4.4: Arithmetic Shift

Exam Board:

Eduqas / WJEC

Specification:

2020 + 

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. [2]

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. [4]

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]

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