Placing GND on AN1 and AN2 turns the respective input on. Using what are referred to as pull up resisters between AN1 and AN2 and 5V will turn the respective input off.
In digital mode you connect AN1 and AN2 through pull up resisters to 5V to turn each input OFF. To turn either AN1 or AN2 on, connect the respective input to GND through some type switch, leaving the 10K resisters connected to 5V.
When the ANx input is connected to GND, the input will turn on. When the GND is removed, the pull up resisters will turn the input off. The EZIOxx cannot come with these pull up resisters installed as that would prevent AN1 and AN2 from operating in analog mode.
Either 1/4 watt or 1/2 watt 10K resisters are fine.