Arrange the following numbers in ascending order a. Binary 1011 b. Decimal 8 c. Hexadecimal F Select one: a. All numbers are equal b. b,a,c c. a, b, c d. c,b,a
The Correct Answer and Explanation is:
To arrange the given numbers in ascending order, we need to convert all of them into a common number system, typically decimal (base 10), to make the comparison straightforward. Let’s break down each number:
- Binary 1011:
- The binary system uses base 2, where each digit represents a power of 2. Starting from the right, we have: 1×23+0×22+1×21+1×20=8+0+2+1=111 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 0 + 2 + 1 = 111×23+0×22+1×21+1×20=8+0+2+1=11
- So, 1011 in binary is equal to 11 in decimal.
- Decimal 8:
- This is already in decimal, so it remains 8.
- Hexadecimal F:
- The hexadecimal system uses base 16, and “F” represents the decimal number 15 (since hexadecimal digits range from 0 to F, where F corresponds to 15).
- So, F in hexadecimal is equal to 15 in decimal.
Now, we can compare these values:
- Binary 1011 = 11 (decimal)
- Decimal 8 = 8
- Hexadecimal F = 15 (decimal)
To arrange them in ascending order:
- Decimal 8 comes first (8).
- Then, Binary 1011 comes next (11).
- Finally, Hexadecimal F comes last (15).
Thus, the correct ascending order is: b, a, c.
So, the answer is:
b. a, b, c.
