Almost OT: Pushbutton switch latching

This should be a much simpler problem than I'm making it, but at the moment my brain doesn't want to come up with a solution. Picture this - a number of switches, say, eight. Momentary contact, normally open switches. And then eight outputs, one for each switch, TTL level. I want to be able to push one switch and bring it's corresponding output high, and have it stay high even when the switch is released. But, making this more complicated, I only want to be able to allow one switch to be active at a time. So, say switch four is pressed, output four is high. Then, switch one is pressed, and output four goes low, and output 1 goes high. Timing is not critical. I know this should be a simple array of flip flops, in some fashion, but at the moment, the solution eludes me. I feel like there is probably even a single/two chip solution to this. Now, I know that this is probably off-topic, but I'd be using this in on-topic hardware... -Ian