Question

The MOSFET switches shown in the circuit are ideal.

Which of the following is the correct option for Boolean logical expression of the output (OUT), and the maximum possible power (P) consumed by the circuit?

• A. OUT = \(\overline{AB + \bar C}\), P = 5 mW
• B. OUT = \(\overline{(A + B)\bar C}\), P = 5 mW
• C. OUT = \(\overline{AB\bar C} + \bar C\), P = 7.5 mW
• D. OUT = \(\overline{ABC}\), P = 7.5 mW

Hint:

OUT is pulled low only when every pull-down switch conducts together; find which input combination makes both resistor branches draw current at once.

Answer 1

The Correct Option is D

Step 1: List when the pull-down path is complete.
Build a small table of the three NMOS conditions. The path from OUT to ground is only complete when every switch along it is closed, that is when $A=1$ and $B=1$ and $C=1$ simultaneously. In all other 7 combinations of $A,B,C$, at least one switch is open and OUT floats up to the supply through the $5$ k$\Omega$ resistor.

Step 2: Write out the truth table.
$$A\,B\,C:\ 000,001,010,011,100,101,110\ \to\ OUT=1;\qquad 111\ \to\ OUT=0$$

Step 3: Recognize the function.
A function that is $0$ only at $A=B=C=1$ and $1$ everywhere else is exactly the 3-input NAND:
\[ OUT=\overline{ABC} \]

Step 4: Compute power branch by branch, at each relevant condition.
The $5$ k$\Omega$ path draws $5\text{ V}/5\text{ k}\Omega=1$ mA (so $5$ mW) only at $A=B=C=1$. The $10$ k$\Omega$ path (with its own transistor switch gated by $C$) draws $5\text{ V}/10\text{ k}\Omega=0.5$ mA (so $2.5$ mW) at any input with $C=1$, independent of $A,B$.

Step 5: Add up power for every case with $C=1$ and see which gives the largest total.
For $C=1$ with $A=B=1$: both branches draw current, total $=5+2.5=7.5$ mW.
For $C=1$ with $A,B$ not both $1$ (say $A=0,B=1,C=1$): only the $10$ k$\Omega$ path draws, total $=2.5$ mW.
For $C=0$: the $5$ k$\Omega$ path needs $A=B=C=1$, which fails since $C=0$, so it draws nothing either; total $=0$ mW.

Step 6: Pick the largest.
The largest total power over all $8$ input combinations is $7.5$ mW, occurring at $A=B=C=1$.
\[ \boxed{OUT=\overline{ABC},\ P_{max}=7.5\text{ mW}} \]