Convert 16 decimal to hexadecimal.
Understand the Problem
The question is asking for the conversion of the decimal number 16 into its equivalent hexadecimal representation. The approach will involve understanding the relationship between decimal and hexadecimal number systems.
Answer
The hexadecimal representation of the decimal number 16 is $10$.
Answer for screen readers
The hexadecimal representation of the decimal number 16 is $10$.
Steps to Solve
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Identify the base of the number systems
Hexadecimal (base 16) consists of digits 0-9 and letters A-F, where A=10, B=11, C=12, D=13, E=14, and F=15. Decimal (base 10) uses digits 0-9. -
Divide the decimal number by 16
We start by dividing 16 by 16 and writing down the quotient and the remainder to find out the hexadecimal digits.
$$ 16 \div 16 = 1 \quad \text{(Quotient)} $$ $$ 16 \mod 16 = 0 \quad \text{(Remainder)} $$ -
Continue dividing the quotient
Now we take the quotient (1) and divide again by 16.
$$ 1 \div 16 = 0 \quad \text{(Quotient)} $$ $$ 1 \mod 16 = 1 \quad \text{(Remainder)} $$ -
Write the hexadecimal digits
The remainders collected in reverse order give us the hexadecimal number. From our calculations, we have:
- First remainder: 0
- Second remainder: 1
So, reading from bottom to top, we get:
$$ 10_{16} $$
- Combine the results
The hexadecimal representation of the decimal number 16 is $10$.
The hexadecimal representation of the decimal number 16 is $10$.
More Information
Hexadecimal is often used in computer science for its efficiency in representing binary values. Each hexadecimal digit represents four binary digits (bits), making it easier to read large binary numbers.
Tips
- Confusing the order of remainders when writing down the final hexadecimal result. Remember to read from bottom to top when combining remainders.
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