This transfer is possible in two ways: direct transfer and using the decimal system.
first, let\'s make a direct transfer.
let\'s do a direct translation from hexadecimal to binary like this:
214.A666_{16} = 2 1 4. A 6 6 6 = 2_{(=0010)} 1_{(=0001)} 4_{(=0100)}. A_{(=1010)} 6_{(=0110)} 6_{(=0110)} 6_{(=0110)} = 1000010100.101001100110011_{2}
answer: 214.A666_{16} = 1000010100.101001100110011_{2}
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
2∙16^{2}+1∙16^{1}+4∙16^{0}+10∙16^{1}+6∙16^{2}+6∙16^{3}+6∙16^{4} = 2∙256+1∙16+4∙1+10∙0.0625+6∙0.00390625+6∙0.000244140625+6∙1.52587890625E5 = 512+16+4+0.625+0.0234375+0.00146484375+9.1552734375E5 = 532.64999389648438_{10}
got It: 214.A666_{16} =532.64999389648438_{10}
Translate the number 532.64999389648438_{10} в binary like this:
the Integer part of the number is divided by the base of the new number system:
532  2          
532  266  2         
0  266  133  2        
 0  132  66  2       
  1  66  33  2      
   0  32  16  2     
    1  16  8  2    
     0  8  4  2   
      0  4  2  2  
       0  2  1  
        0   

the Fractional part of the number is multiplied by the base of the new number system:

0.  64999389648438*2 
1  .29999*2 
0  .59998*2 
1  .19995*2 
0  .3999*2 
0  .7998*2 
1  .59961*2 
1  .19922*2 
0  .39844*2 
0  .79688*2 
1  .59375*2 
the result of the conversion was:
532.64999389648438_{10} = 1000010100.1010011001_{2}
answer: 214.A666_{16} = 1000010100.1010011001_{2}