Arithmetic Binary Shifts

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Courses GCSE Computer Science Data Representation Arithmetic Binary Shifts

Arithmetic Right Shift

In an arithmetic right shift, each bit in a binary number is shifted to the right by a specified number of positions.

The leftmost bit (the sign bit) is replicated to fill the vacated positions.
If the number is positive, zeros are shifted in from the left.
If the number is negative, ones are shifted in from the left.

Arithmetic right shifts are commonly used for division by powers of two in signed integer arithmetic.

Arithmetic Right Shift - Example

Original number: 1101 (decimal -3)

After arithmetic right shift by 1: 1110 (decimal -2)

Arithmetic right shift is a division operation that effectively divides the number by [[2]] for each shift.

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Arithmetic Left Shift

In an arithmetic left shift, each bit in a binary number is shifted to the left by a specified number of positions.

The leftmost bit is lost (shifted out)
zeros are shifted in from the right.

Arithmetic left shifts are commonly used for multiplication by powers of two in signed integer arithmetic.

Arithmetic Left Shift - Example

Original number: 1101 (decimal -3)

After arithmetic left shift by 1: 1010 (decimal -6)

Interactive Demonstration

Arithmetic shifts are commonly used in programming languages to perform multiplication and division by powers of [[2]].

{"cloze_text": "Arithmetic shifts are commonly used in programming languages to perform multiplication and division by powers of [[2]]."}

Summary Example - 10001010 (Shift 1)

Left Shift

Right Shift

Logical

zeros are filled in the vacated positions on the right.
The sign bit is treated as just another bit.

00010100

Zeros are filled in the vacated positions on the left.
The sign bit is treated as just another bit.

01000101

Arithmetic

The sign bit is replicated to fill the vacated positions on the left.
The sign bit preserved

11000101

Review: Fill in the Blanks

In an arithmetic right shift, each bit in a binary number is shifted to the right by a specified number of positions. The leftmost bit (the ) is replicated to fill the vacated positions. If the number is , zeros are shifted in from the left. Conversely, if the number is negative, ones are shifted in from the left. Arithmetic right shifts are commonly used for division by powers of two in signed integer .

In an arithmetic left shift, each bit in a binary number is shifted to the left by a specified number of positions. The leftmost bit is lost (shifted out), and zeros are shifted in from the . Arithmetic left shifts are commonly used for multiplication by powers of two in signed integer .

For example, consider the original number 1101 (decimal -3). After performing an arithmetic right shift by 1, the result is 1110 (decimal -2). In contrast, if we perform an arithmetic left shift by 1 on the same original number, the result changes to 1010 (decimal -6). It is important to understand how the sign bit is treated during these and its effect on the final values.

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Positive Sign Bit Right Arithmetic Arithmetic Shifts

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