1. GCSE COMPUTER SCIENCE
Topic 3 - Data
3.3 Logical and Arithmetic Shifts

2. Performed on unsigned integers (normal binary numbers)
Binary Shifts
A binary shift is an operation done to all bits of a binary number in which they are moved a set number of places either left or right
Logical Shift
Performed on unsigned integers (normal binary numbers)
Arithmetic Shift
Performed on signed integers (negative binary numbers using two’s complement)

3. Binary Shifts
In denary (decimal) when we want to multiply a number by 10 we move each number one place to the left and add a 0 to the end (and vice versa for division)
To multiply by 10 we move
digits to the left and add a 0
To divide by 10 we move
digits to the right and remove a 0 3 1 2 8
A left shift of 1 is used for multiplying by 10
A right shift of 1 is used for dividing by 10

4. Logical shifts allow you to multiply and divide binary numbers
Binary Shifts: Logical
Logical shifts allow you to multiply and divide binary numbers
Because binary is a base-2 number system, left and right shifts can be used for multiplying and dividing by powers of 2

5. Binary Shifts: Logical
Direction
Purpose
Example 1
Left
Multiply by 2
1010 (10)
10100 (20) = 2
Left
Multiply by 4
1010 (10)
(40) = 3
Left
Multiply by 8
1010 (10)
(80) =

6. Binary Shifts: Logical
Direction
Purpose
Example 1
Right
Divide by 2
(40)
(20) = 2
Right
Divide by 4
(40)
(10) = 3
Right
Divide by 8
(40)
(5) =

7. Copy these examples into your workbook
Binary Shifts: Logical
Shift
Direction
Purpose
Example 1
Left
Multiply by 2
1010 (10)
10100 (20) = 2
Left
Multiply by 4
1010 (10)
(40) = 1
Right
Divide by 2
(40)
(20) = 2
Right
Divide by 4
(40)
(10) =
Copy these examples into your workbook

8. Activity Shift Direction Purpose Example Result 1 Left Multiply by 2
0101 (5)
01010 (10) = 2
Left
Multiply by 4
1111 (15)
(60) = 1
Right
Divide by 2
(50)
(25) = 2
Right
Divide by 4
(80)
(20) =