Understanding arithmetic shifts and bitwise operations

The process data from IO-Link sensors often has to be calculated and split up for further processing of the information (especially if the IO-Link master does not provide an IODD interpretation on board - e.g. when using the SIG350 via the REST API). To do this, it is necessary to know the most common operations.

Bitwise Left Shift (<<):
The bitwise left shift operator (<<) shifts the bits of a binary number to the left by a specified number of positions. The vacant positions on the right are filled with zeros. Each left shift effectively multiplies the number by 2, so each shift by n positions is equivalent to multiplication by 2^n.

Example:

Bitwise Right Shift (>>):
The bitwise right shift operator (>>) shifts the bits of a binary number to the right by a specified number of positions. The vacant positions on the left are filled based on the sign bit (0 for positive numbers, 1 for negative numbers in two's complement representation). Each right shift effectively divides the number by 2, so each shift by n positions is equivalent to division by 2^n.

Example:

Note: This is true for positive integers. When using bit shifts and multiplication for negative numbers or floating-point numbers, additional considerations may be necessary, especially due to rounding behavior and the representation of negative numbers in two's complement.

Bitmask and logical AND (&):
A bitmask is a sequence of bits that are used to perform bitwise operations. It is often used to extract, set or clear specific bits in a binary number.

Example - extract the last bit from the original 8-bit binary number:

Example with real data:
Please check and consider the correct bit/ byte order of your used sensor!

We receive 2 bytes of process data from the sensor. The first 14 bits correspond to a distance value and the last 2 bits to the switching outputs.

• Process Data: 2 Byte  = Distance (14 Bit) + Q1 + Q2
• byte [0] = 31
• byte [1] = 65

First we can extract the information from Q1 and Q2 (in the second byte) via a bitmask:

• Q1 = byte [1] & 00000010
  • Q1 = 0
• Q2 = byte [1] & 00000001
  • Q2 = 1

Then we can get the distance information through bit shifts:

• Distance = (byte [0] << 6) + (byte [1] >> 2)
  • Distance = 2000

Alternatively, first add the 2 bytes together to get the full 16 bit process data and then shift out the last two bits:

• Distance = ((byte [0] << 8) + byte [1]) >> 2

If 4 bytes have to be combined, they must be shifted further depending on the order e.g:

• pd = (byte [0] << 24) + (byte [1] << 16) + (byte [2] << 8) + byte [3]

Or with the multiplication 2^n (2^24 = 16.777.216; 2^16 = 65.536; 2^8 = 256):

• pd = (byte [0] * 16.777.216) + (byte [1] * 65.536) + (byte [2] * 256) + byte [3]

The operation may look slightly different depending on the programming language or application, but the principle remains the same. For example, in Excel, "=BITRSHIFT()" is used for a bitwise right shift (>>) and "=BITLSHIFT()" for a bitwise left shift (<<).

In summary

Bitwise left shift and right shift are operations that move the bits of a binary number to the left or right, respectively.
Bitmasks are used in conjunction with bitwise operations to manipulate or extract specific bits within a binary number.