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Consider a digital display system $\text{(DDS)}$ shown in the figure that displays the contents  of register $\text{X}.$ A $16 – \text{bit}$ code word is used to load a word in $\text{X},$ either from $\text{S}$ or from $\text{R}.$ $\text{S}$ is a $1024-$word memory segment and $\text{R}$ is a $32-$word register file. Based on the value of mode bit  $\text{M, T}$ selects an input word to load in $\text{X. P}$ and $\text{Q}$ interface with the corresponding bits in the code word to choose the addressed word. Which one of the following represents the functionality of  $\text{P, Q,}$ and $\text{T}?$

1. $\text{P}$ is $10:1$ multiplexer$; \qquad \; \;\text{Q}$ is $5:1$ multiplexer$; \qquad \; \text{T}$ is $2:1$ multiplexer
2. $\text{P}$ is $10:2^{10}$ decoder$; \qquad \quad \text{Q}$ is $5:2^{5}$ decoder$; \qquad \quad \text{T}$ is $2:1$ encoder
3. $\text{P}$ is $10:2^{10}$ decoder$; \qquad \quad \text{Q}$ is $5:2^{5}$ decoder$; \qquad \quad \text{T}$ is $2:1$ multiplexer
4. $\text{P}$ is $1:10$ de-multiplexer$; \quad \; \;\text{Q}$ is $1:5$ de-multiplexer$; \quad \text{T}$ is $2:1$ multiplexer

If we observe, For T, there is select line, input and output lines shown in the diagram.

There are no select lines associated with P and Q ( only input and output lines shown in diagram )

Therefore P and Q are neither Multiplexers nor De-Multiplexers.

Those can be Decoders and T is Multiplexer of size 2x1

Option C is correct