What is the hexadecimal equivalent of the decimal number 256?
The Correct Answer and Explanation is:
The hexadecimal equivalent of the decimal number 256 is 0x100.
Explanation:
To convert a decimal number (base 10) to hexadecimal (base 16), we repeatedly divide the decimal number by 16 and record the remainders. The hexadecimal system uses the digits 0–9 for values zero to nine, and the letters A–F for values ten through fifteen. Here’s how you can convert 256 into hexadecimal step by step:
Step 1: Divide 256 by 16.
[
256 \div 16 = 16 \text{ (quotient)}, \text{ remainder } = 0
]
So, the remainder is 0.
Step 2: Divide the quotient (16) by 16.
[
16 \div 16 = 1 \text{ (quotient)}, \text{ remainder } = 0
]
So, the remainder is 0.
Step 3: Divide the quotient (1) by 16.
[
1 \div 16 = 0 \text{ (quotient)}, \text{ remainder } = 1
]
So, the remainder is 1.
Now that we have all the remainders, we can write them in reverse order: 1, 0, 0.
Step 4: Convert the remainders into hexadecimal digits.
- The first remainder, 1, is already a hexadecimal digit.
- The second and third remainders, both 0, are also valid hexadecimal digits.
Thus, reading the remainders from top to bottom, the hexadecimal equivalent of the decimal number 256 is 0x100.
Key Concepts:
- Base Conversion: Decimal is a base-10 system, while hexadecimal is a base-16 system. Each place in a hexadecimal number represents a power of 16.
- Hexadecimal System: Hexadecimal digits range from 0 to 15, with 10 to 15 represented as the letters A to F. For example, 10 in hexadecimal is represented as A, 11 as B, and so on.
- Procedure: The conversion process involves dividing the decimal number by 16, tracking the remainders, and then reading them from bottom to top. This method works for any decimal number you wish to convert to hexadecimal.
In conclusion, 256 in decimal is equivalent to 0x100 in hexadecimal.