What is half of 0x1002

What is Half of 0x1002?

Understanding hexadecimal numbers is essential for programming, engineering, and computer science. When dealing with hexadecimal values, calculating their half may seem complex at first glance. In this article, we’ll break down how to compute half of 0x1002 step-by-step.

What is Hexadecimal?

Hexadecimal, often abbreviated as hex, is a base-16 numeral system. It uses 16 symbols:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
In this system:

• A represents 10,
• B represents 11,
• and so on up to F, which represents 15.

Hexadecimal numbers are commonly used in computing because they compactly represent binary values.

What Does 0x Mean?

The prefix 0x is used to denote hexadecimal numbers. For example:
0x1002 means the value is hexadecimal and not decimal.

Step-by-Step Calculation of Half of 0x1002

To calculate half of 0x1002, we need to first convert it to a decimal value, perform the division, and, if necessary, convert the result back to hexadecimal.

Step 1: Convert 0x1002 to Decimal

Each digit in the hexadecimal number is multiplied by 16 raised to the power of its position (counted from right, starting at 0).

0x1002=(1×163)+(0×162)+(0×161)+(2×160)0x1002 = (1 \times 16^3) + (0 \times 16^2) + (0 \times 16^1) + (2 \times 16^0)0x1002=(1×163)+(0×162)+(0×161)+(2×160)

Breaking it down:

• 1×163=1×4096=40961 \times 16^3 = 1 \times 4096 = 40961×163=1×4096=4096
• 0×162=00 \times 16^2 = 00×162=0
• 0×161=00 \times 16^1 = 00×161=0
• 2×160=22 \times 16^0 = 22×160=2

Adding these together:
$4096+0+0+2=4098$

Thus, 0x1002 in decimal is 4098.

Step 2: Divide by 2

Now, calculate half of 4098:

$$4098÷2=2049$$

Step 3: Convert Back to Hexadecimal (Optional)

To convert 2049 back to hexadecimal, divide the number by 16 repeatedly and record the remainders.

1. $2049÷16=128$ remainder $1$
2. $128÷16=8$ remainder $0$
3. $8÷16=0$ remainder $8$

Reading the remainders from bottom to top, 2049 in hexadecimal is 0x801.

Final Answer

Half of 0x1002 is 0x801 in hexadecimal or 2049 in decimal.

Why is This Important?

Understanding how to work with hexadecimal numbers is vital for:

• Debugging low-level programs,
• Configuring hardware,
• Working with memory addresses in operating systems.

By breaking problems into manageable steps, handling hexadecimal calculations becomes straightforward.