ISC (Science) ISC Class 12 - CISCE Important Questions for Computer Science (Theory)

According to De Morgan's law (a +b + c')' will be equal to ______.

The dual of (X' + 1) · (Y' + 0) = Y' is ______.

The reduced expression of the Boolean function F(P, Q) = P' · + P · Q is ______.

Verify if (A + A')' is a Tautology, Contradiction or a Contingency.

Given the Boolean function F(A, B, C, D) = ∑(2, 3, 6, 7, 8, 10, 12, 14, 15).

1. Reduce the above expression by using 4- variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs.
2. Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Give the Boolean function F(A, B, C, D,) π(0, 1, 2, 4, 5, 8, 10, 11, 14,15).

1. Reduce the above expression by using 4-variable Karnaugh mpa, showing the various groups (i.e., octal quads and pairs)
2. Draw the logic gate diagrams for the reduced expression. Assume that the variables and their complements are available as inputs.

A shopping mall allows customers to shop using the cash or credit card of any nationalised bank. In awards bonus points to their customers on the basis of criteria given below:

• The customer is an employee of the shopping mall and makes the payment using a credit card.
  OR
• The customer shops items which carry bonus points and makes the payment using a credit card with a shopping amount of less than  ₹10,000.
  OR
• The customer is not an employee of the shopping mall and makes the payment not through a credit card in cash for the shopping amount above ₹10,000/-

The inputs are:

(In all the above cases, 1 indicates yes and 0 indicates no.) 

Output: X[1 indicates bonus point awarded, 0 indicates bonus point not awarded for all cases]

Draw the truth table for the inputs and outputs given above and write the POS expression for X(C, A, F, I).

Verify the following expression by using the truth table:

(A ☉ B)' = A ⊕ B

From the logic diagram given below, write the Boolean expression for (1) and (2). Also, derive the Boolean expression (F) and simplify it.

With reference to the code given below, answer the questions that follow along with dry run/working.boolean num(int x)

{ int a=1}
   for (int c=x; c>0; c/<10}
      a*=10;
   return (x*x%a)=x;
}

1. What will the function num() return when the value of x = 25?
2. What is the method num() performing?

Convert the following cardinal expression to its canonical form:

F(P, Q, R) = π(0, 1, 3, 4).

According to the Principle of duality, the Boolean equation

(A+ B') • (A+ 1) =A+ B' will be equivalent to ______.

Assertion: For proposition ∼A=> B, its contrapositive is B =>∼A

Reason: Contrapositive is the converse of inverse for any proposition.

The complement of the Boolean expression (P' • Q) (R • S') is ______.

Write the canonical SOP expression for F (A, B) = A <=> B.

To be recruited as the Principal in a renowned College, a candidate must satisfy any one of the following criteria:

• The candidate must be a Postgraduate and should either possess a B.Ed. degree or a teaching experience of more than 15 years?
                                 OR
• The candidate must be an employee of the same college with a teaching experience of more than 15 years.
                                 OR
• The candidate must be a Postgraduate but not an employee of the same college and should have a teaching experience of more than 15 years.

The inputs are:

(In all the above cases, 1 indicates yes and 0 indicates no)

Output: X - Denotes eligibility of a candidate [1 indicates eligibility and 0 indicates ineligibility in all cases]

Draw the truth table for the inputs and outputs given above and write the SOP expression for X (P, S, E, B).

Verify if the following proposition is a Tautology, Contradiction or Contingency using a truth table.

((A=>B)^∧(B=>C))=>(A=>C)

Reduce the above expression X (P, S, E, B) by tiifig 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Reduce the Boolean function F (A,B,C,D) = π (0, 2, 4, 6, 8, 9, 10, 11, 14) by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

Find the complement of the following expression and reduce it by using Boolean laws.

P•( 13 ± Q)•Q•(Q+R')