Almost OT: Pushbutton switch latching

[Mr Ian Primus]

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