Question
Download Solution PDFGiven the function F = P’ + QR, where F is a function in three Boolean variables P, Q and R and P’ = !P, consider the following statements.
(S1) F = ∑ (4, 5, 6)
(S2) F = ∑ (0, 1, 2, 3, 7)
(S3) F = Π (4, 5, 6)
(S4) F = Π (0, 1, 2, 3, 7)
Which of the following is true?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Sum of product (SOP) – The concept of sum of products mainly includes minterm. Minterm is a Boolean expression resulting in 1 for the output of a single cell and 0’s for all other cells in K-Map. MInterm is all the 1’s in the truth table.
Product of sum (POS) – Product of sum mainly includes max term. Max term is a Boolean expression resulting in 0 for the output of a single cell and 1 for all other cells in K-Map. Maxterm is all the 0’s in the truth table.
Explanation:
Function: F = P’ + QR
Construct the truth table for this function:
|
P |
Q |
R |
F =P’+QR |
|
0 |
0 |
0 |
1 |
|
0 |
0 |
1 |
1 |
|
0 |
1 |
0 |
1 |
|
0 |
1 |
1 |
1 |
|
1 |
0 |
0 |
0 |
|
1 |
0 |
1 |
0 |
|
1 |
1 |
0 |
0 |
|
1 |
1 |
1 |
1 |
Here
K-MAP for the given function :
F = P’ + QR
So, here S2 and S3 is true.
S1 and S4 is false.
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