Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
The simplest Boolean expression for the Karnaugh map below is ________.
1)
A)
ABC+ ABC + ABC
B)
X = AC + B
C)
X = AB
D)
AB +AB
2)
Which of the figures is the DeMorgan equivalent of the Reference Circuit shown below?
2)
A)
Figure (A)
B)
Figure (B)
C)
Figure (C)
D)
Figure (D)
3)
The Quine–McCluskey method ________.
3)
A)
lends itself to computer reduction of Boolean expressions
B)
requires fewer steps than Karnaugh mapping
C)
can, under certain circumstances, provide incorrect results
D)
is described by all of the above
4)
Which rule of Boolean algebra does the figure below illustrate?
4)
A)
A + 1 = 1
B)
A · 1 = A
C)
A + 0 = A
D)
A · 0 = 0
5)
For the network shown below, the boolean expression for X is ________.
5)
A)
(AC + BC)D
B)
A + BC + D
C)
D(A + B + C)
D)
((A + B) · C) + D
6)
Which statement below best describes a Karnaugh map?
6)
A)
Variable complements can be eliminated by using Karnaugh maps.
B)
The Karnaugh map eliminates the need for using NAND and NOR gates.
C)
Karnaugh maps provide a graphic approach to simplifying Boolean expressions.
D)
A Karnaugh map can be used to replace Boolean rules.
7)
What is the primary motivation for using Boolean algebra to simplify logic expressions?
7)
A)
It may make it easier to understand the circuit.
B)
It may reduce the number of inputs required.
C)
It may reduce the number of gates.
D)
All of the above are correct.
8)
Which of the following is a correct form of Boolean multiplication?
8)
A)
0 · 1 = 0
B)
0 + 1 = 0
C)
0 · 1 = 1
D)
0 + 1 = 1
A
9)
Which of the following expressions is in the sum–of–products form?
9)
A)
AB(CD)
B)
(AB)(CD)
C)
(A + B)(C + D)
D)
AB + CD
D
10)
The Boolean expression for the symbol in Figure 4–3 is ________.
10)
A)
X = (A + B)(B + C)
B)
X = ABCD
C)
X = AB + BC
D)
X = A + B + C + D
D
D
11)
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.
11)
A)
8
B)
5
C)
4
D)
6
12)
When grouping cells within a Karnaugh map, the cells must be combined in groups of ________.
12)
A)
3s
B)
2s
C)
2, 4, 8, etc.
D)
4s
13)
Which of the Karnaugh maps below represents the expression, X = AC + BC + B?
13)
A)
Figure I
B)
Figure II
C)
Figure III
D)
Figure IV
4
14)
In Boolean algebra, the expression “________” means the complement of A.
14)
A)
inverse A
B)
A negative
C)
not A
D)
negative A
15)
The expression for a 3–input NOR gate is ________.
15)
A)
X =A+B+C
B)
X =A/B/C
C)
X =A · B · C
D)
X =A + B + C
D
16)
The Boolean expression for the symbol in Figure 4–2 is ________.
16)
A)
X = ABCD
B)
X = (A + B)(B + C)
C)
X = A + B + C + D
D)
X = AB + BC
A
17)
Which of the following is a form of DeMorgan’s theorem?
17)
A)
X + 0 = 0
B)
XY =X+Y
C)
X(l) = X
D)
X + Y =X+Y
B
18)
Which of the following expressions is in the product–of sums form?
18)
A)
AB(CD)
B)
AB + CD
C)
(A + B)(C + D)
D)
(AB)(CD)
C
C
19)
Which of the examples below expresses the commutative law of multiplication?
19)
A)
AB = B + A
B)
AB = BA
C)
AB = A B
D)
A + B = B + A
20)
The symbol shown in Figure 4–3 is a(n) ________ gate.
20)
A)
Exclusive–OR
B)
OR
C)
AND–OR
D)
AND
21)
_______
According to DeMorgan‘s theorem, (AB) + C equals ________.
21)
A)
AB +C
B)
ABC
C)
(A + B)C
D)
AB + C
22)
The symbol shown below is a(n) ________, and the output will be ________ for the input shown.
22)
A)
inverter, A
B)
inverter, 1
C)
buffer, not A
D)
buffer, 1
23)
Which of the following is a correct form of Boolean addition?
23)
A)
0 · 0 = 0
B)
0 + 1 = 1
C)
0 + 1 = 0
D)
0 · 1 = 0
24)
Which of the examples below expresses the distributive law?
24)
A)
(A + B) + C = A + (B + C)
B)
A + (B + C) = AB + AC
C)
A(B + C) = AB + AC
D)
A(BC) = (AB) + C
25)
Which of the following is an important feature of the sum–of–products form of expressions?
25)
A)
No signal must pass through more than 2 gates (not including inverters).
B)
The delay times are greatly reduced over other forms.
C)
All logic circuits are reduced to nothing more than simple AND and OR gates.
D)
The maximum number of gates that any signal must pass through is reduced by a factor of
two.
26)
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 ________.
26)
A)
spurious, 1s, 0s,
B)
don’t care, 1s, 0s,
C)
duplicate, 1s, 0s,
D)
spurious, ANDs, ORs,
Figure 4–2
27)
The symbol shown in Figure 4–2 is a(n) ________ gate.
27)
A)
AND
B)
OR
C)
AND–OR
D)
NAND
28)
Which of the following combinations cannot be combined into Karnaugh–map groups?
28)
A)
Overlapping combinations
B)
Diagonal corners
C)
Corners in the same column
D)
Corners in the same row
29)
Which of the examples below expresses the associative law of addition?
29)
A)
A(BC) = (AB) + C
B)
A + (B + C) = (A + B) + C
C)
A + (B + C) = A + (BC)
D)
ABC = A + B + C
30)
A Karnaugh map ________.
30)
A)
provides a means of reducing complex Boolean expressions
B)
allows any circuit to be implemented with just AND and OR gates
C)
gives an overall picture of how the signals flow through the logic circuit
D)
produces the simplest sum–of–products expression
31)
The figure below represents one line from the truth table for a two–input NAND gate.
A B X
1 0 ?
For the inputs shown, what is the value of X?
31)
A)
1
B)
0
C)
B
D)
not A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
32)
Reduce the following equation using Boolean Algebra.
A B C +A B C+ A B C +A B C + A B C
32)
TRUE/FALSE. Write ‘T’ if the statement is true and ‘F’ if the statement is false.
33)
When mapping an SOP expression using a Karnaugh map a 0 is placed in each cell corresponding
to the value of the product term.
33)
34)
According to the distributive law, Figure 4–1 shows one possible logic implementation of the
expression X = A(B+C).
34)
35)
The Product–of–Sum (POS) form is a standard form of Boolean expression.
35)
36)
DeMorgan‘s theorem states that X + Y =X Y.
36)
37)
DeMorgan‘s theorem states that XY = X + Y.
37)
38)
The complement of 1 is 0.
38)
39)
In Boolean algebra, 1 · 0 = 0.
39)
40)
The Boolean expression X = ABC describes a three–input AND gate.
40)
41)
Boolean multiplication is symbolized by A + B.
41)
42)
The Karnaugh maps provide graphic approaches to simplifying Boolean expressions.
42)
43)
The Sum–of–Product (SOP) form is a standard form of Boolean expression.
43)
Figure 4–1
44)
For the circuit in Figure 4–1, X = 0 whenever A = 0, regardless of the levels applied to inputs B and
C.
44)
45)
When a two–input NAND gate has inputs of 1 and 0, the output is 0.
45)
46)
The commutative law of Boolean algebra states that A + B = A · B.
46)
11
Answer Key
Testname: C4
Answer Key
Testname: C4