Bitwise Manipulation & Masks (OCR A Level Computer Science): Revision Note
What are Logical Shifts?
Logical shifts are the process of moving the bits in a binary number to the left or right by a specified number of places
Bitwise manipulation uses logical operators like AND, OR, XOR, and NOT to manipulate binary numbers
Logical Shifts
Logical binary shifts are operations performed on binary numbers where all the bits in the number are moved left or right by a specified number of positions
These shifts are commonly used in computer programming and digital systems
There are two types of logical binary shifts: Left and Right
Example left shift
The following number is shifted by two places to the left.

Original number: 00001110 = 14
Left shift (2) result: 00111000 = 56
Each left shift has doubled the number:
Original value = 14
Left shift 1 - Doubled the number to 28
Left shift 2 - Doubled the number to 56
Example right shift
The following number is shifted by three places to the right.

Original number: 11001000 = 200
Right shift (3) result: 00011001 = 25
Each right shift has halved the number:
Original value = 200
Right shift 1 - Halved the number to 100
Right shift 2 - Halved the number to 50
Right shift 3 - Halved the number to 25
Bitwise Manipulation
Bitwise AND operation
If both bits are 1 in the binary number and the mask, the result will be 1. Otherwise, the result will be 0.
Description | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
---|---|---|---|---|---|---|---|---|
Binary | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
Mask | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
Result | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
Bitwise OR operation
If either bit is 1 in the binary number or the mask, the result will be 1. Otherwise, the result will be 0.
Description | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
---|---|---|---|---|---|---|---|---|
Binary | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
Mask | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
Result | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 |
Bitwise XOR operation
If only 1 of the bits is 1 in the binary number or the mask, the result will be 1. Otherwise, the result will be 0.
Description | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
---|---|---|---|---|---|---|---|---|
Binary | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
Mask | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
Result | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
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