Discrete Mathematics Questions and Answers – Boolean Algebra – Karnaugh Maps

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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

Answer: a
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.
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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

Answer: a
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

Answer: c
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

Answer: a
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

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

Answer: a
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

Answer: b
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

Answer: d
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

Answer: a
Explanation: The Karnaugh map (KM or K-map) is invented by Maurice Karnaugh in 1953 that is a method of simplifying Boolean expressions.
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10. In Gray coding, the adjacent code values differ by _______
a) single bit
b) 3 bits
c) 10 bits
d) 0 bit
View Answer

Answer: a
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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn