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?

To determine the functions of components P, Q, and T:

1. Component P (Addressing Memory S):

   • Memory segment $S$ has $1024 = 2^{10}$ words.

   • To select one specific word among $1024$ locations, a 10-bit address is required.

   • An address decoder converts $n$ address lines to $2^n$ unique select lines.

   • Therefore, $P$ is a $10:2^{10}$ (or $10:1024$) decoder.

2. Component Q (Addressing Register File R):

   • Register file $R$ contains $32 = 2^5$ words.

   • To select one of the $32$ registers, a 5-bit address is needed.

   • Therefore, $Q$ is a $5:2^5$ (or $5:32$) decoder.

3. Component T (Selecting between S and R):

   • $T$ receives two word inputs (one from $S$ and one from $R$) and selects one to load into register $X$ based on the 1-bit mode control signal $M$.

   • A component that selects one of two data inputs based on a control/select line is a $2:1$ multiplexer (MUX).

Notice that the total code word size is $1\text{ (for } M) + 10\text{ (for } S\text{)} + 5\text{ (for } R\text{)} = 16\text{ bits}$, which matches the prompt.

Hence, P is a $10:2^{10}$ decoder; Q is a $5:2^5$ decoder; T is a $2:1$ multiplexer, which corresponds to option (C).