Boolean Algebra and Logic Simplification

Q1: Determine the values of A, B, C, and D that make the product term equal to 1.

A A = 0, B = 1, C = 0, D = 1

B A = 0, B = 0, C = 0, D = 1

C A = 1, B = 1, C = 1, D = 1

D A = 0, B = 0, C = 1, D = 0

Q2:
Convert the following SOP expression to an equivalent POS expression.

A

B

C

D

Q3: 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

Q4: For the SOP expression , how many 1s are in the truth table's output column?

A 1

B 2

C 3

D 5

Q5: 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

Q6: Determine the values of A, B, C, and D that make the sum term equal to zero.

A A = 1, B = 0, C = 0, D = 0

B A = 1, B = 0, C = 1, D = 0

C A = 0, B = 1, C = 0, D = 0

D A = 1, B = 0, C = 1, D = 1

Q7: Applying the distributive law to the expression , we get ________.

A

B

C

D

Q8: AC + ABC = AC

A True

B False

Q9: When grouping cells within a K-map, the cells must be combined in groups of ________.

A 2s

B 1, 2, 4, 8, etc.

C 4s

D 3s

Q10: For the SOP expression , how many 0s are in the truth table's output column?

A zero

B 1

C 4

D 5

Q11: 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

Q12:
Derive the Boolean expression for the logic circuit shown below:

A

B

C

D

Q13: Which output expression might indicate a product-of-sums circuit construction?

A

B

C

D

Q14:
Mapping the SOP expression , we get ________.

A (A)

B (B)

C (C)

D (D)

Q15: Which of the following expressions is in the sum-of-products (SOP) form?

A (A + B)(C + D)

B (A)B(CD)

C AB(CD)

D AB + CD

Q16: 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

Q17: 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

Q18: Applying DeMorgan's theorem to the expression , we get ________.

A

B

C

D

Q19: The commutative law of Boolean addition states that A + B = A × B.

A True

B False

Q20: An OR gate with schematic "bubbles" on its inputs performs the same functions as a(n)________ gate.

A NOR

B OR

C NOT

D NAND

Q21: Applying DeMorgan's theorem to the expression , we get ________.

A

B

C

D

Q22: The systematic reduction of logic circuits is accomplished by:

A using Boolean algebra

B symbolic reduction

C TTL logic

D using a truth table

Q23: 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]?

A associative

B commutative

C Boolean

D distributive

Q24: How many gates would be required to implement the following Boolean expression after simplification? XY + X(X + Z) + Y(X + Z)

A 1

B 2

C 4

D 5

Q25: When are the inputs to a NAND gate, according to De Morgan's theorem, the output expression could be:

A X = A + B

B

C X = (A)(B)

D

Q26: 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

Q27: Applying DeMorgan's theorem to the expression , we get ________.

A

B

C

D

Q28:
Which is the correct logic function for this PAL diagram?

A

B

C

D

Q29: An AND gate with schematic "bubbles" on its inputs performs the same function as a(n)________ gate.

A NOT

B OR

C NOR

D NAND

Q30:
Derive the Boolean expression for the logic circuit shown below:

A

B

C

D

Q31: The truth table for the SOP expression  has how many input combinations?

A 1

B 2

C 4

D 8

Q32: A truth table for the SOP expression has how many input combinations?

A 1

B 2

C 4

D 8

Q33: Which of the following combinations cannot be combined into K-map groups?

A corners in the same row

B corners in the same column

C diagonal

D overlapping combinations

Q34:
From the truth table below, determine the standard SOP expression.

A

B

C

D

Q35: Determine the binary values of the variables for which the following standard POS expression is equal to 0. 

A (0 + 1 + 0)(1 + 0 + 1)

B (1 + 1 + 1)(0 + 0 + 0)

C (0 + 0 + 0)(1 + 0 + 1)

D (1 + 1 + 0)(1 + 0 + 0)

Q36: 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

Q37:
Mapping the SOP expression , we get ________.

A (A)

B (B)

C (C)

D (D)

Q38: 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.

Q39: One of De Morgan's theorems states that . Simply stated, this means that logically there is no difference between:

A a NOR and an AND gate with inverted inputs

B a NAND and an OR gate with inverted inputs

C an AND and a NOR gate with inverted inputs

D a NOR and a NAND gate with inverted inputs

Q40: How many gates would be required to implement the following Boolean expression before simplification? XY + X(X + Z) + Y(X + Z)

A 1

B 2

C 4

D 5

Q41: The Boolean expression  is logically equivalent to what single gate?

A NAND

B NOR

C AND

D OR

Q42: 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

Q43: 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

Q44: 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.

Q45: A Karnaugh map is a systematic way of reducing which type of expression?

A product-of-sums

B exclusive NOR

C sum-of-products

D those with overbars

Q46: Applying DeMorgan's theorem to the expression , we get ________

A

B

C

D


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