Convert 0x1000 to decimal.

Understand the Problem

The question is asking to convert the hexadecimal number 0x1000 into its decimal equivalent. Hexadecimal is a base-16 number system and needs to be converted to base-10.

Answer

$4096$

Steps to Solve

Identify the hexadecimal components The hexadecimal number 0x1000 contains digits from 0 to F, where each digit represents a power of 16. The digits here are 1, 0, 0, and 0.
Assign power values to each digit Starting from the right, assign powers of 16 to each digit based on its position:

The rightmost digit (0) is in the $16^0$ position,
The next digit (0) is in the $16^1$ position,
The next digit (0) is in the $16^2$ position,
The leftmost digit (1) is in the $16^3$ position.

Compute the decimal value Now, compute the decimal value by multiplying each digit by its corresponding power of 16:

( 1 \times 16^3 = 1 \times 4096 = 4096 )
( 0 \times 16^2 = 0 \times 256 = 0 )
( 0 \times 16^1 = 0 \times 16 = 0 )
( 0 \times 16^0 = 0 \times 1 = 0 )

Sum the results Now, add all the computed values together: $$ 4096 + 0 + 0 + 0 = 4096 $$

The decimal equivalent of the hexadecimal number 0x1000 is $4096$.

More Information

The conversion from hexadecimal to decimal is a common task in computing, as hex is often used in programming and memory addressing. Each hexadecimal digit corresponds to 4 binary digits (bits), making conversions straightforward and useful in digital electronics.

Tips

Failing to correctly assign powers of 16 to each digit can lead to incorrect calculations.
Misreading the hexadecimal number, such as forgetting about leading zeros or interpreting letters incorrectly (for example, confusing 'A' with 'a').

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