SN74LS181: The comparison function, A=B, not operating
It's difficult to be sure that we're interpreting everything correctly without you supplying a schematic diagram (a picture is worth a thousand words etc.).  

However your main question has a clear explanation:


  I intend to utilise the A=B output [...] 


From the datasheet:


"The A = B output is open-collector so that it can be wire-AND connected to give a comparison for more than four bits."


See this extract from the datasheet - the A = B output (which I've marked in red) is open-collector, whereas the other outputs are standard "totem pole":



Therefore you can't measure a meaningful change of state between low &amp; high, unless a suitable pull-up resistor is added between the A = B output and VCC.

I think you are saying that the A = B output always remains low. That is expected. An open-collector output pin without a pull-up will always appear to be low (either it's actively driven low or it is undriven, which will also measure as low with a multimeter - read about open-collector outputs for more details)

Try a 4.7k pull-up to VCC on the A = B pin and re-test. You should find that the A = B output is then low, unless you correctly configure the chip and supply equal input words, when it should become high to indicate equality.