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

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 $2BC$.