Boolean Algebra and Logic Simplification MCQs : This section focuses on the "Boolean Algebra and Logic Simplification". These Multiple Choice Questions (MCQs) should be practiced to improve the Boolean Algebra and Logic Simplification skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.
How many gates would be required to implement the following Boolean expression after simplification? XY + X(X + Z) + Y(X + Z)
Which Boolean algebra property allows us to group operands in an expression in any order without affecting the results of the operation [for example, A + B = B + A]?
Use Boolean algebra to find the most simplified SOP expression for F = ABD + CD + ACD + ABC + ABCD.
A. F = ABD + ABC + CD
B. F = CD + AD
C. F = BC + AB
D. F = AC + AD
The commutative law of Boolean addition states that A + B = A × B.
Which of the following is an important feature of the sum-of-products (SOP) form of expression?
A. All logic circuits are reduced to nothing more than simple AND and OR gates.
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.
Which of the following expressions is in the sum-of-products (SOP) form?
A. (A + B)(C + D)
D. AB + CD
What is the primary motivation for using Boolean algebra to simplify logic expressions?
A. It may make it easier to understand the overall function of the circuit.
B. It may reduce the number of gates.
C. It may reduce the number of inputs required.
D. all of the above
Occasionally, a particular logic expression will be of no consequence in the operation of a circuit, such as a BCD-to-decimal converter. These result in ________terms in the K-map and can be treated as either ________ or ________, in order to ________ the resulting term.
A. don't care, 1s, 0s, simplify
B. spurious, ANDs, ORs, eliminate
C. duplicate, 1s, 0s, verify
D. spurious, 1s, 0s, simplify
The expression W(X + YZ) can be converted to SOP form by applying which law?
A. associative law
B. commutative law
C. distributive law
D. none of the above
Which of the examples below expresses the distributive law of Boolean algebra?
A. (A + B) + C = A + (B + C)
B. A(B + C) = AB + AC
C. A + (B + C) = AB + AC
D. A(BC) = (AB) + C
Which of the following combinations cannot be combined into K-map groups?
A. corners in the same row
B. corners in the same column
D. overlapping combinations
AC + ABC = AC
The NAND or NOR gates are referred to as "universal" gates because either:
A. can be found in almost all digital circuits
B. can be used to build all the other types of gates
C. are used in all countries of the world
D. were the first gates to be integrated
An OR gate with schematic "bubbles" on its inputs performs the same functions as a(n)________ gate.
A Karnaugh map is a systematic way of reducing which type of expression?
B. exclusive NOR
D. those with overbars
Which of the examples below expresses the commutative law of multiplication?
A. A + B = B + A
B. AB = B + A
C. AB = BA
D. AB = A × B
The commutative law of addition and multiplication indicates that:
A. we can group variables in an AND or in an OR any way we want
B. an expression can be expanded by multiplying term by term just the same as in ordinary algebra
C. the way we OR or AND two variables is unimportant because the result is the same
D. the factoring of Boolean expressions requires the multiplication of product terms that contain like variables
Which statement below best describes a Karnaugh map?
A. A Karnaugh map can be used to replace Boolean rules.
B. The Karnaugh map eliminates the need for using NAND and NOR gates.
C. Variable complements can be eliminated by using Karnaugh maps.
D. Karnaugh maps provide a cookbook approach to simplifying Boolean expressions.
Converting the Boolean expression LM + M(NO + PQ) to SOP form, we get ________.
A. LM + MNOPQ
B. L + MNO + MPQ
C. LM + M + NO + MPQ
D. LM + MNO + MPQ
The systematic reduction of logic circuits is accomplished by:
A. using Boolean algebra
B. symbolic reduction
C. TTL logic
D. using a truth table
When grouping cells within a K-map, the cells must be combined in groups of ________.
B. 1, 2, 4, 8, etc.
An AND gate with schematic "bubbles" on its inputs performs the same function as a(n)________ gate.
How many gates would be required to implement the following Boolean expression before simplification? XY + X(X + Z) + Y(X + Z)