bitwise-manipulation-and-masks

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.

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.

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.