**Digital Circuits Questions and Answers – K-Map Simplification**

This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “K-Map Simplification”.

**1. Which statement below best describes a Karnaugh map?**

a) It is simply a rearranged truth table

b) The Karnaugh map eliminates the need for using NAND and NOR gates

c) Variable complements can be eliminated by using Karnaugh maps

d) A Karnaugh map can be used to replace Boolean rules

**Answer:**a

**Explanation:**K-map is simply a rearranged truth table. It is a pictorial representation of truth table having a specific number of cells or squares, where each cell represents a Maxterm or a Minterm.

**2. Which of the examples below expresses the commutative law of multiplication?**

a) A + B = B + A

b) A • B = B + A

c) A • (B • C) = (A • B) • C

d) A • B = B • A

**Answer: d**

**Explanation:**The commutative law of multiplication is (A * B) = (B * A).

The commutative law of addition is (A + B) = (B + A).

**3. The Boolean expression Y = (AB)’ is logically equivalent to what single gate?**

a) NAND

b) NOR

c) AND

d) OR

**Answer:**a

**Explanation:**If A and B are the input for AND gate the output is obtained as AB and after inversion we get (AB)’, which is the expression of NAND gate. NAND gate produces high output when any of the input is 0 and produces low output when all inputs are 1.

**4. The observation that a bubbled input OR gate is interchangeable with a bubbled output AND gate is referred to as:**

a) A Karnaugh map

b) DeMorgan’s second theorem

c) The commutative law of addition

d) The associative law of multiplication

**Answer:**b

**Explanation:**DeMorgan’s Law: ~(P+Q) <=> (~P).(~Q) Also,

~(P.Q) <=> (~P)+(~Q).

**5. The systematic reduction of logic circuits is accomplished by:**

a) Symbolic reduction

b) TTL logic

c) Using Boolean algebra

d) Using a truth table

**Answer:**c

**Explanation:**The systematic reduction of logic circuits is accomplished by using boolean algebra.

**6. Each “1” entry in a K-map square represents:**

a) A HIGH for each input truth table condition that produces a HIGH output

b) A HIGH output on the truth table for all LOW input combinations

c) A LOW output for all possible HIGH input conditions

d) A DON’T CARE condition for all possible input truth table combinations

**Answer:**a

**Explanation:**Each “1” entry in a K-map square represents a HIGH for each input truth table condition that produces a HIGH output. Thus, it represents a minterm.

**7. Each “0” entry in a K-map square represents:**

a) A HIGH for each input truth table condition that produces a HIGH output

b) A HIGH output on the truth table for all LOW input combinations

c) A LOW output for all possible HIGH input conditions

d) A DON’T CARE condition for all possible input truth table combinations

**Answer:**a

**Explanation:**Each “0” entry in a K-map square represents a LOW output for all possible HIGH input conditions. Thus, it represents a Maxterm.

**8. Which of the following statements accurately represents the two BEST methods of logic circuit simplification?**

a) Actual circuit trial and error evaluation and waveform analysis

b) Karnaugh mapping and circuit waveform analysis

c) Boolean algebra and Karnaugh mapping

d) Boolean algebra and actual circuit trial and error evaluation

**Answer:**c

**Explanation:**The two BEST methods of logic circuit simplification are Boolean algebra and Karnaugh mapping. Boolean Algebra uses the Laws of Boolean Algebra for minimization of Boolean expressions while Karnaugh Map is a pictorial representation and reduction of the Boolean expression.

**9. Looping on a K-map always results in the elimination of __________**

a) Variables within the loop that appear only in their complemented form

b) Variables that remain unchanged within the loop

c) Variables within the loop that appear in both complemented and uncomplemented form

d) Variables within the loop that appear only in their uncomplemented form

**Answer:**c

**Explanation:**Looping on a K-map always results in the elimination of variables within the loop that appear in both complemented and uncomplemented form.

**10. Which of the following expressions is in the sum-of-products form?**

a) (A + B)(C + D)

b) (A * B)(C * D)

c) A* B *(CD)

d) A * B + C * D

**Answer:**d

**Explanation:**Sum of product means that it is the sum of all product terms. Thus, the number is multiplied first and then it is added: A * B + C * D.

**11. Which of the following is an important feature of the sum-of-products form of expressions?**

a) All logic circuits are reduced to nothing more than simple AND and OR operations

b) The delay times are greatly reduced over other forms

c) No signal must pass through more than two gates, not including inverters

d) The maximum number of gates that any signal must pass through is reduced by a factor of two

**Answer:**a

**Explanation:**An important feature of the sum-of-products form of expressions in the given option is that all logic circuits are reduced to nothing more than simple AND and OR operations. Sum Of Product means it is the sum of product terms containing variables in complemented as well as uncomplemented forms.

**12. Which of the following expressions is in the product-of-sums form?**

a) (A + B)(C + D)

b) (AB)(CD)

c) AB(CD)

d) AB + CD

**Answer: **a

**Explanation:** (A + B)(C + D) represents the product-of-sums form.

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