Fixed-Point Blockset

Shifts

Nearly all microprocessors and digital signal processors support well-defined bit-shift (or simply shift) operations for integers. For example, consider the 8-bit unsigned integer 00110101. The results of a 2-bit shift to the left and a 2-bit shift to the right are shown below.

Shift Operation	Binary Value	Decimal Value
No shift (original number)	00110101	53
Shift left by 2 bits	11010100	212
Shift right by 2 bits	00001101	13

You can perform a shift with the Fixed-Point Blockset using the Shift Arithmetic block. Use this block to perform a bit shift, a radix point shift, or both. See Block Reference for more information on performing bit and radix point shifts using the Shift Arithmetic block.

Shifting Bits to the Right

The special case of shifting bits to the right requires consideration of the treatment of the left-most bit, which may contain sign information. A shift to the right can be classified either as a logical shift right or an arithmetic shift right. For a logical shift right, a 0 is incorporated into the most significant bit for each bit shift. For an arithmetic shift right, the most significant bit is recycled for each bit shift.

The Shift Arithmetic block performs an arithmetic shift right and, therefore, recycles the most significant bit for each bit shift right. For example, given the fixed-point number 11001.011 (-6.625), a bit shift two places to the right with the radix point unmoved yields the number 11110.010 (-1.75), as shown in the model below.

To perform a logical shift right on a signed number using the Shift Arithmetic block, use the Conversion block to cast the number as an unsigned number of equivalent length and scaling, as shown below. The model shows that the fixed-point signed number 11001.001 (-6.625) becomes 00110.010 (6.25).

Division

Example: Conversions and Arithmetic Operations