Convert the following decimal numbers to its hexadecimal equivalent. Show your solutions. 1) 96 2) 378 3) 700

Question image

Understand the Problem

The question asks for the conversion of specific decimal numbers (96, 378, and 700) into their hexadecimal equivalents, with an emphasis on showing the solutions to these conversions.

Answer

1) $60$, 2) $17A$, 3) $2BC$
Answer for screen readers
  1. $60$
  2. $17A$
  3. $2BC$

Steps to Solve

  1. Convert 96 to Hexadecimal

    To convert 96 to hexadecimal, divide the number by 16 and keep track of the quotient and the remainder.

    $$ 96 \div 16 = 6 \quad \text{(quotient)}$$ $$ 96 \mod 16 = 0 \quad \text{(remainder)}$$

    The hexadecimal is constructed from the remainders. Therefore, 96 in hexadecimal is $60$.

  2. Convert 378 to Hexadecimal

    Divide 378 by 16 and note the quotient and remainder.

    $$ 378 \div 16 = 23 \quad \text{(quotient)}$$ $$ 378 \mod 16 = 10 \quad \text{(remainder)}$$ Here, 10 in hexadecimal is represented as $A$.

    Now, divide the quotient by 16:

    $$ 23 \div 16 = 1 \quad \text{(quotient)}$$ $$ 23 \mod 16 = 7 \quad \text{(remainder)}$$

    The remainders give us the hexadecimal representation from bottom to top: thus, 378 in hexadecimal is $17A$.

  3. Convert 700 to Hexadecimal

    Divide 700 by 16:

    $$ 700 \div 16 = 43 \quad \text{(quotient)}$$ $$ 700 \mod 16 = 12 \quad \text{(remainder)}$$ Here, 12 in hexadecimal is represented as $C$.

    Now, divide the quotient by 16:

    $$ 43 \div 16 = 2 \quad \text{(quotient)}$$ $$ 43 \mod 16 = 11 \quad \text{(remainder)}$$ Here, 11 in hexadecimal is represented as $B$.

    Now for the last division:

    $$ 2 \div 16 = 0 \quad \text{(quotient)}$$ $$ 2 \mod 16 = 2 \quad \text{(remainder)}$$

    Reading from bottom to top gives us the hexadecimal representation: thus, 700 in hexadecimal is $2BC$.

  1. $60$
  2. $17A$
  3. $2BC$

More Information

Hexadecimal numbers are based on 16, using digits 0-9 and letters A-F to represent values 10-15. This system is commonly used in computing and digital electronics.

Tips

  • Forgetting to convert remainders from decimal to hexadecimal (e.g., treating 10 as "10" instead of "A").
  • Not reading remainders in reverse order when forming the final hexadecimal number.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!
Use Quizgecko on...
Browser
Browser