Logical Shifts
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
What is a mask?
- A mask is a binary number used in bitwise operations to isolate, modify, or test specific bits in another binary value
- Think of a mask as a filter: it lets certain bits through and blocks others, depending on the bitwise operation being used
Why use a mask?
- To extract certain bits from a binary number (e.g. the lower 4 bits)
- To set specific bits to 1
- To clear specific bits (set them to 0)
- To toggle (flip) specific bits
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 |