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 octal to binary like this:
557_{8} = 5 5 7 = 5_{(=101)} 5_{(=101)} 7_{(=111)} = 101101111_{2}
answer: 557_{8} = 101101111_{2}
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
5∙8^{2}+5∙8^{1}+7∙8^{0} = 5∙64+5∙8+7∙1 = 320+40+7 = 367_{10}
got It: 557_{8} =367_{10}
Translate the number 367_{10} в binary like this:
the Integer part of the number is divided by the base of the new number system:
367  2         
366  183  2        
1  182  91  2       
 1  90  45  2      
  1  44  22  2     
   1  22  11  2    
    0  10  5  2   
     1  4  2  2  
      1  2  1  
       0   

the result of the conversion was:
367_{10} = 101101111_{2}
answer: 557_{8} = 101101111_{2}