essay 5 points for the following boolean logic statement, create the appropriate karnaugh map. logic gates…

Explanation:

Step1: Identify logic - gate functions

The AND - gate outputs 1 when both inputs are 1. The NOT - gate inverts the input. The OR - gate outputs 1 when at least one of its inputs is 1. Let the two inputs to the AND - gate be (A) and (B), and the input to the NOT - gate be (C). The Boolean expression for the circuit is (Y=(A\cdot B)+\overline{C}).

Step2: Determine number of variables

There are 3 variables (A), (B), and (C). A 3 - variable Karnaugh map has (2^3 = 8) cells.

Step3: Set up Karnaugh - map structure

Label the rows with (A) (0 and 1) and the columns with (B) and (C) combinations ((00), (01), (11), (10)).

Step4: Fill the Karnaugh map

For the term (A\cdot B), when (A = 1) and (B = 1), regardless of (C) value, the output is 1. So, fill the cells where (A = 1) and (B = 1) (i.e., the two cells in the (A = 1) row and (B = 1) columns). For the term (\overline{C}), when (C=0), regardless of (A) and (B) values, the output is 1. So, fill the four cells in the (C = 0) columns.

The Karnaugh map for (Y=(A\cdot B)+\overline{C}) has 1s in the following cells:

(BC)\(A)	00	01	11	10
0	1	1	1	1
1	0	0	1	1

Answer:

The Karnaugh map is as shown above with 1s in the appropriate cells based on the Boolean expression (Y=(A\cdot B)+\overline{C}).