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GATE Overflow Test Series | Mixed Subjects | Test 2 | Question: 22

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With four $2-to-4$ line decoders we can get $16$ distinct outputs.

These $4$ decoders can be controlled by one another $2-to-4$ line decoder.

Thus, total number of decoders needed $=4+1 = 5.$
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Number of $’N’$ bit Mux/Demux/Decoder/Encoder to construct $’M’$ bit Mux/Demux/Decoder/Encoder is $ = \left \lceil \dfrac{M-1}{N-1} \right \rceil.$

Here, $M = 16,N = 4$

Then, number of decoders $ =  \left \lceil \dfrac{16-1}{4-1} \right \rceil = \left \lceil \dfrac{15}{3} \right \rceil = 5.$

So, the correct answer is $5.$
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