Question

Minimize the following boolean function-
F(A, B, C) = Em(0,1,6,7) + Ed(3, 5)
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Answer 1

Explanation:

Minimize the following boolean function-

F(A, B, C) = Em(0,1,6,7) + Ed(3, 5)

Answer 2

The minimized boolean expression is-

F(A, B, C) = AB + A’B’

Given,

F(A, B, C) = Em(0,1,6,7) + Ed(3, 5)

To Find,

We have to find the minimize form of the Boolean function - F(A, B, C) = Em(0,1,6,7) + Ed(3, 5)

Solution,

• Since the given boolean expression has 3 variables, so we draw a 2 x 4 K Map.
• We fill the cells of K Map in accordance with the given boolean function.
• Then, we form the groups in accordance with the above rules.

Now, we have to follow the above picture

Now,

F(A, B, C)

= A'(B’C’ + B’C) + A(BC + BC’)

= A’B’ + AB

Then the minimized boolean expression is-

F(A, B, C) = AB + A’B’

• It may be noted that there is no need of considering the quad group.
• This is because even if we consider that group, we will have to consider the other two duets.
• So, there is no use of considering that quad group.

Hence, the minimized boolean expression is- F(A, B, C) = AB + A’B’

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