shift by 3 |
|---|---|---|---|---|
| 4 | 0100 | 0010 | 0001 | 0000 |
| -4 | 1100 | 1110 | 1111 | 1111 |
| 8 | 1000 | 0100 | 0010 | 0001 |
| -8 | 1000 | 1100 | 1110 | 1111 |
Example of Arithmetic Right Shift Calculator
Let’s walk through an example of an arithmetic right shift.
Example Calculation
Suppose we have the number -6 and we want to perform an arithmetic right shift by 2 positions.
- Convert to Binary: -6 in binary (8-bit representation) is
11111010. - Right Shift by 2: Shifting the bits to the right by 2 positions:
- Original:
11111010 - Shifted:
11111110(the two leftmost bits are filled with the sign bit)
- Original:
- Convert Back to Decimal: The resulting binary number
11111110is -2 in decimal.
Therefore, the arithmetic right shift of -6 by 2 positions is -2.
Most Common FAQs
An arithmetic right shift preserves the sign of the number by filling the leftmost bits with the sign bit, while a logical right shift fills the leftmost bits with zeros.
Use an arithmetic right shift when working with signed binary numbers to ensure that the sign of the number is maintained during the shift operation.
To convert a negative decimal number to binary, use its two’s complement representation, which involves inverting the bits of the positive counterpart and adding one to the least significant bit.