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

1. P is 10:1 multiplexer; Q is 5:1 multiplexer; T is 2:1 multiplexer
2. P is 10:2¹⁰ decoder; Q is 5:2⁵ decoder; T is 2:1 encoder
3. P is 10:2¹⁰ decoder; Q is 5:2⁵ decoder; T is 2:1 multiplexer
4. P is 1:10 de-multiplexer; Q is 1:5 de-multiplexer; T is 2:1 multiplexer

Correct answer: P is 10:2¹⁰ decoder; Q is 5:2⁵ decoder; T is 2:1 multiplexer

Solution

The correct option describes P as a decoder that converts a 10-bit input to one of 1024 outputs, which is necessary for addressing the 1024-word memory segment S. Q is a decoder that converts a 5-bit input to one of 32 outputs, suitable for addressing the 32-word register file R. T functions as a multiplexer that selects between the outputs of P and Q based on the mode bit M, allowing the system to load the appropriate word into register X.

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