Answer:
Sure, I'd be happy to help!
A Karnaugh map (or K-map) is a useful tool in Boolean algebra to simplify expressions. It's used to minimize logical expressions in computer engineering and digital logic.
Your Boolean expression is `E = A’B’C’D + A’CD + A’C’ + C`. This is a 4-variable function, with variables A, B, C, and D. We will use a 4-variable K-map to simplify it.
A 4-variable K-map has 16 cells, corresponding to the 16 possible truth values of A, B, C, and D. The cells are arranged such that only one variable changes value from one cell to the next, either horizontally or vertically. This is known as Gray code ordering. Here's how the variables are arranged:
```
CD\AB | 00 | 01 | 11 | 10 |
---------------------------
00 | | | | |
01 | | | | |
11 | | | | |
10 | | | | |
```
Now, let's fill in the values from your expression:
1. `A’B’C’D`: This term corresponds to the cell where A=0, B=0, C=0, D=1. So, we will fill a "1" in this cell.
2. `A’CD`: This term corresponds to the cells where A=0, C=1, D=1. There are two cells that match this because B can be either 0 or 1. So, we will fill "1"s in both of these cells.
3. `A’C’`: This term corresponds to the cells where A=0, C=0. There are four cells that match this because B and D can be either 0 or 1. So, we will fill "1"s in all of these cells.
4. `C`: This term corresponds to the cells where C=1. There are eight cells that match this because A, B, and D can be either 0 or 1. So, we will fill "1"s in all of these cells.
After filling in the values, your K-map should look like this:
```
CD\AB | 00 | 01 | 11 | 10 |
---------------------------
00 | 1 | 1 | 1 | 1 |
01 | 1 | 1 | 1 | 1 |
11 | 1 | 1 | 1 | 1 |
10 | 1 | 1 | 1 | 1 |
```
Looking at the K-map, we see that all cells are filled with "1", which means your simplified Boolean expression is just `E = 1`. In other words, the function E is always true regardless of the values of A, B, C, and D.