The key to understand the operation of TTL circuits is to understand inverse active region of BJT. Transistor is in inverse active region when Vbc = 0.7V and Vec > 0.2V (approximately). The other way to view this is to exchange emitter and collector. When working in this way the transistor has gain of less than 1, but it can work.
I'll assume that there is only one input (i.e. B tied to Vcc) Operation of circuit is as follows: 1. A = 0 V -> Q1 (the one with base connected to Vcc via resistor) is in saturation, Q2 (output BJT) is off -> Vout = Vcc 2. When input A rises above Vbe_2 + Vecs_1 Q1 enters inverse active region and Q2 starts to conduct in direct active region. In this region the output voltage drops as input voltage increases. 3. At some point the output transistor will saturate and increasing the input voltage won't affect output.
Hope this helps...
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