Convert 0xF to binary. Remember to add the lowercase b at the end of the binary number to identify it as binary!
The Correct Answer and Explanation is:
To convert 0xF to binary, let’s break it down step-by-step:
Step 1: Understand the Hexadecimal System
The “0x” prefix indicates that the number is in hexadecimal (base 16). In hexadecimal, the digits range from 0 to 15, which is represented by the characters 0-9 and A-F. Here, F represents the decimal number 15.
Step 2: Convert Hexadecimal to Decimal
In hexadecimal, the digits correspond to the following values:
- F = 15 (in decimal)
Step 3: Convert the Decimal Number to Binary
Now, let’s convert the decimal number 15 into binary. The binary system (base 2) uses only the digits 0 and 1. To convert 15 into binary, we perform successive division by 2:
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
Reading the remainders from bottom to top, we get the binary representation of 15 as 1111.
Step 4: Final Representation
Now that we have the binary equivalent of 15, we can write it as 1111b to indicate that this is a binary number.
Thus, 0xF in hexadecimal is 1111b in binary.
Explanation of Hexadecimal and Binary Relationship
Hexadecimal is commonly used in computing because it provides a more compact representation of binary numbers. Each hexadecimal digit corresponds to exactly 4 binary digits (bits), making it easier to read and manage long binary strings.
For example, in the case of 0xF:
- A single hexadecimal digit can represent 4 binary digits (bits), and F (hexadecimal) maps directly to the 4-bit binary sequence 1111. If we were to convert multiple hexadecimal digits, each one would similarly represent a 4-bit binary number, making the conversion between the two systems efficient.
This relationship helps in contexts like machine-level programming, memory addressing, and working with low-level hardware where binary numbers are crucial.
