How to gently stop your young child interrupting your conversation

You're familiar with the scene, you're talking to your partner or a friend and out of nowhere your child interrupts.  Multiple times.  You try explaining that it's rude or that they need to wait until you've finished talking yet it keeps happening.

The thing is, they're not being rude.  Often they haven't even fully grasped the concept of what rude is in a social setting (other than bad words).  They're not thinking about interrupting you, it's not a premeditated action.  They'll get an idea or thought in their head and they just need to share it, instantly.  They have no idea how long you'll be talking for, when you'll stop or even if you'll stop.  Often they'll mistake a pause for an end and interject.