Digital Logic Design GATE previous year questions with answer

Given Boolean Expression:
F(P, Q, R, S) = PQ + P'QR + P'QR'S
Simplify the last two terms using the absorption law.
• Focus on P'QR + P'QR'S.
• Factor out the common term P'Q:
    P'Q(R + R'S)
• Apply the Boolean identity (X + X'Y = X + Y). Here, X = R and Y = S.
    So, (R + R'S) simplifies to (R + S).
• Substitute this back:
    P'Q(R + S) = P'QR + P'QS
• The expression now becomes:
    F = PQ + P'QR + P'QS
Simplify the first two terms using the absorption law.
• Focus on PQ + P'QR.
• Factor out the common term Q:
    Q(P + P'R)
• Apply the Boolean identity (X + X'Y = X + Y). Here, X = P and Y = R.
    So, (P + P'R) simplifies to (P + R).
• Substitute this back:
    Q(P + R) = PQ + QR
• The expression now becomes:
    F = PQ + QR + P'QS
Simplify the remaining expression.
• We have F = PQ + QR + P'QS.
• Factor out the common term Q from all terms:
    F = Q(P + R + P'S)
• Focus on the terms inside the parenthesis: (P + R + P'S).
• Rearrange to group P with P'S: (P + P'S + R).
• Apply the Boolean identity (X + X'Y = X + Y). Here, X = P and Y = S.
    So, (P + P'S) simplifies to (P + S).
• Substitute this back into the parenthesis:
    (P + S + R)
• Now substitute this back into the full expression for F:
    F = Q(P + S + R)
• Distribute Q:
    F = QP + QS + QR
• Rearrange the terms for standard form:
    F = PQ + QR + QS