Arithmetic Shift Functions

Arithmetic Shift Functions

Introduction to Shift Functions

• Shift functions are important mathematical operations in computer science.
• They function by shifting the bits of a binary number either to the left or to the right.
• This operation can have the effect of multiplying or dividing the value of the number, depending on the direction of the shift.

Logical and Arithmetic Shift

• There are two main types of shift functions: logical shift and arithmetic shift.
• Logical shift moves the bits left or right and fills the vacant spaces with zeros.
• Arithmetic shift, often used for signed numbers, keeps the sign bit (the most significant bit) intact. When shifting right, it fills the vacant spaces with the value of the sign bit to preserve the sign of the number.

Arithmetic Shift Right

• Arithmetic Shift Right (ASR) divides a signed binary number by 2, keeping the sign intact.
• The shifted bits fall off the end and are discarded.
• It fills the most left bit (the sign bit position) with duplicates of the original sign bit to retain the number’s sign.

Arithmetic Shift Left

• Arithmetic Shift Left (ASL) multiplies a signed binary number by 2.
• The shifted bits fall off on the left side and are lost, while on the right, a 0 is filled in.
• Keep in mind, if the sign bit changes during an ASL operation, it suggests an overflow error has occurred.

Importance of Arithmetic Shifts

• Arithmetic shifts are critical for performing quick multiplications or divisions of binary numbers in computer systems.
• They are a fundamental part of arithmetic operations in computing.