Q. If the decimal number 15 is converted to binary, what is the resulting binary number?
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A.
1110
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B.
1111
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C.
1101
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D.
1011
Solution
The decimal number 15 is represented as 1111 in binary.
Correct Answer: B — 1111
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Q. If the decimal number 255 is converted to binary, what is the resulting binary number?
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A.
11111111
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B.
11011111
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C.
10111111
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D.
10011111
Solution
The decimal number 255 converts to binary as 11111111.
Correct Answer: A — 11111111
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Q. In a base-5 numeral system, what is the decimal equivalent of the number 243?
Solution
The base-5 number 243 converts to decimal as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.
Correct Answer: B — 61
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Q. In a base-5 numeral system, which of the following digits is not valid?
Solution
In a base-5 numeral system, valid digits are 0, 1, 2, 3, and 4; thus, 5 is not valid.
Correct Answer: D — 5
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Q. In converting the hexadecimal number 1A to decimal, what is the result?
Solution
The hexadecimal number 1A converts to decimal as 1*16^1 + 10*16^0 = 26.
Correct Answer: A — 26
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Q. In the context of numeral systems, what does the term 'base' refer to?
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A.
The number of unique digits used.
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B.
The maximum value of a digit.
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C.
The total number of digits in a system.
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D.
The value of the first digit.
Solution
The term 'base' refers to the number of unique digits used in a numeral system.
Correct Answer: A — The number of unique digits used.
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Q. In the context of numeral systems, which of the following statements is true about the binary system?
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A.
It uses base 8.
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B.
It consists of only two digits: 0 and 1.
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C.
It is the most commonly used system in human history.
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D.
It is less efficient than the decimal system.
Solution
The binary system is a base-2 numeral system that uses only two digits: 0 and 1.
Correct Answer: B — It consists of only two digits: 0 and 1.
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Q. What is the decimal equivalent of the binary number 1010?
Solution
The binary number 1010 is equivalent to the decimal number 10.
Correct Answer: B — 10
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Q. What is the primary advantage of using the octal system in computing?
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A.
It simplifies binary representation.
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B.
It is easier for humans to read than binary.
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C.
It is the only system used in programming.
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D.
It is more efficient than hexadecimal.
Solution
The octal system simplifies binary representation by grouping bits into sets of three.
Correct Answer: A — It simplifies binary representation.
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Q. What is the result of adding the binary numbers 1011 and 1101?
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A.
11000
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B.
10100
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C.
10010
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D.
11110
Solution
Adding 1011 and 1101 in binary results in 11110.
Correct Answer: D — 11110
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Q. Which numeral system is most efficient for representing large binary numbers?
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A.
Decimal
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B.
Octal
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C.
Hexadecimal
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D.
Base-64
Solution
The hexadecimal system is most efficient for representing large binary numbers due to its compactness.
Correct Answer: C — Hexadecimal
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Q. Which numeral system is primarily used in digital electronics?
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A.
Decimal
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B.
Binary
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C.
Octal
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D.
Hexadecimal
Solution
The binary system is primarily used in digital electronics due to its two-state nature.
Correct Answer: B — Binary
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Q. Which of the following best describes a positional numeral system?
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A.
It uses fixed symbols for each value.
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B.
The position of a digit affects its value.
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C.
It is limited to a specific number of digits.
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D.
It does not allow for zero.
Solution
In a positional numeral system, the position of a digit determines its value, such as in decimal or binary systems.
Correct Answer: B — The position of a digit affects its value.
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Q. Which of the following is a characteristic of the hexadecimal system?
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A.
It uses base 10.
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B.
It includes the digits 0-9 and letters A-F.
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C.
It is primarily used in human communication.
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D.
It is less compact than the binary system.
Solution
The hexadecimal system is a base-16 system that includes the digits 0-9 and letters A-F.
Correct Answer: B — It includes the digits 0-9 and letters A-F.
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Q. Which of the following statements about numeral systems is correct?
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A.
All numeral systems are based on the same principles.
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B.
Different numeral systems can represent the same value.
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C.
The decimal system is the only system used in mathematics.
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D.
Base systems are irrelevant in modern computing.
Solution
Different numeral systems can represent the same value, such as the decimal 10 and binary 1010.
Correct Answer: B — Different numeral systems can represent the same value.
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