Triggering a relay using CL100 transistor
TTL is not so good at sourcing current for a high output. You'll perhaps get the ability to drive a few mA or so and the output voltage will sag.
Let's assume worst case that the logic out drops to 2.7V and you need 0.9V on the base of the CL100 the base current is going to be:
(2.7 - 0.9)/270 ~6mA for a 270 ohm resistor
The rule of thumb is you can saturate a load of 10x this or about 60mA.
So this might work if the operating current of the relay is no more than 60mA or so.