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