سوال ۸۳ کنکور ارشد مهندسی کامپیوتر ۱۴۰۱

A $4{:}1$ MUX with select lines $S_1=A$ (MSB), $S_0=B$ (LSB) routes one data input to the output for each $(A,B)$ combination:

$F = \bar{A}\bar{B}\,I_0 + \bar{A}B\,I_1 + A\bar{B}\,I_2 + AB\,I_3.$

The data inputs read from the circuit are

$I_0=C,\quad I_1=D,\quad I_2=\bar{C},\quad I_3=\bar{C}\,\bar{D}.$

Minterm index uses $m = 8A+4B+2C+D$. Evaluate each MUX region:

Details of the upper half ($A=1$):

• $A=1,B=0$: base $=8$, output $=\bar{C}$ is $1$ for $C=0$, i.e. $(C,D)=(0,0),(0,1)\Rightarrow$ minterms $8,9$.
• $A=1,B=1$: base $=12$, output $=\bar{C}\bar{D}$ is $1$ only for $(C,D)=(0,0)\Rightarrow$ minterm $12$.

Collecting all on-set minterms:

$F(A,B,C,D)=\sum m(2,3,5,7,8,9,12).$

This is option 2.

Exam trick: With $S_1=A,\,S_0=B$, each MUX data line owns a fixed $4$-minterm block ($\{0\text{-}3\},\{4\text{-}7\},\{8\text{-}11\},\{12\text{-}15\}$). Just expand each data expression in the remaining variables $C,D$ within its block and read off the minterms.