ISRO2015-8

Question

Minimum number of $2 \times 1$ multiplexers required to realize the following function, $f = \overline{A} \;\overline{B} C + \overline{A}\; \overline{B} \;\overline{C}$

Assume that inputs are available only in true form and Boolean a constant $1$ and $0$ are available.

• A. $1$
• B. $2$
• C. $3$
• D. $7$

Comments

Answer is 2 Right
first Simplify the equation and get the equation A(bar)B(bar)
than at the first mux take the input I(zero)=1 and I(one) =0 and take the select line A than output will be A (bar) and At the second Mux take the input A(bar) at I(zero) than and take select line as B at Second Mux and u can take Input Line I(1) as Zero than output Will be A(bar)B(bar)

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Is it not possible to implement this using only one mux? That is, give A as selection line, B' to 0 input and 0 to 1 input. Then if A is 0, choose B'. B is 0 means output is 1. B is 1 means output is 0. In case if A is 1, then 1 input has 0.

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We cant use B' as input, as it is mentioned in the question that all inputs are available in true form only.

Answer 1

• The given function $f = A'B'C + A'B'C'$ can be simplified using Boolean algebra to $f = A'B'$.
• This means the output is $1$ only when both $A$ and $B$ are $0$, regardless of $C'$s value.

1. First Multiplexer:

   • Select between $C$ and $C'$ using $A'B'$ as the select line.
   • When $A'B'$ is $1$, the output of this multiplexer will be either $C$ or $C'$, depending on the value of $A'B'$.

2. Second Multiplexer:

   • Select between the output of the first multiplexer (which is either $C$ or $C'$) and constant $0$ using $A'B'$ as the select line again.
   • When $A'B'$ is $1$, the output of this multiplexer will be the same as the output of the first multiplexer (either $C$ or $C'$).
   • When $A'B'$ is $0$, the output will be $0$, ensuring the correct output for $f = A'B'$.

Answer 2

1. The given function $f = A'B'C + A'B'C'$ can be simplified using Boolean algebra to $f = A'B'$.
2. This means the output is $1$ only when both $A$ and $B$ are $0$, regardless of $C'$s value.

1. First Multiplexer:

   • Select between $C$ and $C'$ using $A'B'$ as the select line.
   • When $A'B'$ is $1$, the output of this multiplexer will be either $C$ or $C'$, depending on the value of $A'B'$.

2. Second Multiplexer:

   • Select between the output of the first multiplexer (which is either $C$ or $C'$) and constant $0$ using $A'B'$ as the select line again.
   • When $A'B'$ is $1$, the output of this multiplexer will be the same as the output of the first multiplexer (either $C$ or $C'$).
   • When $A'B'$ is $0$, the output will be 0, ensuring the correct output for $f = A'B'$.