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Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
A.
ABCDEF
B.
AB
C.
A + B + C + D + E + F
D.
A + B(C+D(E+F))
Correct Answer B. AB
Explanation Repeated application of the absorption theorem x + xy = x, gives the desired result.
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2.
An equivalent representation for the Boolean expression A' + 1 is
A.
1
B.
A
C.
A'
D.
0
Correct Answer A. 1
Explanation From the Boolean property A + 1 = 1, let A = A'. It's that simple!
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3.
Which of the following is the best definition of a literal?
A.
1 or 2
B.
The complement of a Boolean variable
C.
The actual understanding of a Boolean variable
D.
A Boolean variable
Correct Answer A. 1 or 2
Explanation A literal can be defined as either 1 or 2. In Boolean algebra, a literal is a variable or its complement, represented by either its true or false value. So, option 1 or 2 accurately describes this definition of a literal. Option 3, "A Boolean variable," is not a complete definition of a literal as it does not include the concept of complement. Option 2, "The actual understanding of a Boolean variable," is not a clear or accurate definition of a literal.
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4.
Draw a logic table for the diagram above and determine the output.
A.
No answer is needed. You can skip this question.
B.
No answer is needed. You can skip this question.
Correct Answer A. No answer is needed. You can skip this question.
5.
The OR function is Boolean multiplication and the AND function is Boolean addition.
A.
True
B.
False
Correct Answer B. False
Explanation The given statement is false. The OR function in Boolean logic is actually Boolean addition, where the output is true if at least one of the inputs is true. On the other hand, the AND function is Boolean multiplication, where the output is true only if both inputs are true.
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6.
In Boolean algebra, A + 1 = 1.
A.
True
B.
False
Correct Answer A. True
Explanation In Boolean algebra, the value of 1 represents "true" or "on" while the value of 0 represents "false" or "off". The logical OR operation (represented by "+") states that if any one of the inputs is true, the output will be true. In this case, the input A is being ORed with 1. Since 1 represents true, the result will always be true regardless of the value of A. Therefore, the statement A + 1 = 1 is true in Boolean algebra.
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7.
SOP stands for sum-of-powers
A.
True
B.
False
Correct Answer B. False
Explanation The statement is false because SOP does not stand for "sum-of-powers." SOP stands for "Standard Operating Procedure," which refers to a set of step-by-step instructions or guidelines that must be followed to carry out a specific task or operation.
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8.
The symbol shown below is for a 2-input NAND gate.
A.
True
B.
False
Correct Answer B. False
Explanation The symbol shown below is not for a 2-input NAND gate.
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9.
By applying De Morgan's theorem to a NOR gate, two identical truth tables can be produced.
A.
True
B.
False
Correct Answer A. True
Explanation De Morgan's theorem states that the complement of a logical operation can be obtained by interchanging the operation with its complement and negating the result. In the case of a NOR gate, it performs the logical operation of OR followed by negation. By applying De Morgan's theorem to a NOR gate, we can interchange the OR operation with its complement (AND) and negate the result. This results in a new gate that performs the AND operation followed by negation, which is equivalent to a NAND gate. Since the truth tables for NOR and NAND gates are identical, it is true that two identical truth tables can be produced by applying De Morgan's theorem to a NOR gate.
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10.
In boolean logic, what symbol can be used to represent AND?
Correct Answer . (full stop)
Explanation In boolean logic, the symbol "." (full stop) is used to represent the AND operation. This symbol is used to combine two or more conditions or statements, and it returns true only if all the conditions are true.
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11.
Also OR can be represented by?
Correct Answer + (plus)
Explanation The correct answer is + (plus) because the symbol "+" is commonly used to represent the logical operator "OR" in computer programming and boolean algebra. It signifies that at least one of the conditions or operands is true.
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12.
This image represents a gate.
Correct Answer NOT
Explanation The easiest way to remember this is that it has a "knot" at the tip of the triangle
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13.
Which of the following is true of a NOR gate?
A.
It always yields a positive result.
B.
It always yields a negative result.
C.
It is the negative of the OR gate
D.
It is the same as the OR gate
Correct Answer C. It is the negative of the OR gate
Explanation With the NOR gate, where ever the OR gate would have yielded a 1(positive), it becomes a negative (0)
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14.
When output is determined solely by output, it is called a logic.
Correct Answer Combinational
Explanation When output is determined solely by input, it is called combinational logic. In this type of logic, the output is a function of the current input values and does not depend on any previous inputs or outputs. It is called "combinational" because the output is determined by combining the input values using logical operations such as AND, OR, and NOT. This is in contrast to sequential logic, where the output also depends on the previous state of the system.