TomGeorge:
Hi,If your collector current is 1.1A then your minimum base current, assuming a gain of 1000 will be for saturation of the TIP120.
Base Current = Collector Current / Gain.
Base Current = 1.1 / 1000 = 0.0011 Amps
or 1.1mA to saturate or fully turn ON the TIP120.
as a note here, the data sheet for a transistor will list hfe.
the TIP120 has an hfe of 1,000 = gain of 1,000
as shown in the line above.
I think Tom did a good job laying it out and I just wanted to point this bit out as every transistor has a different hfe so this calculation needs to be adjusted for other ones.