Deck 4: Boolean Algebra and Logic Simplification

Question 1

Boolean multiplication is symbolized by A + B.

Answer 1

False

Question 2

In Boolean algebra, 1 · 0 = 0.

Answer 2

True

Question 3

The complement of 1 is 0.

Answer 3

True

Question 4

The Boolean expression X = ABC describes a three- input AND gate.

Question 5

When a two- input NAND gate has inputs of 1 and 0, the output is 0.

Question 6

The commutative law of Boolean algebra states that A + B = A · B.

Question 7

-According to the distributive law, Figure 4- 1 shows one possible logic implementation of the expression X = A(B+C).

Question 8

-For the circuit in Figure 4- 1, X = 0 whenever A = 0, regardless of the levels applied to inputs B and C.

Question 9

DeMorgan's theorem states that

Question 10

DeMorgan's theorem states that

Question 11

The Karnaugh maps provide graphic approaches to simplifying Boolean expressions.

Question 12

The Sum- of- Product (SOP) form is a standard form of Boolean expression.

Question 13

The Product- of- Sum (POS) form is a standard form of Boolean expression.

Question 14

When mapping an SOP expression using a Karnaugh map a 0 is placed in each cell corresponding to the value of the product term.

Question 15

Which of the following is a correct form of Boolean addition?

A) 0 · 0 = 0
B) 0 · 1 = 0
C) 0 + 1 = 0
D) 0 + 1 = 1

Question 16

Which of the following is a correct form of Boolean multiplication?

A) 0 + 1 = 1
B) 0 · 1 = 0
C) 0 · 1 = 1
D) 0 + 1 = 0

Question 17

In Boolean algebra, the expression "_________"means the complement of A.

A) not A
B) negative A
C) inverse A
D) A negative

Question 18

The symbol shown below is a(n)______ and the output will be______ for the input shown.

A) inverter, 1
B) inverter,
C) buffer, not A
D) buffer, 1

Question 19

-The symbol shown in Figure 4- 2 is a(n)________gate.

A) AND- OR
B) AND
C) OR
D) NAND

Question 20

-The Boolean expression for the symbol in Figure 4- 2 is _______.

A) X = (A +B) (B +C)
B) X = ABCD
C) X = A + B + C + D
D) X = AB + BC

Question 21

-The symbol shown in Figure 4- 3 is a(n) _______gate.

A) Exclusive- OR
B) AND- OR
C) AND
D) OR

Question 22

-The Boolean expression for the symbol in Figure 4- 3 is .

A) X = AB + BC
B) X = A + B + C + D
C) X = (A +B) (B + C)
D) X = ABCD

Question 23

The figure below represents one line from the truth table for a two- input NAND gate.

For the inputs shown, what is the value of X?

A) B
B) 1
C) 0
D) not A

Question 24

The expression for a 3- input NOR gate is _________.

A) X = A/B/C
B) X = A · B · C
C)
D)

Question 25

Which of the examples below expresses the commutative law of multiplication?

A) AB = BA
B) AB = A ÷ B
C) AB = B + A
D) A + B = B + A

Question 26

Which of the examples below expresses the associative law of addition?

A) A(BC) = (AB) + C
B) ABC = A + B + C
C) A + (B + C) = (A + B) + C
D) A + (B + C) = A + (BC)

Question 27

Which of the examples below expresses the distributive law?

A) (A + B) + C = A + (B + C)
B) A + (B + C) = AB + AC
C) A(BC) = (AB) + C
D) A(B + C) = AB + AC

Question 28

Which rule of Boolean algebra does the figure below illustrate?

A) A · 1 = A
B) A + 1 = 1
C) A · 0 = 0
D) A + 0 = A

Question 29

Which of the following is a form of DeMorgan's theorem?

A) X(l) = X
B)
C) X + 0 = 0
D)

Question 30

Which of the figures is the DeMorgan equivalent of the Reference Circuit shown below?

A) Figure (A)
B) Figure (B)
C) Figure (C)
D) Figure (D)

Question 31

According to DeMorgan's theorem, equals _________ .

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

Question 32

For the network shown below, the boolean expression for X is _________.

A) D(A + B + C)
B) ((A + B) · C) + D
C) (AC + BC)D
D) A + BC + D

Question 33

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

A) (A + B)(C + D)
B) AB(CD)
C) AB + CD
D) (AB)(CD)

Question 34

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

A) The maximum number of gates that any signal must pass through is reduced by a factor of two.
B) The delay times are greatly reduced over other forms.
C) No signal must pass through more than 2 gates (not including inverters).
D) All logic circuits are reduced to nothing more than simple AND and OR gates.

Question 35

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

A) AB + CD
B) AB(CD)
C) (A + B)(C + D)
D) (AB)(CD)

Question 36

What is the primary motivation for using Boolean algebra to simplify logic expressions?

A) It may reduce the number of inputs required.
B) It may reduce the number of gates.
C) It may make it easier to understand the circuit.
D) All of the above are correct.

Question 37

Which statement below best describes a Karnaugh map?

A) The Karnaugh map eliminates the need for using NAND and NOR gates.
B) Karnaugh maps provide a graphic approach to simplifying Boolean expressions.
C) A Karnaugh map can be used to replace Boolean rules.
D) Variable complements can be eliminated by using Karnaugh maps.

Question 38

Which of the Karnaugh maps below represents the expression, X = AC + BC + B?

A) Figure I
B) Figure II
C) Figure III
D) Figure IV

Question 39

The simplest Boolean expression for the Karnaugh map below is _______.

A)
B)
C) X = AC + B
D)

Question 40

When grouping cells within a Karnaugh map, the cells must be combined in groups of _________ .

A) 2s
B) 4s
C) 3s
D) 2, 4, 8, etc.

Question 41

Occasionally, a particular logic expression will be of no consequence in the operation of a circuit, such as in a BCD- to- decimal converter. These result in_________terms in the K- map and can be treated as either _________or_________.

A) spurious, 1s, 0s,
B) don't care, 1s, 0s,
C) spurious, ANDs, ORs,
D) duplicate, 1s, 0s,

Question 42

Which of the following combinations cannot be combined into Karnaugh- map groups?

A) Corners in the same row
B) Diagonal corners
C) Corners in the same column
D) Overlapping combinations

Question 43

A Karnaugh map _________ .

A) provides a means of reducing complex Boolean expressions
B) gives an overall picture of how the signals flow through the logic circuit
C) produces the simplest sum- of- products expression
D) allows any circuit to be implemented with just AND and OR gates

Question 44

Reduce the following equation using Boolean Algebra.

Question 45

The Quine- McCluskey method of reducing complex Boolean expressions is used in place of a Karnaugh map when the original expression contains_________ or more variables.

A) 5
B) 8
C) 6
D) 4

Question 46

The Quine- McCluskey method___________

A) lends itself to computer reduction of Boolean expressions
B) can, under certain circumstances, provide incorrect results
C) requires fewer steps than Karnaugh mapping
D) is described by all of the above