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The Level Shifting Shield allows you to use older Arduino shields that are not 3.3V compatible - also know as 1.0 pinout or R3 compatible shields. It provides level shifting on all standard Arduino pins, allows you to reroute the SPI and I2C pins, and properly level shifts for those protocols as well. The DigiX Level Shifting Shield can also be used with the Arduino Due, UDOO, Spark Core, Maple, etc to allow them to use legacy Arduino shields.
Boards such as the DigiX and Arduino Due are still relatively new, and there are few shields that are compatible. The microcontrollers on the older Arduino and Arduino compatible boards work at 5V, whereas the microcontrollers on the new boards operate at 3V. If you try to use a shield designed for one of these older 5V logic boards (and it is not designed for 5V AND 3V usage), it most likely won't work with (and will most likely destroy!!) these newer and lower-powered boards.
The DigiX Level Shifter Shield, which converts the 5V signals of the shield into the 3V signals that the DigiX and Arduino Due require (and also converts their 3V signals into the 5V signals the shields require). However, if the shield has an IOREF pin, and has been properly designed, then the DigiX Level Shifter Shield is not required.