A) Define a 4 X 4 Multiplexer b) Design a 4 X 4 multiplexer using MSI component

Here is the solution for question 1:

Question 1:

a) Defined a 4 X 4 Multiplexer

b) Design a 4 X 4 multiplexer using MSI component

Step 1: Define a Multiplexer and a 4x4 Multiplexer.
A multiplexer (MUX) is a combinational logic circuit that selects one of $N$ input data lines and routes it to a single output line. The selection is controlled by a set of $S$ select lines, where $N = 2^S$.

A 4x4 multiplexer typically refers to a 4-bit wide 4-to-1 multiplexer. This means it has four 4-bit input data lines (e.g., $D_0, D_1, D_2, D_3$), two select lines ($S_0, S_1$), and one 4-bit output line ($Y$). Based on the binary value of the select lines, one of the four 4-bit input data lines is chosen and transferred to the 4-bit output. For example, if $S_1S_0 = 00_2$, then $Y = D_0$.

Step 2: Design a 4x4 multiplexer using MSI components.
To design a 4-bit wide 4-to-1 multiplexer using MSI components, we can use two 74LS153 dual 4-to-1 multiplexer chips. Each 74LS153 chip contains two independent 4-to-1 multiplexers that share common select lines. We will use one 74LS153 for the lower two bits of the 4-bit data and another 74LS153 for the upper two bits.

The inputs are four 4-bit data lines: $D_0[3:0], D_1[3:0], D_2[3:0], D_3[3:0]$.
The select lines are $S_1, S_0$.
The output is a single 4-bit data line: $Y[3:0]$.

• Chip 1 (74LS153_1): This chip handles the least significant bits (LSBs) of the 4-bit data.

  • MUX A (1Y output) will select and output $Y[0]$. Its inputs will be $D_0[0], D_1[0], D_2[0], D_3[0]$.
  • MUX B (2Y output) will select and output $Y[1]$. Its inputs will be $D_0[1], D_1[1], D_2[1], D_3[1]$.
  • The select lines $S_0$ and $S_1$ are connected to the common select inputs (A and B) of this chip.
  • Both enable pins (1G and 2G) are connected to ground (active low enable).

• Chip 2 (74LS153_2): This chip handles the most significant bits (MSBs) of the 4-bit data.

  • MUX A (1Y output) will select and output $Y[2]$. Its inputs will be $D_0[2], D_1[2], D_2[2], D_3[2]$.
  • MUX B (2Y output) will select and output $Y[3]$. Its inputs will be $D_0[3], D_1[3], D_2[3], D_3[3]$.
  • The select lines $S_0$ and $S_1$ are connected to the common select inputs (A and B) of this chip, in parallel with Chip 1.
  • Both enable pins (1G and 2G) are connected to ground (active low enable).

The block diagram below illustrates this design:

\begin{array}{c} Input Data Lines \\ \begin{array}{|c|} \hline D_0[3:0] \\ D_1[3:0] \\ D_2[3:0] \\ D_3[3:0] \\ \hline \end{array} \end{array} \quad \xrightarrow{\quad} \quad \begin{array}{|c|c|c|} \hline \multicolumn{3}{|c|}{4x4 Multiplexer Design} \\ \hline Chip 1 (74LS153) & Chip 2 (74LS153) \\ \hline \begin{array}{l} MUX A (1Y): \\ \quad Inputs: D_0[0], D_1[0], D_2[0], D_3[0] \\ \quad Output: Y[0] \\ MUX B (2Y): \\ \quad Inputs: D_0[1], D_1[1], D_2[1], D_3[1] \\ \quad Output: Y[1] \\ Select: S_0, S_1 \\ Enable: GND \end{array} & \begin{array}{l} MUX A (1Y): \\ \quad Inputs: D_0[2], D_1