Construct a 16 × 1 multiplexer using 2 × 1 multiplexer. How many 2 × 1 multiplexer are required to construct?a)16b)15c)8d)4Correct answer is option 'B'. Can you explain this answer?

Question

Construct a 16 &times; 1 multiplexer using 2 &times; 1 multiplexer. How many 2 &times; 1 multiplexer are required to construct?a)16b)15c)8d)4Correct answer is option 'B'. Can you explain this answer?

Answer

Here is a 16-line poem:

In the golden dawn of a new day,
Nature awakens in a splendid display.
Birds sing their joyful melodies,
Dancing among the swaying trees.

Sunlight filters through the leaves,
Gently kissing the morning breeze.
Flowers bloom in vibrant hues,
Their fragrant scents the air infuse.

Rivers flow with a gentle grace,
Reflecting the beauty of this place.
Mountains stand tall, majestic and grand,
Covered in a blanket of green land.

Wildlife roams freely, untamed,
Their presence in this world proclaimed.
Stars twinkle in the velvet night,
Guiding us with their eternal light.

From dawn to dusk, nature's show,
A masterpiece that continues to grow.
Let us cherish and protect this Earth,
Preserving its wonders, for all it's worth.

Answer

To implement 2ⁿ × 1 MUX using 2 × 1 MUX, the total number of 2 × 1 MUX required is (2ⁿ - 1).

∴ The number of 2 × 1 multiplexer required to implement 16 × 1 MUX will be:

n = 16 - 1 = 15

Or we can follow the below steps to calculate the same:

1^ststage = 16/2 = 8

2^nd stage = 8/2 = 4

3^rd stage = 4/2 = 2

4^th stage = 2/2 = 1

The sum will give the total number of MUX required to implement 16 × 1 multiplexer using 2 × 1, i.e.

n = 8 + 4 + 2 + 1 = 15

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