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
$4096$
Answer for screen readers
The decimal equivalent of the hexadecimal number 0x1000 is $4096$.
Steps to Solve
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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.
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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').
