GATE CS 2014 Set 3 Q.18 (CS Q.8): Combinational Circuits

Consider the following combinational function block involving four Boolean variables $x, y, a, b$ where $x, a, b$ are inputs and $y$ is the output.

f (x, y, a, b)
{
    if (x is 1) y = a;
    else y = b;
}

Which one of the following digital logic blocks is the most suitable for implementing this function?

Full adder

Priority encoder

Multiplexor

Flip-flop

Official answer and solution

Solution

Identify the logic function as selecting between two input data lines based on a single control line.

The function pseudocode is:
```
if (x is 1) y = a;
else y = b;
```
Expressed as a Boolean logic equation:
$y = x \cdot a + \overline{x} \cdot b.$
This Boolean function takes:
- A selection/control input $x$
- Two data inputs $a$ and $b$
- A single data output $y$
This matches the standard definition and architecture of a 2-to-1 Multiplexor (MUX).

Hence, a Multiplexor is the most suitable digital block (option C).

Final answer

Common trap

Confusing a multiplexor with a priority encoder, which encodes active input lines into binary codes rather than routing data.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

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