This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Boolean Algebra – Karnaugh Maps”.

1. K-map is used for _______

a) logic minimization

b) expression maximization

c) summing of parity bits

d) logic gate creation

View Answer

Explanation: K-map(Maurice Karnaugh of Bell labs in 1953) is defined as a diagrammatic method for logic minimization and it is a pictorial view of truth table which shows the relationship between inputs and output. It is more efficient than Boolean algebra. K-map is a diagram made up of squares in which each square represents a minterm or maxterm of the logic function.

2. To display time in railway stations which digital circuit is used?

a) seven segment decoder

b) eight segment encoder

c) 8:3 multiplexer

d) 9 bit segment driver

View Answer

Explanation: A seven segment decoder is a digital circuit which is used to construct a common type of digital display device i.e., a set of LED (or LCD) segments that display numbers from 0 through 9 at the command of a four-bit code. Moreover, the behavior of the display driver IC is represented by a truth table with seven outputs.

3. Simplify the expression using K-maps: F(A,B,C,D)=Σ (1,3,5,6,7,11,13,14).

a) AB+BC’D+A’B’C

b) BCD’+A’C’D+BD’

c) A’D+BCD+A’BC+AB’C’

d) AC’D’+BC+A’BD+C’D’

View Answer

Explanation: By solving the given expression we have minterms such as A’D+BCD+A’BC+AB’C’. So, we can get the required expression A’D+BCD+A’BC+AB’C’.

4. When designing a circuit to emulate a truth table, both Product-of-Sums (POS) expressions and Sum-of-Products (SOP) expressions can be derived from?

a) k-map

b) NAND gate

c) NOR gate

d) X-NOR gate

View Answer

Explanation: A Karnaugh map can be used to build the appropriate POS expression for designing a circuit to form the truth table. Karnaugh maps are not limited to SOP expressions only for minimizing boolean functions.

5. Simplify the expression using K-maps: F(A,B,C) = Σ (1,3,5,6,7).

a) AC’+B’

b) AB+C

c) AB’+B’C’

d) A’BC+B’C+AC

View Answer

Explanation: By solving the given expression, the minterms are: C and AB. Hence, we can get the required expression C+AB.

6. Simplify the expression using K-maps: F(A,B,C) = π(0,2,4,5,7).

a) (x+y)(y+z)(x+z)(x’+z’)

b) (x+z’)(y+z)(x+y)

c) (x+y’+z)(x+z’)

d) (y’+z’)(x’+y)(z+y’)

View Answer

Explanation: By solving the given expression, the maxterms are: (x+y), (x’+y), (x+z) and (x’+z’). Hence, we can get required expression (x+y)(x’+y)(x+z)(x’+z’).

7. Addition of two or more bits produces how many bits to construct a logic gate?

a) 108

b) 2

c) 32

d) 64

View Answer

Explanation: Addition of bits requires carry-in and carry-out bits. Addition of two terms (bits) a and b, and a carry-in bit Cin is required to compute a sum bit S and a carry-out bit Cout. Hence, two bits are produced in general.

8. Use Karnaugh map to find the simplified expression of the function: F = x’yz + xy + xy’z’.

a) xz’+y’z’

b) xy’z+xy

c) y’z+x’y+z

d) yz+xy+xy’z

View Answer

Explanation: F = x’yz + xyz + xy z’ + xy’z’ is the canonical form for the function. Now, using k-map the minimal form must be: yz+xy+xy’z.

9. Who has invented K-map?

a) Maurice Karnaugh

b) Edward Veitch

c) George Boole

d) Adam Smith

View Answer

Explanation: The Karnaugh map (KM or K-map) is invented by Maurice Karnaugh in 1953 that is a method of simplifying Boolean expressions.

10. In Gray coding, the adjacent code values differ by _______

a) single bit

b) 3 bits

c) 10 bits

d) 0 bit

View Answer

Explanation: In Gray coding, the adjacent code values differ only by a single bit. If the given code-word is 01, then the previous and the next code-words are to be 11 or 00 but cannot be 10 in any case. Each cell within a K-map has a definite place-value which is obtained by using this encoding technique. The rows and the columns of the table use Gray code-labeling which in turn represents the values of the corresponding input variables and each K-map cell can be addressed using a unique Gray Code-Word.

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