Hi,
There is no general need for pullup/pulldown.
But you need to ensure valid logic levels in either case.
Only couple logic families have a valid logic level when unconnected, most logic families inputs are not defined when not connected.
Therefore my general recommendation is: not to leave logic inputs unconnected (Used gates as well as unused gates. Unless it is particularely written in the datasheet.)
Each logic family has it´s own V_IL, V_IH, I_IL, I_IH specificatons, therefore you need to consult the datasheet. We all need to consult the datasheet.
Example on 74LS00 (TI datasheet):
Given: 5V supply, V_IH =2V, V_IL=0.8V, I_IH=20uA, I_IL =-0.4mA.
Pulldown to ensure valid low level: R = V / I = V_IL / I_IL = 0.8V / 0.4mA = 2000Ohms. or less. --> use 1K (down to 0R)
Pullup to ensure valid high level: R = (5V - V_IH) / I_IH = (5V - 2V) / 20uA = 3V/20uA = 150k. or less. --> Use 10k (down to 0R)
Klaus
Added:
You asked to use ONE pullup/pulldown for multiple inputs.
--> the theshold voltages wont change (V_IL, V_IH), but the current will be multiplied (I_IL, I_IH).
Therefore you need to divide the (single) resistance value by the count of connected inputs:
Example before:
pulldown for 1 input: 2k
for 2 inputs: 1k
for 5 inputs 400R
for 10 inputs: 200R
.. and so on