Determining transistor circuit output

This is utilized when Creating Gates as (CMOS) Circuits

You only really have to look at 1 half of the circuit to know the truth table (i.e. you can look at just the bottom half)

• Looking at the more “parallel” half is easier most of the time.

If there is connection between Y and $V_{cc}$, then the output is 1 If Y and ground are connected, then the output is 0

Examples

1. For the first one, looking at the bottom half is easier since it’s parallel:
   1. When A is false OR b is false, then Y is connected to the ground.
      1. $(\neg A\vee \neg B)\leftrightarrow ground$
      2. $\neg (A\wedge B)\leftrightarrow ground$ via De Morgan’s Law yay
      3. $A\wedge B\leftrightarrow V_{cc}$
   2. it’s an AND gate!
2. For the second one, looking at the top is easier:
   1. When A or B are true, then Y is connected to $V_{cc}$
   2. So it’s simply an or gate
3. For the third one, we have some parallel and some series. Let’s look at that bottom half since there’s a bit more consistency between the series “sub-circuits” (?):
   1. When A and B are true, Y is connected to ground, or
   2. When A and B are false, Y is connected to ground
   3. $(A\wedge B)\vee (\neg A\wedge \neg B)\leftrightarrow ground$
   4. $\neg (\neg A\vee \neg B)\vee \neg (A\vee B)\leftrightarrow ground$
   5. $(\neg A\vee \neg B)\wedge (A\vee B)\leftrightarrow V_{cc}$
   6. Would you look at that; this looks exactly like a XOR gate!