Question

Minimize F = (AB)’ + AB’C + AC using Boolean laws.​

Answer 1

Answer:

Just use the laws of boolean algebra. Most of the rules are just arithmetic rules but changed a little for binary operation.

Y = A'B'C' + A'B + ABC' + AC

Y = A'(B'C' +B) + A(BC'+C) (Just factor out the terms like algebra)

Now work on the sub terms (B'C' +B) and (BC' + C) to reduce them.

B'C' + B (using AND distributive law) becomes

(B + B')(B+C') Now (B+B') is simply = 1

Use the same step for the (BC'+C) which becomes (B+C)

NOW..

Y = A'(B+C') + A(B+C)

Y = A'B + A'C' + AB + AC (OR distributive law) (you distribute to see if you can combine and reduce any more terms.)

Y = A'B + AB + A'C' + AC

Y = B(A'+A) + A'C' + AC where (A' + A) = 1

Y = A'C' + AC + B

To verify this you will have to perform the operation manually for the original equation and the reduced equation. You input all possible combinations of 3 variables. You have to brute force this and if the output is the same for both the original equation and the reduced equation then the answer is correct.

Explanation:

if anything is wrong then sorry :\