Q. Which of the following is a characteristic of the decimal system?
-
A.
It is a base-10 system.
-
B.
It uses only odd numbers.
-
C.
It is not used in everyday calculations.
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D.
It is less efficient than the binary system.
Solution
The decimal system is a base-10 system, which is widely used in everyday calculations.
Correct Answer:
A
— It is a base-10 system.
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Q. Which of the following is a characteristic of the hexadecimal system?
-
A.
It uses base 10.
-
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 is a correct conversion of the decimal number 10 into binary? (2023)
-
A.
1010
-
B.
1001
-
C.
1100
-
D.
1110
Solution
The decimal number 10 is represented as 1010 in binary.
Correct Answer:
A
— 1010
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Q. Which of the following is a valid base-4 number?
-
A.
123
-
B.
234
-
C.
345
-
D.
456
Solution
In base-4, valid digits are 0, 1, 2, and 3. Therefore, 123 is valid, while 234, 345, and 456 contain digits not allowed in base-4.
Correct Answer:
A
— 123
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Q. Which of the following is NOT a valid numeral in the octal system? (2023)
Solution
The octal system only uses digits 0-7, so 8 is not a valid numeral.
Correct Answer:
B
— 8
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Q. Which of the following is the correct conversion of the decimal number 10 into binary?
-
A.
1010
-
B.
1001
-
C.
1100
-
D.
1110
Solution
The decimal number 10 is represented as 1010 in binary.
Correct Answer:
A
— 1010
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Q. Which of the following is the correct order of the base systems from least to most complex? (2023)
-
A.
Decimal, Binary, Hexadecimal
-
B.
Binary, Decimal, Hexadecimal
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C.
Hexadecimal, Binary, Decimal
-
D.
Decimal, Hexadecimal, Binary
Solution
Binary is the simplest (base-2), followed by Decimal (base-10), and then Hexadecimal (base-16), making the correct order Binary, Decimal, Hexadecimal.
Correct Answer:
B
— Binary, Decimal, Hexadecimal
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Q. Which of the following is the correct representation of the decimal number 10 in base-3?
-
A.
101
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B.
110
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C.
100
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D.
111
Solution
To convert 10 to base-3, divide by 3: 10 ÷ 3 = 3 remainder 1, 3 ÷ 3 = 1 remainder 0, 1 ÷ 3 = 0 remainder 1. Reading the remainders from bottom to top gives 110.
Correct Answer:
B
— 110
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Q. Which of the following numeral systems is most commonly used in digital electronics?
-
A.
Decimal
-
B.
Binary
-
C.
Octal
-
D.
Hexadecimal
Solution
The binary system is the most commonly used in digital electronics due to its two-state nature.
Correct Answer:
B
— Binary
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Q. Which of the following numeral systems is not positional?
-
A.
Decimal
-
B.
Binary
-
C.
Roman
-
D.
Hexadecimal
Solution
The Roman numeral system is not positional, as it does not use place value to determine the value of digits.
Correct Answer:
C
— Roman
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Q. Which of the following statements about base systems is incorrect? (2023)
-
A.
Base 2 is used in digital electronics.
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B.
Base 10 is the most widely used numeral system.
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C.
Base 16 can represent more values than base 10.
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D.
Base 8 is more efficient than base 2.
Solution
Base 8 (octal) is not more efficient than base 2 (binary); it simply represents values in a different way.
Correct Answer:
D
— Base 8 is more efficient than base 2.
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Q. Which of the following statements about numeral systems is correct?
-
A.
All numeral systems are based on the same principles.
-
B.
Different numeral systems can represent the same value.
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C.
The decimal system is the only system used in mathematics.
-
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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Q. Which of the following statements about numeral systems is incorrect?
-
A.
Base-10 is the most commonly used system.
-
B.
Base-16 is used in color codes in web design.
-
C.
Base-2 is used in human languages.
-
D.
Base-8 is less common than base-2.
Solution
Base-2 (binary) is not used in human languages; it is primarily used in computing.
Correct Answer:
C
— Base-2 is used in human languages.
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Q. Which of the following statements about the decimal system is incorrect? (2023)
-
A.
It is a base 10 system.
-
B.
It uses digits from 0 to 9.
-
C.
It is the only system used in mathematics.
-
D.
It is widely used in everyday life.
Solution
The statement that the decimal system is the only system used in mathematics is incorrect; other systems like binary and hexadecimal are also used.
Correct Answer:
C
— It is the only system used in mathematics.
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Q. Which of the following statements is true regarding the base-8 number system?
-
A.
It uses digits 0-7
-
B.
It uses digits 0-8
-
C.
It is a binary system
-
D.
It is a hexadecimal system
Solution
The base-8 number system, also known as octal, uses digits from 0 to 7. Therefore, the correct statement is that it uses digits 0-7.
Correct Answer:
A
— It uses digits 0-7
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