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
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
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).
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?
b) NAND gate
c) NOR gate
d) X-NOR gate
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).
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).
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?
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’.
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
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
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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