Page 89 - Computer Science Class 11 Without Functions
P. 89
6. State and prove De Morgan's laws in Boolean Algebra. [Delhi 2011C, Delhi 2009C, Delhi 2008]
7. State the following laws in Boolean Algebra:
a. Absorption law b. Distributive Law c. Involution Law
8. Verify one of De Morgan's Laws using a truth table. [Delhi 2013C, Delhi 2008, AI 2007]
9. Draw a logic circuit for each of the following Boolean expressions:
a. A.B' + (C + B').A' [Delhi 2013C]
b. X'.(Y' + Z) [Delhi 2008]
c. A.(B + C') [AI 2008]
d. A'.(B + C) [Delhi 2008C]
10. Verify the following equations using truth table:
a. X + X' = 1 [Delhi 2012]
b. X.X' = 0 [Delhi 2012, AI 2012]
c. X + 1 = 1 [AI 2012]
d. u.(u' + v) = (u + v) [Delhi 2011]
11. Give a logic diagram for each of the following gates using only NOR gate:
a. AND b. OR c. NOT d. XOR
12. Represent the Boolean expression XY'+ YZ' using only NAND gate. [Delhi 2005C]
13. State the Distributive law of Boolean algebra. Verify the law using a truth table. [Delhi 2008C, Delhi 2007, Delhi 2006]
14. Draw a truth table of a 2-input NAND gate and a 3-input NAND gate.
15. Give a truth table for the Boolean Expression (X+Y')'.
16. Using a truth table, prove that: AB + BC + CĀ = AB + CĀ.
Case Based Questions
1. Smriti knows that the NOR gate is a universal gate, therefore any logic circuit can be implemented using NOR gate. She
wants to implement AND gate using NOR gates only, but she is not able to complete it. Help her to complete the task.
2. Ruhaan has studied circuit diagrams while studying series and parallel electrical connections in Physics. However, while
studying boolean operators - AND and OR, he is getting confused between the two. Two electrical circuits (one in series and
the other a parallel circuit) are given below. Draw the equivalent truth tables for AND and OR operators.
Circuit 1: Circuit 2:
Voltage ∼ Voltage ∼
A AND B A OR B
A
B
A B
Multiple Choice Questions
1. (d) 2. (c) 3. (b) 4. (a) 5. (a) 6. (a) 7. (c) 8. (a) 9. (c)
10. (a) 11. (d) 12. (c)
True or False
1. (F) 2. (F) 3. (T) 4. (T) 5. (T) 6. (T)
Fill in the blanks
1. binary 2. 1 3. true 4. Involution 5. NAND, NOR
Boolean Logic 87

