GATE CS 2022 Q.40: Combinational Circuits

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?

Digital Display System block diagram: 16-bit Code Word has fields M, S-address (into P then S), and R-address (into Q then R). Outputs of S and R go into T controlled by M, and output of T loads register X connected to DDS.

P is 10:1 multiplexer; Q is 5:1 multiplexer; T is 2:1 multiplexer

P is $10:2^{10}$ decoder; Q is $5:2^5$ decoder; T is 2:1 encoder

P is $10:2^{10}$ decoder; Q is $5:2^5$ decoder; T is 2:1 multiplexer

P is 1:10 de-multiplexer; Q is 1:5 de-multiplexer; T is 2:1 multiplexer

Official answer and solution

Official answer: C
From: Official GATE 2022 answer key

Solution

Identify the logic blocks required for memory addressing and data path selection.

Analyzing the components:

Block P receives an address and selects one word from memory segment S. Memory segment S has 1024 words, requiring $\log_2(1024) = 10$ address lines. To select 1 out of $2^{10} = 1024$ locations, P acts as a $10:2^{10}$ decoder.
Block Q receives an address and selects one register from register file R. Register file R contains 32 words, requiring $\log_2(32) = 5$ address lines. To select 1 out of $2^5 = 32$ registers, Q acts as a $5:2^5$ decoder.
Block T takes two word inputs (one from memory S and one from register file R) and uses the 1-bit mode signal M to select which word to load into register X. Thus, T is a $2:1$ multiplexer.

Hence, P is a $10:2^{10}$ decoder, Q is a $5:2^5$ decoder, and T is a $2:1$ multiplexer, matching Option (C).

Final answer

Option (C)

Common trap

Confusing decoders (which convert $n$ address lines to $2^n$ word select lines) with multiplexers.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2022 Computer Science and Information Technology (CS)
Question: 40 of 65
Section: Computer Science and Information Technology

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