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GATE CSE 2022 Q40: Roles of P, Q and T in a digital display system

Question

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?

Code word split into M, S-address and R-address fields; S-address feeds P which drives memory S, R-address feeds Q which drives register file R; S, R and the M bit feed T, whose output goes to register X attached to DDS
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Answer: C (official GATE 2022 final answer key)

Concept used: An address of kk bits selects one of 2k2^k words through a decoder; choosing one of two data sources by a control bit is a multiplexer.

First step: S has 1024=2101024 = 2^{10} words and R has 32=2532 = 2^5 words, so find how many address bits each needs and what device turns them into word selects.

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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key

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