Topic: Digital Circuits
In the given figure, find the value of (X0, X1, X2, X3, X4, X5, X6, X7) to realise the function $F=A+\overline{B}$
- A. (1,1,0,0,1,1,1,1)
- B. (1,1,1,1,0,0,1,1)
- C. (1,1,0,1,0,1,1,1)
- D. (0,0,1,1,1,1,1,1)
Answer: B. (1,1,1,1,0,0,1,1)
Explanation: The final 2:1 MUX outputs $F = \overline{B} \cdot MUX_{top} + B \cdot MUX_{bot}$.
We want $F = A + \overline{B}$.
If $B=0$, $F = A + 1 = 1$. This means the top MUX must output 1 regardless of its select lines (A and C). Therefore, $X0=X1=X2=X3=1$.
If $B=1$, $F = A + 0 = A$. This means the bottom MUX must output A. The bottom MUX has select lines $S_1=A$ and $S_0=C$. Its output is $\overline{A}\overline{C}X_4 + \overline{A}CX_5 + A\overline{C}X_6 + ACX_7$. For this to equal $A$, the terms where $A=0$ must be 0 (so $X_4=0, X_5=0$), and the terms where $A=1$ must be 1 (so $X_6=1, X_7=1$).
Combining these, we get (1, 1, 1, 1, 0, 0, 1, 1).