How to convert a boolean function into K-map

Question

I would like to know how can I convert the following boolean function into a truth table and accordingly construct the k-map

$$F=A′B′C′+B′CD′+A′BCD′+AB′C′$$

thanks in advance :)

Answer 1

To construct the truth table, you need to manually assess each combination. A table works well, hence the name "truth table"! I assume you understand logical ANDs and ORs, to make sense of this answer.

First, you want to solve each ANDed group separately. Boolean algebra has the same order of precedence as standard algebra, with AND treated like multiplication, and OR treated like addition. Put these answers in a table. Don't worry, I'll attach a picture to demonstrate. Once you have all of these statements figured out, then you can OR them together. Follow the red lines on the following table:

Now that the table is completed, you can build a map. One of the standard configurations is shown below. You have two bits defining the columns, and the other two bits defining the rows. Find the square that intersects the binary inputs (A, B, C, and D), and fill in the answer from your truth table. I've done two of them, in Purple and Orange:

I'll leave the rest for you! You didn't ask how to solve the K-Map. I assume you know how?

Take care!

(P.S. I've included a typo in the truth table. Can you find it?)

Answer 2

To draw truth table with four input A,B,C,D and output F

Output will be at logic 1 at

A'B'C'(000x) => 0000 & 0001

B'CD' (x010) => 0010 & 1010

A'BCD' (0110) => 0110

AB'C' (100x) => 1000 & 1001

For all other states output will be at logic 0