Design a combinational logic circuit with 4 inputs A, B, C, D. The output Y goes high if and only if A and C are high. Draw the truth table, minimize the boolean function using K-map, draw the circuit diagram.

Answer:

Step 1: Truth Table

The first step in designing a combinational logic circuit is to define the problem in terms of the inputs and the required output. This is usually done using a truth table. For the given problem, the truth table would look like this:

A	B	C	D	Y
0	0	0	0	0
0	0	0	1	0
0	0	1	0	0
0	0	1	1	0
0	1	0	0	0
0	1	0	1	0
0	1	1	0	0
0	1	1	1	0
1	0	0	0	0
1	0	0	1	0
1	0	1	0	1
1	0	1	1	1
1	1	0	0	0
1	1	0	1	0
1	1	1	0	1
1	1	1	1	1

From the truth table, we can see that the output Y is high (1) only when both A and C are high (1), regardless of the values of B and D.

Step 2: Karnaugh Map (K-Map)

The next step is to minimize the boolean function using a Karnaugh map (K-map). A K-map is a graphical representation of a logic function’s truth table. It is used to simplify the boolean function.

For a 4-variable K-map, the map is a 4x4 grid, with the rows representing the combinations of A and B, and the columns representing the combinations of C and D. The cells are filled with the corresponding output Y from the truth table.

The K-map for the given problem would look like this:

	00	01	11	10
00	0	0	0	0
01	0	0	0	0
11	0	0	1	1
10	0	0	1	1

From the K-map, we can see that the minimized boolean function is Y = AC.

Step 3: Circuit Diagram

The final step is to draw the circuit diagram. The circuit diagram for the minimized boolean function Y = AC is quite simple. It consists of two inputs A and C connected to an AND gate, with the output of the AND gate being the output Y.

Here is a simple representation of the circuit diagram:

A ------
       |
       AND ---- Y
       |
C ------

In this circuit, the output Y will be high (1) only when both A and C are high (1), which is exactly the behavior defined in the problem statement.