Boolean Algebra

Multiple choice questions 10. How can a Boolean function be converted from
algebraic expression to a product of max terms.
1. What are universal gates? (a) Using Graphical Representation
(a) AND (b) OR (b) Using Truth table
(c) NAND (d) None of these
(c) Using Canonical Conversion Method
2. The other name of Boolean algebra is
(d) Both b and c
(a) Algebra
11. What is the De Morgan’s theorem ?
(b) Linear algebra
(a) (AB)’ is equal to A’ + B.’
(c) Arithmetic algebra
(b) (A + B)’ is equal to A’ *B
(d) Switching algebra
(c) A’+ B’ is equal to A’B’
3. If we want to perform product of max terms, the
Boolean function must be brought into (d) A’ + B’= A’B’

(a) NAND terms (b) OR terms 12. which is the reduced form of A + BC
(c) NOT terms (d) NAND terms (a) A’B + AB’C
4. Which of the following is the expression for (b) AB + BC
absorption law (c) (A + B) (A + C)
(a) A + AB = A (d) (A + C)B
(b) A + AB = B 13. Which of the following is correct for x.x according
(c) AB + AA’ is equal to A to Boolean Algebra theorems
(d) A + B is equal to B + A (a) x (b) 1
5. X*Y = Y*X is the (c) 0 (d) x’
(a) Commutative law (b) Inverse property 14. What is the symbol of AND operation?
(c) Associative law (d) Identity element (a) (+) (b) (.)
6. Boolean algebra is a set of (c) (-) (d) (/)
(a) Three values (b) Two values 15. In Boolean Algebra, 0 is a
(c) Four values (d) Five values (a) Commutative property
7. To evaluate Boolean expressions, the first operator (b) Additive identity
precedence is (c) Associated identity
(a) Parentheses (b) AND (d) Identity element
(c) OR (d) NOT 16. Which algebraic structure with two Mathematic
8. (A + B + C)’ is equal to operations are used in Boolean algebra
(a) A’B’C’ (b) A’+ B’+ C’ (a) Addition and subtraction
(c) ABC (d) A + B + C (b) Subtraction and multiplication
9. What is the function A’B’C’using theorem and (c) Addition and multiplication
laws ? (d) Addition and division
(a) (A’) + B + C (b) (A + B)’+ C 17. What do we call the logical sum of two or more
(c) A + B + C (d) A’+B’ +C’ logical product terms ?
 (a) Sum of Product SOP 27. (x*y)*z=x*(y*z) is the
(b) Product of Sum POS (a) Commutative property
(c) OR operation (b) Inverse property
(d) NAND operation (c) Identity element
18. Which of the following property is correct for X + (d) Associative property
0=0+X=X? 28. According to Boolean Law, A + 1 = ?
(a) Commutative property (a) 1 (b) A
(b) Inversion property (c) 0 (d) A’
(c) Associative property 29. Which is equal to X.X’.
(d) Identity element
(a) 0 (b) 1
19. Identify the correct identity element w r t addition
(c) X (d) X’
(a) X - 1 (b) x + 1
30. What do we call an Exclusive OR
(c) X - 0 (d) x + 0
(a) Prime function (b) Undefined function
20. What do you understand by Sum of Product?
(c) Even function (d) Odd function
(a) Sum of Minterms
31. X + XY =
(b) Sum of Maxterms
(a) Y (b) 1
(c) Both a and b
(c) 0 (d) X
(d) Max terms
32. Solve Y = AB’ + (A’ + B)C
21. What is the other name of OR relation ?
(a) AB + AC (b) AB’ + C
(a) Logical multiplication
(d) A’B + AC’ (d) AB + A
(b) Logical addition
33. NAND is the complement of
(c) Logical Subtraction
(a) AND (b) OR
(d) None of these
(c) NOT (d) XOR
22. What is the other name of AND relation?
34. What is the complement of NOR ?
(a) Logical multiplication
(a) AND (b) OR
(b) Logical addition
(c) NOT (d) XOR
(c) Logical Subtraction
35. Which of the following logic sense is involved in
(d) None of these
the inverter circuit ?
23. When grouping cells within a K-map, the cells
must be combined in groups of (a) Division (b) Addition

(a) 2 (b) 1,2,4,8 etc (c) Boolean variable (d) Subtraction

(c) 4 (d) 3 36. Simplify the following expressions:

24. NAND and NOR gates are also called Universal F(A, B, C) = S(2, 3, 5, 4)
gates because (a) What will be the smallest number of groups
(a) It can be found in almost all digital circuits. and their types formed for reduction?
(b) It can be used to build all other types of gates. (i) 2 pairs (ii) 1 pair
(c) These are used in all countries of the world. (iii) 4 pairs (iv) 3 pairs
(d) These were the first gates to be integrated. (b) 
The reduced appearance of the Boolean
25. State the Commutative Law of addition for two function given above is:
variables (i) AB + AB (ii) AB + BA
(a) A + B = A.B (b) A + B = B + A (iii) A + B (iv) A
(c) AB = A + B (d) None of these 37. Given the Boolean expression A’B + CD’ identify:
26. (A + B)(A’ *B’) = ? (a) Complement of the expression is
(a) 1 (b) 0 (i) (A’ + B)(C’ + D) (ii) (A + B’)(C’ + D)
(c) AB (d) AB’ (iii) (A’ + B)(C’ + D) (iv) (A + B’)(C + D’)
 (b) The law used: (b) A + (B + C) = (A + B) + C
(i) Distributive Law (c) A + (B + C) = (A + B)(A + C)
(ii) De Morgan Law (d) A + B + C = A + B + C
(iii) Associative Law 47. Name the correct law for X(Y + Z) = XY + XZ.
(iv) Idempotent Law (a) Commutative law
(b) Associative law
Fill in the blanks
(c) Absorption law
38. Logical addition is done by ________operator. (d) Distributive law
(a) OR (b) AND 48. What do you mean by Minterms ?
(c) NOT (d) NOR (a) Product of binary variables
39. According to De Morgan’s Theorem, the (b) Sum of binary variables
complement of a sum of variables is equal to (c) Difference of binary variables
the_____ of the variables. (d) Complement of binary variables
(a) Sum of complement 49. What is Maxterms ?
(b) Complement of product (a) Product of binary variables
(c) Product of complement (b) Sum of binary variables
(d) A sum term (c) Difference of binary variables
40. A mathematical system invented by _______ (d) Complement of binary variables
________ for formulating logical statement with
symbol is called Boolean algebra Match the following
(a) George Boole (b) John Mauchly
50. Match the columns:
(c) J Presper Eckert (d) Robert Noyce
Group A Group B
41. Binary values 0 and 1 used in Boolean algebra
1. an octect (i) 1
called_________________ .
2. a quad (ii) 3
(a) Boolean values (b) Boolean constants
3. a pair (iii) 2
(c) Boolean digits (d) Boolean elements
4. (x’)’ (iv) A
42. The ___________ is inverse of a variable and is
5. A(A + B) (v) x
indicated by a bar over the variable.
(a) 1-(ii), 2-(iii), 3-(i), 4-(v), 5-(iv)
(a) Inversion (b) Complement
(b) 2-(ii), 1-(iii), 3-(v), 4-(i), 5-(iv)
(c) Sum (d) Product
(c) 3-(ii), 4-(iii), 5-(v), 1-(i), 2-(iv)
43. If two or more sum terms are multiplied by
(e) 4-(ii), 5-(iii), 1-(v), 2-(i), 3-(iv)
Boolean multiplication, the final expression is a
________ form. 51. Match the columns:
(a) Product of sum (b) Sum of product Group A Group B

(c) Complement (d) Constant 1. Simplification law (i) SOP and POS
44. ________. gives all the values of logical variables 2. canonical forms of (ii) M.(~M + N) =
Boolean Expres- M.N
and the possible results of given combinations of
sions
values.
3. universal logic (iii) X-NOR
(a) Truth table (b) Operators gates
(c) Expression (d) Complement 4. logic gate that pro- (iv) NAND and
45. OR, AND and NOT are the _______ operations. vides high output NOR
(a) Relational (b) Logical (a) 1-(ii), 2-(i), 3-(iv), 4-(iii)
(c) Arithmetic (d) Literal (b) 1-(i), 2-(ii), 3-(iv), 4-(iii)
46. Associative law of addition is ________ . (c) 1-(ii), 2-(i), 3-(iii), 4-(iv)
(a) A + B = B + A (d) 1-(ii), 2-(iv), 3-(i), 4-(iii)
52. Match the columns: 53. Match the columns:
Group A Group B Group A Group B
1. Addition of vari- (i) C 1. A + 1 = (i) A
ables 2. involution of A (ii) 1
2. C + CD (ii) maxterms 3. A(A + B) = (iii) (AB)’ = A’ + B’
3. OR operation (iii) A + AB = A 4. DeMorgan’s (iv) A
4. Absorption law (iv) Associative theorem
properties (a) 1-(ii), 2-(i), 3-(iv), 4-(iii)
(a) 1-(ii), 2-(i), 3-(iv), 4-(iii) (b) 1-(i), 2-(ii), 3-(iv), 4-(iii)
(b) 1-(i), 2-(ii), 3-(iv), 4-(iii) (c) 1-(ii), 2-(i), 3-(iii), 4-(iv)
(c) 1-(ii), 2-(i), 3-(iii), 4-(iv) (d) 1-(iii), 2-(iv), 3-(i), 4-(ii)
(d) 1-(ii), 2-(iv), 3-(i), 4-(iii)

Answers

Multiple choice questions 10. (d) Both b and c

Explanation: A truth table is a mathematical
1. (c) NAND table used in logic—specifically in connection
Explanation: The NAND gate is a universal gate with Boolean algebra, boolean functions, and
since it can implement the AND, OR and NOT propositional calculus.
functions. Conversion of POS form to standard POS form or
2. (d) Switching algebra Canonical coversion method
3. (b) OR terms 11. (a) (AB)’ is equal to A’+ B’
Explanation: Maxterms. , a sum term in which Explanation: (A.B)’ = A’ + B’
each of the n variables appears once.
(A + B)’ = A’.B’
4. (a) A + AB = A
12. (c) (A + B) (A + C)
Explanation: Absorption law states that (i) X + XY
Explanation: A + (B.C) = (A + B).(A + C) (AND
= X and (ii) X(X + Y) = X.
Distributive Law
5. (a) Commutative law
13. (a) X
Explanation: X • Y = Y • XCommutative Law.
Explanation: (i) X • X = X (ii) X + X = X Idempotent
6. (b) Two values
Law
Explanation: Boolean algebra is the algebra of
14. (a) (AB)’ is equal to A’ + B.’
two-valued logics.
15. (b) Additive identity
7. (a) Parentheses
Explanation: Expressions inside brackets are Explanation: 0 is additive identity as The first
always evaluated first. Boolean identity is that the sum of anything and
zero is the same as the original “anything.”
8. (a) A’B’C’
16. (c) Addition and multiplication
Explanation: 1. (A’B’)’= A + B
2. (AB)’= A’+B’ 17. (b) Product of Sum POS

3. (A + B) = A’B’ Explanation: The logical sum of two or more

logical product terms, is called SOP (i.e. sum of
Thus (A + B + C)’= A’B’C’
product). The logical product of two or more
9. (d) A’+B’ +C’
logical sum terms is called POS (i.e. product of
Explanation: 1. (A’B’)’= A + B sums).
2. (AB)’ = A’ + B’ 18. (a) Commutative property
3. (A + B) = A’B’ Explanation: Commutative Law states that the
Thus A’B’C’ = (A + B + C)’ interchanging of the order of operands in a
 Boolean equation does not change its result. For gate that gives a true (1 or HIGH) output when
example: the number of true inputs is odd.
OR operator ® A + B = B + A 31. (d) X
AND operator ® A * B = B * A) Explanation: X + X•Y = X•(1 + Y) = X•1 = X
19. (d) x + 0 32. (b) AB’ + C
Explanation: A + 0 = A A⋅1 = A - identity element. Explanation: Y = AB’ + (A’ + B)C = AB’ + (AB’)’C =
20. (a) Sum of Minterms (AB’ + C)(AB’ + (AB’)’) = (AB’ + C).1 = (AB’ + C).
21. (b) Logical addition 33. (a) AND
Explanation: The logical OR symbol is used Explanation: NAND gate is actually a combination
in Boolean algebra to indicate an inclusive of two logic gates: AND gate followed by NOT
disjunction between two statements. An gate. So its output is complement of the output of
inclusive disjunction is true if either, or both, of an AND gate.
its components are true. 34. (b) OR
22. (a) Logical multiplication Explanation: The NOR gate represents the
23. (b) 1,2,4,8 etc complement of the OR operation.

Explanation: When grouping cells within a 35. (c) Boolean variable

K-map, the cells can be combined in groups of 2, Explanation: Boolean variables can either be True
4, 8, etc. or False and are stored as 16-bit (2-byte) values.
24. (b) It can be used to build all other types of gates. 36. (a) (i) 2 pairs
Explanation: The NOR gate and NAND gate are (b) (i) AB + AB
universal gates. This means that you can create Explanation:
any logical Boolean expression using only NOR
gates or only NAND gates.
25. (b) A + B = B + A
Explanation: Commutative Law states that the
interchanging of the order of operands in a
Boolean equation does not change its result. For
37. (a) (ii) (A + B’)(C’ + D)
example:
(b) (ii) De Morgan Law
OR operator ® A + B = B + A. AND operator ® A
* B = B * A. Fill in the blanks
26. (b) 0
Explanation: (a + b)(a’ b’) 38. (a) OR
= (a’b’)(a+b) Explanation: Boolean addition is equivalent to the
OR logic function.
= a’b’a+a’b’b
= 0*b’+a’*0 39. (c) Product of complement

= 0+0 (Theorem 3) Explanation: De-Morgan’s Theorems 1. The

complement of a product of variables is equal to
= 0
the sum of the complements of the variables.
27. (d) Associative property
40. (a) George Boole
28. (a) 1
41. (b) Boolean constants
Explanation: A + 1 = 1 - Annulment
Explanation: A Boolean constant can have
29. (a) 0
two values, TRUE and FALSE, where TRUE is
Explanation: X • X’ = 0 X + X’ = 1 Complement equivalent to 1 and FALSE is equivalent to 0.
Law.
42. (a) Inversion
30. (d) Odd function
Explanation: The complement is the inverse of a
Explanation: XOR gate (sometimes EOR, or EXOR variable and is indicated by a bar over variable.
and pronounced as Exclusive OR) is a digital logic
43. (b) Sum of product 47. (b) Associative law
Explanation: The Product of Sum expression is Explanation: Distributive Law – This law permits
equivalent to the logical OR-AND function which the multiplying or factoring out of an expression.
gives the AND Product of two or more OR Sums A(B + C) = A.B + A.C
to produce an output. 48. (d) Complement of binary variables
44. (a) Truth table Explanation: Each minterm = 1 for only one
Explanation: a table that shows the truth-value of combination of values of the variables, = 0
a compound statement for every truth-value of its otherwise.
component statements also : a similar table (as for 49. (a) Product of binary variables
a computer logic circuit) showing the value of the
Explanation: A maxterm is a Boolean expression
output for each value of each input.
resulting in a 0 for the output of a single cell
45. (a) Relational expression, and 1s for all other cells in the
Explanation: The logical operators *AND and Karnaugh map, or truth table.
*OR specify the relationship between operands in
a logical expression. The logical operator *NOT is Match the following
used to negate logical variables or constants.
50. (a) 1-(ii), 2-(iii), 3-(i), 4-(v), 5-(iv)
46. (b) A + (B + C) = (A + B) + C
51. (a) 1-(ii), 2-(i), 3-(iv), 4-(iii)
Explanation: Associative Law – This law allows
the removal of brackets from an expression and 52. (a) 1-(ii), 2-(i), 3-(iv), 4-(iii)
regrouping of the variables. 53. (a) 1-(ii), 2-(i), 3-(iv), 4-(iii)
A + (B + C) = (A + B) + C = A + B + C)