Boolean Algebra and Logic
Simplifying (AB)′ + A′B to most basic form yields which of the following expressions? A′ B′ A + B B (AB)′
(AB)'
Given the function F(A, B, X, Y) = AB + X′Y, the most simplified Boolean representation for F′ is: (AB)′ + (X′Y) A′B′ + XY′ (A′+ B′)(X + Y′) (AB + X′Y)′ (AB)′(X′Y)′
(A′+ B′)(X + Y′)
Which logic circuit represents the Boolean expression (a) (b) (c) (d)
(b)
Find the most simplified form of the following expression: C + (BC)'
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An equivalent representation for the Boolean expression A + A′ is: 1 0 A A′ A′A
1
An equivalent representation for the Boolean expression A′ + 1 is: A A′ 1 0
1
Find the most simplified form of the following expression: (AB)'(A' + B)(B' + B)
1
Find the most simplified form of the following expression: C + (BC)'
1
Simplify the following expression: Y = (A' + B)' + BC' + ((A' + B)' · (C + D))' 0 1 A'B' + BC' + AB' + C'D' AB' + BC' + A'BC'D'
1
Find the most simplified form of the following expression: (AB)'(A' + B)(B' + B)
??
Simplification of the Boolean expression AB + A(BC)′ yields which of following results? A BC B AB (BC)′
A
Simplification of the Boolean expression (A + B + C) + (A + B + C)′(D + E) yields which of the following results? A + B + C D + E A′B′C′ D′E′ A + B + C + D + E
A + B + C + D + E
Find the most simplified form of the following expression: A'(A + B) + (B + AA)(A + B')
A+B
Simplification of the Boolean expression (A+B+C)(D+E)′ + (A+B+C)(D+E) yields which of the following results? A + B + C D + E A′B′C′ D′E′ None of the above
A+B+C
Find the most simplified form of the following expression: (A + C)(AD + AD') + AC + C
A+C
Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results? ABCDEF AB AB + CD + EF A + B + C + D + E + F A + B(C + D(E + F))
AB
The Boolean equation for the logic symbol is
ABC
The logic symbol drawn is that of the:
AND function
In conventional logic circuits, binary 1 represents: the presence of a signal. the occurrence of some event. a high voltage level. All of these choices are correct
All of these choices are correct
The logic function(s) used by PLCs is (are): AND OR NOT All of these choices are correct
All of these choices are correct
Simplification of the Boolean expression (A + B)′(C + D + E)′ + (A + B)′ yields which of the following results? A + B A′B′ C + D + E C′D′E′ A′B′C′D′E′
A′B'
Find the most simplified form of the following expression: BC + BC' + BA
B
Simplify the following expression: DC + (DC + CAA)D' C+AD A+C'+D' CA+CD C+D'
C+D'
Given that F = (A + B′ + C)(D + E), which of the following represents the only correct expression for F′? F′ = A′BC′ + D′ + E′ F′ = AB′C + DE F′ = (A′ + B + C′)(D′ + E′) F′ = A′BC′ + D′E′ F′ = (A + B′ + C)(D′ + E′)
F′ = A′BC′ + D′E′
Given that F = A′B′ + C′ + D′ + E′, which of the following represent the correct expression for F′? F′= A + B + C + D + E F′= ABCDE F′= AB + CDE F′= AB + C′ + D′ + E′ F′= (A + B)CDE
F′= (A + B)CDE
Inverting the output of an OR gate will result in creating a NOR gate. true false
Inverting the output of an OR gate will result in creating a NOR gate. true false
The logic symbol drawn is that of the: AND function. OR function. NOR function. NAND function
NAND Fuction
The logic symbol drawn is that of the: NOT function. NOR function. NAND function. OR function.
NOT function
If you want to know when one or both matching bits in two different words are ON, you would use the logic instruction. AND XOR OR NOT
OR
The logic symbol shown is that of the:
OR function
The Boolean expression for the logic circuit drawn is: Y = ABC Y = A + B + C Y = (A + B)C Y = AB + C
Y = AB + C
The Boolean expression for the logic circuit drawn is: Y=(AB)(CD) Y=(A+B+C)D Y=ABC+D Y=ABC+D
Y=(A+B+C)D
Which logic circuit represents the Boolean expression Y = A(BC + D) ?] (a) (b) (c) (d)
a
An OR gate operates on the same principle as: a series circuit. a parallel circuit. a series-parallel circuit. None of these choices are correct
a parallel circuit.
An AND gate operates on the same principle as: a series circuit. a parallel circuit. a series-parallel circuit. None of these choices are correct
a series circuit
The Boolean equation for the logic symbol is: A = Y A = B a=y A=y
a=y
A NOR gate is: an AND gate with an inverter connected to the output. an OR gate with an inverter connected to the output. equivalent to a series circuit. equivalent to a parallel circuit.
an OR gate with an inverter connected to the output.
The binary concept makes use of the fact that certain information: can exist in one of two possible states. can be broken down into smaller units for easier analysis. can be divided into two or more categories. can be divided into two, or multiples of two, categories.
can exist in one of two possible states.
A NOT function is used when a logic 1 must ________ some device. activate deactivate switch light
deactivated
A two input OR function, expressed as a Boolean equation, would be Y= AB. true false
f
All gates are devices that have one input with which they perform logic decisions and produce a result at one or more of their outputs. true false
f
All inputs to a NAND gate must be 1 to produce a 1 output. true false
f
All inputs to a NOR gate must be 1 to produce a 1 output. true false
f
The AND function, implemented using switches, will mean switches connected in parallel. true false
f
The output of the NAND gate is exactly the opposite of the OR gate for the same combinations of inputs. true false
f
The output of the NOR gate is exactly the same as the AND gate. true false
f
When any of the inputs are 1 for a NAND gate, the output will be 0. true false
f
The + symbol is used to express the AND operation. true false
false
The basic rule for an AND gate is: if all inputs are 1, the output will be 1. if all inputs are 1, the output will be 0. if all inputs are 0, the output will be 1. if all inputs are 1, the output will be 1 and 0.
if all inputs are 1, the output will be 1
The basic rule for an OR gate is: if one or more inputs are 1, the output is 1. if one or more inputs are 1, the output is 0. if one or more inputs are 0, the output is 1. if one or more inputs are 1, output is 0 and if one or more inputs are 0, the output is 1.
if one or more inputs are 1, the output is 1.
The basic rule for an XOR function is: if one or the other, but not both, inputs are 1, the output is 1. if one or more inputs are 1, the output is 1. if one or more inputs are 1, the output is 0. if one or more inputs are 0, the output is 1.
if one or the other, but not both, inputs are 1, the output is 1.
With reference to the logic circuit, the output Y will be at a logic 1 when inputs A and B are logic 1. input A or B is logic 1. input A is at logic 1 and input B is at logic 0. input A is at logic 0 and input B is at logic 1.
input A is at logic 1 and input B is at logic 0.
Given the function F(X, Y, Z) = XZ + Z(X′+ XY), the equivalent, most simplified Boolean representation for F is: Z + YZ Z + XYZ XZ X + YZ none of the above
none of the above
The OR function, implemented using contacts, requires contacts connected in: series. parallel. series/parallel. parallel/series.
pararell
A gate is a device that: allows current flow in one direction only. changes alternating current to direct current. performs a logical decision based on its inputs. performs a logical decision based on its outputs.
performs a logical decision based on its inputs
A truth table shows each possible input to the gate along with its resultant output. true false
t
All inputs to an AND gate must be 1 to produce a 1 output. true false
t
Normally, a binary 1 represents the presence of a signal, while a binary 0 represents the absence of a signal. true false
t
Only one input to an OR gate must be 1 to produce a 1 output. true false
t
The + symbol is used to express the OR function in Boolean algebra. true false
t
The OR gate is essentially a parallel circuit that produces an output voltage when a voltage appears at any input. true false
t
Which of the following relationships represents the dual of the Boolean property x + x′y = x + y? Choose the best answer. x′(x + y′) = x′y′ x(x′y) = xy xx′ + y = xy x′(xy′) = x′y′ x(x′ + y) = xy
x(x′ + y) = xy
Which of the following relationships represents the dual of the Boolean property x + x′ = 1? x′x = 1 xx′= 1 x + x′= 0 xx′= 0 x′x = 0
xx"=1
