Convert decimal 32 to hexadecimal.
Understanding Decimal to Hexadecimal Conversion
Number systems are ways of representing numbers. The decimal system (base 10) is the one we use every day, using digits 0-9. The hexadecimal system (base 16) uses digits 0-9 and letters A-F to represent values 10-15. Converting a number from decimal to hexadecimal is a common task in computer science and mathematics.
Steps for Converting Decimal 32 to Hexadecimal
To convert a decimal number to hexadecimal, we use the method of repeated division by the base of the target system, which is 16 for hexadecimal. Here are the steps for converting the decimal number 32:
- Divide the decimal number by 16.
- Note down the remainder. This remainder is the least significant digit in the hexadecimal number.
- Take the quotient from the division and repeat step 1 with this new quotient.
- Continue this process until the quotient becomes 0.
- Collect all the remainders in reverse order (from the last remainder to the first). This sequence of remainders is the hexadecimal representation of the original decimal number.
Applying the Conversion Steps to Decimal 32
Let's apply these steps to convert decimal 32:
| Division | Quotient | Remainder | Hexadecimal Digit |
|---|---|---|---|
| \(\frac{32}{16}\) | $2 | $0 | $0 |
| \(\frac{2}{16}\) | $0 | $2 | $2 |
The division stops when the quotient is 0. The remainders obtained are 0 and 2, starting from the first division. Reading the remainders from bottom to top (in reverse order), we get 2 then 0.
So, the hexadecimal representation of decimal 32 is 20.
Let's quickly verify this:
The hexadecimal number 20 can be converted back to decimal using the place value system:
\((20)_{16} = 2 \times 16^1 + 0 \times 16^0 = 2 \times 16 + 0 \times 1 = 32 + 0 = 32_{10}\)
This confirms that our conversion is correct.
Checking the Options
We converted decimal 32 to hexadecimal and found the result to be 20. Let's compare this with the given options:
- Option 1: 20
- Option 2: 30
- Option 3: 10
- Option 4: 40
Our calculated hexadecimal value, 20, matches Option 1.
Revision Table: Key Conversion Concepts
| Concept | Description | Example |
|---|---|---|
| Decimal System | Base 10, uses digits 0-9. | \(32_{10}\) |
| Hexadecimal System | Base 16, uses digits 0-9 and letters A-F (A=10, B=11, C=12, D=13, E=14, F=15). | \(20_{16}\) |
| Conversion Method | Repeated division by 16, collecting remainders in reverse order. | \(32 \div 16 = 2\) R $0; \(2 \div 16 = 0\) R $2. Result: 20. |
Additional Information on Number Systems
Besides decimal and hexadecimal, other important number systems include:
- Binary (Base 2): Uses only digits 0 and 1. Fundamental in computing.
- Octal (Base 8): Uses digits 0-7. Sometimes used as a shorthand for binary.
Conversions between these systems (like binary to decimal, binary to hexadecimal, etc.) also involve similar principles of division or multiplication by the base, depending on the direction of conversion.
Understanding how to convert between different number systems is crucial for working with computers, data representation, and low-level programming.
Important Questions from Number System
What is the Highest Common Factor of 2 3× 3 5and 3 3× 5 2?
Four prime numbers are arranged in ascending order. The product of the first three numbers is 255 and that of the last three is 1955. The largest prime number is:
Find the number of all prime numbers less than 55.
Value of the square root of \(\frac{36.1}{102.4}\) is:
For any natural number n, 6n - 5n always ends with
