Correct way to drive an LED using 74HCxx logic
The circuits you propose won't work (the LED will not light up) because you're trying to make the current flow through the LED in the wrong direction (reverse mode).

Also it is a must to use a series resistor. Yeah sure, it will work without a series resistor but that puts a lot of stress on the logic gate and the LED. Also without the resistor the current through the LED is very uncontrolled and that should be avoided.

Let's cut to the chase and let me show you how it is done:







simulate this circuit &ndash; Schematic created using CircuitLab

For this circuit D1 and D2 will light up when "signal" is high (one = 1 = +5 V)

Resistors R1 and R2 limit the current to about 3 mA when using a 5 V supply. For modern LEDs 3mA will be enough current. If you're using old LEDs you might need up to 20 mA and then it is better to use an additional transistor to make that current flow as logic gates aren't designed to supply such a current.