Express the following decimal numbers into hexadecimal numbers. (i) 548 (ii) 4052 (iii) 58 (iv) 100.25

Express the following decimal numbers into hexadecimal numbers.

(i) 548

(ii) 4052

(iii) 58

(iv) 100.25

To convert the given decimal numbers to their hexadecimal equivalents, we follow the steps outlined in the chapter. Below are the conversions for each number:

(i) $548_{10}$

First, divide the decimal number by 16 and note the remainder: $$ 548 \div 16 = 34 \text{ remainder } 4 $$

Then, divide the quotient (34) by 16: $ 34 \div 16 = 2 \text{ remainder } 2 $

Finally, the remainder after the final division is the quotient itself.

Collect the remainders from bottom to top: $$ (548_{10}) = \text{(2 2 4)}_{16} = 224_{16} $$

(ii) $4052_{10}$

First, divide the decimal number by 16 and note the remainder: $$ 4052 \div 16 = 253 \text{ remainder } 4 $$

Then, divide the quotient (253) by 16: $$ 253 \div 16 = 15 \text{ remainder } 13 $$ (Note that 13 in hexadecimal is D)

Finally, divide the quotient (15) by 16: $$ 15 \div 16 = 0 \text{ remainder } 15 $$ (Note that 15 in hexadecimal is F)

Collect the remainders from bottom to top:

$$ (4052_{10}) = \text{(F D 4)}_{16} = FD4_{16} $$

(iii) $58_{10}$

First, divide the decimal number by 16 and note the remainder: $$ 58 \div 16 = 3 \text{ remainder } 10 $$ (Note that 10 in hexadecimal is A) Finally, divide the quotient (3) by 16: $$ 3 \div 16 = 0 \text{ remainder } 3 $$

Collect the remainders from bottom to top: $$ (58_{10}) = \text{(3 A)}_{16} = 3A_{16} $$

(iv) $100.25_{10}$

First, convert the integer part (100) to hexadecimal: $$ 100 \div 16 = 6 \text{ remainder } 4 $$

Next, multiply the fractional part by 16 repeatedly: $$ 0.25 \times 16 = 4.00 \text{ (integer part is 4)} $$

Combine both integer and fractional parts: $$ (100.25_{10}) = (64.4)_{16} $$

Summary

• (i) 548 → 224

• (ii) 4052 → FD4

• (iii) 58 → 3A

• (iv) 100.25 → 64.4