I couldn't find this in the DataSheet. But what happens when an Enable* is not connected to a logic 0 or 1? The DataSheets usually only state the circuit's behaviour when its set to voltage High or low, but what happens when its not connected at all?

I am working on a 74LS151 Multiplexer here, but I dun think the circuit matters in this questions, I just need a general answer. I know the main output will be logic 0. but I haven't tried and can't try at the moment the complement output's logic, but I suspect is 0 because since nothing is connected the device is completed shutdown?

 

Well you newer know, what you get.
In general in TTL floating input is considered as HIGH.
In CMOS floating input in undefined, it can be HIGH or LOW.
Its depend on the noise and input capacitor,
when you touch input node by finger then input capacitor will charge to HIGH level.
And the input will stay in this state for a very long time

http://www.seattlerobotics.org/encoder/mar97/basics.html
http://www.allaboutcircuits.com/vol_4/chpt_3/7.html

 

Well, I connected the device and got an logic 0, I believe I am using TTL, is the output wrong?

 

It has always been considered bad practice to leave inputs floating. They should be tied high or low as appropriate.