Page 83 - Computer Science Class 11 Without Functions
P. 83
12. Which of the following denotes an XOR gate?
a. b. c. d.
B. State whether the following statements are True or False:
1. A AND B yields 1 if either A or B is 1. __________
2. The value of A' is always 0. __________
3. For each Boolean element, its complement is unique. __________
4. The Absorption law states: If a and b are Boolean variables, then a + (a ● b) = a. __________
5. NAND gate is one of the universal gates. __________
6. A NAND B is equivalent to (A●B)' __________
C. Fill in the blanks.
1. Binary logic deals with logical operations on _______ data.
2. The expression A AND B yields 1 if both A and B are __________.
3. The expression true or false yields ___________.
4. According to ____________ law, ∀ a ∈ S, (a')' = a.
5. _________ and _____________ are fundamental gates.
D. Answer the following questions:
1. What is a truth table?
Ans: Given a Boolean expression, its truth table indicates the value that the expression yields for each combination of the values
of the involved variables.
2. Using truth tables verify the following laws of Boolean algebra:
(i) Involution Law
(ii) Associative Law (Any one)
Ans: (i) Involution Law states that ∀ a ∈ S, (a')' = a
a a' (a')'
0 1 0
1 0 1
(ii) Associative Law: ∀, a, b, c ∈ S, (a + b) + c = a + (b + c)
a b c (a + b) (a + b) + c (b + c) a + (b + c)
0 0 0 0 0 0 0
0 0 1 0 1 1 1
0 1 0 1 1 1 1
0 1 1 1 1 1 1
1 0 0 1 1 0 1
1 0 1 1 1 1 1
1 1 0 1 1 1 1
1 1 1 1 1 1 1
3. Obtain the Boolean expression for the logic circuit shown below:
x
y
F
z
Ans: F = XY ● XZ '
'
Boolean Logic 81

