Question

Convert 764.23 from decimal to hexadecimal, then devise a scheme for converting hexadecimal directly to base 4 and convert your answer to base 4.

Answer 1

(764.23)_{10 -->}   is converting to hexadecimal

first we have to take integer part

764/16 = 47 times remainder 12

47/16 = 2 times remainder 15

2/16 = 0 times remainder 2

a bove the values take upward directi and write hexa decimal

(764)₁₀   = (2FC)₁₆

and we have to take fraction part

0,23 * 16 = 3.68 carry 3 fraction 0.68

0.68 *16 = 10.88 carry 10 fraction 0.88

0.88*16 = 14.08 carry 14 fraction 0.08

fraction part take downward diredtion

(0.23)₁₀ =(0.3AE)₁₆

there fore (764.23)₁₀ = (2FC.3AE)₁₆

and directly converting to the hexadecimal numbet to base 4

take hexa decimal number (2FC.3AE)₁₆   = (2FC.3AE * 4)₄

take first part (2FC)16 = (2FC * 4)₄

   = (2333)4

nest take second part (0.3AE)₁₆   = (0.3AE * 4)₄

=(0.032)₄

finally answer is (2FC.3AE)16 -----------> (2333.032)₄