C. True / False
1. The binary number 1111 represents the decimal number 15.
2. The hexadecimal system uses 2 as its base/radix.
3. Octal words come from the Latin word 'oct' which means 8.
4. In the octal number system, the digit '9' is valid.
5. The binary number system can represent any number using only 0 and 1.
6. In the hexadecimal system, the letter 'B' represents the decimal value 12.
7. The Roman number system is an example of a positional number system.
8. Hexa means 6.
9. The radix of the hexadecimal number system is 16.
10. There are two types of basic number systems.
Answer (2)
Let's evaluate each statement to determine if it's true or false:
The binary number 1111 represents the decimal number 15.
This is True . In the binary system, each digit represents a power of 2. Starting from the right, the digits in 1111 represent:
1 × 2 3 + 1 × 2 2 + 1 × 2 1 + 1 × 2 0 = 8 + 4 + 2 + 1 = 15
The hexadecimal system uses 2 as its base/radix.
This is False . The hexadecimal system uses 16 as its base.
Octal words come from the Latin word 'oct' which means 8.
This is True . 'Octal' is derived from 'octo,' which is Latin for eight.
In the octal number system, the digit '9' is valid.
This is False . The octal system only includes digits from 0 to 7.
The binary number system can represent any number using only 0 and 1.
This is True . The binary system uses only two digits, 0 and 1, to represent all numbers.
In the hexadecimal system, the letter 'B' represents the decimal value 12.
This is False . In the hexadecimal system, the letter 'B' represents the decimal value 11.
The Roman number system is an example of a positional number system.
This is False . The Roman numeral system is not positional; it relies on the combination of letters (I, V, X, etc.) to denote values.
Hexa means 6.
This is True . 'Hexa' is derived from Greek, meaning six, but in the context of hexadecimal, it refers to the base-16 numbering system.
The radix of the hexadecimal number system is 16.
This is True . The term 'radix' refers to the base of a number system, and for hexadecimal, it is 16.
There are two types of basic number systems.
This is **False**. There are multiple basic number systems, including binary, octal, decimal, and hexadecimal.
The evaluation of the statements shows several true and false claims about number systems, including binary, octal, and hexadecimal systems. Key accurate points include the representation of binary and hexadecimal values, while the validity of octal numbers is also clarified. Additionally, the misconceptions regarding the Roman numeral system as being positional are addressed.
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