ISC (Science) ISC Class 12 - CISCE Important Questions

The compliment of the Boolean expression Aꞌ • (B • Cꞌ + Bꞌ • C).

According to the Principle of duality, the Boolean equation (Aꞌ + B) • (1 + B) = Aꞌ + B will be equivalent to ______.

Distributive law states that ______.

The complement of the reduced expression of F(A,B) = ∑ (0,1,2,3) is ______.

Study the given propositions and the statements marked Assertion and Reason that follow it. Choose the correct option on the basis of your analysis.

p = I am a triangle

q = I am a three-sided polygon

s1 = p → q

s2 = q → p

Assertion: s2 is converse of s1

Reason: Three-sided polygon must be a triangle.

A shopping mall announces a special discount on all its products as a festival offer only to those who satisfy any one of the following conditions.

• If he/she is an employee of the mall and has a service of more than 10 years.
                                   OR
• A regular customer of the mall whose age is less than 65 years and should not be an employee of the mall.
                                   OR
• If he/she is a senior citizen but not a regular customer of the mall.

The inputs are:

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

Output: X - Denotes eligible for discount [1 indicates YES and 0 indicates NO in all cases]

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

Reduce the above expression X ( E, R, S, C ) by using 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(P,Q,R,S) = (P+Q+R+S) • (P+Q+R+Sꞌ) • (P+Q+Rꞌ+S) • (P+Qꞌ+R+S) • (P+Qꞌ+R+Sꞌ) • (P+Qꞌ+Rꞌ+S) • (P+Qꞌ+Rꞌ+Sꞌ) •(Pꞌ+Q+R+S) • (Pꞌ+Q+R+Sꞌ) by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).

From the given logic diagram:

1. Derive Boolean expression and draw the truth table for the derived expression
2. If A=1, B=0 and C=1, then find the value of X.

Verify if the following proposition is valid using the truth table:

(X ∧ Y) =>Z = (Y => Z) ∧ (X => Y).

Differentiate between half adder and full adder. Write the Boolean expression and draw the logic circuit diagram for the SUM and CARRY of a full adder.

How is Encoder different from a decoder?

Draw the logic circuit for a 4 :1 multiplexer and explain its working.

When a sequence of OR, NOT, NOR are connected in series, the logic gate obtained is ______.

Idempotence Law states that ______.

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

Draw the logic gate diagram for 2-input OR gate using NAND gates only. Show the expression at each Step.

Draw the logic circuit for 3:8 decoder (Octal decoder). Which multiplexer can be derived from the Octal decoder?

A full adder needs five gates and those are 3 AND gates, 1 OR gate and 1 XOR gate. When a full adder is constructed using 2 half adders, it also requires 5 gates. State the names along with the quantity those gates.

Draw the logic circuit to decode the following binary number (0001, 0101, 0111, 1000, 1010, 1100, 1110,1111) to its hexadecimal equivalents. Also, state the Hexadecimal equivalents of the given binary numbers.