Computer Science
A combinational logic circuit with three inputs P,Q,R produces 1 if and only if an odd number of 0's are inputs.
- Draw a truth table.
- Derive a canonical SOP expression for the above truth table.
- Find the complement of the above derived expression using De-Morgan's theorem and verify whether it is equivalent to its POS expression or not.
Boolean Algebra
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Answer
Truth Table
| P | Q | R | Output | Min Terms | Max Terms |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | P'Q'R' | |
| 0 | 0 | 1 | 0 | P+Q+R' | |
| 0 | 1 | 0 | 0 | P+Q'+R | |
| 0 | 1 | 1 | 1 | P'QR | |
| 1 | 0 | 0 | 0 | P'+Q+R | |
| 1 | 0 | 1 | 1 | PQ'R | |
| 1 | 1 | 0 | 1 | PQR' | |
| 1 | 1 | 1 | 0 | P'+Q'+R' |
SOP expression = P'Q'R' + P'QR + PQ'R + PQR'
POS expression = (P+Q+R').(P+Q'+R).(P'+Q+R).(P'+Q'+R')
Complement of P'Q'R' + P'QR + PQ'R + PQR'
= [P'Q'R' + P'QR + PQ'R + PQR']'
= (P'Q'R')'.(P'QR)'.(PQ'R)'.(PQR')'
= (P''+Q''+R'').(P''+Q'+R').(P'+Q''+R').(P'+Q'+R'')
= (P+Q+R).(P+Q'+R').(P'+Q+R').(P'+Q'+R)
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Related Questions
Convert the following cardinal form of expression into canonical form:
F(P, Q, R) = π(1, 3)Given F (X, Y, Z) = (X' + Y').(Y + Z')
Write the function in canonical POS form.In the following truth table x and y are inputs and B and D are outputs:
Input Output x y B D 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 Answer the following questions:
(i) Write the SOP expression for D.
(ii) Write the POS expression for BUsing a truth table, verify the following expression:
X + (Y + Z) = (X + Y) + Z