## What is arithmetic shift?

Arithmetic shift is used to multiply and divide binary numbers.

The effect of shifting left is to multiply a binary number.

The effect is doubled by each place that is shifted.

x

The effect of shifting right is to divide a binary number.

÷

Shifting by 1 has an effect of 2.

Shifting by 2 has an effect of 4.

Shifting by 3 has an effect of 8.

For example, shifting left by 2 places has an effect of multiplying by 4.

Another example: Shifting right by 3 places has an effect of diving by 8.

## How to shift a binary number:

An exam question may ask you to arithmetically shift a binary number of up to 16 digits.

## Questo's Questions

4.4 - Arithmetic Shift:

1a. Draw a diagram to show the effect of multiplying and dividing a binary number. 

1b. Draw a diagram or table to show the effect a shift has for each place from 1 to 4. For example, a shift of 1 place has an effect of 2. 

2. State the effect of the following shifts:

• a. Shift right by 2 places.

• b. Shift left by 1 place.

• c. Shift left 3 places.

• d. Shift right by 4 places.        [1 each]

3. Shift the following binary numbers and state the effect of the shift:

• a. 10101011 : Shift left by 2 places.

• b. 11101100 : Shift right by 3 place.

• c. 00001011 : Shift right by 2 places.

• d. 01101110 : Shift left by 1 place.        [2 each]