Express 534(base 8)in the binary system

Answer 1

To express the number 534 in base 8 (octal) in the binary system, we first need to convert it to base 10. Then we can convert it to binary.

534(base 8) = 5*(8^2) + 3*(8^1) + 4*(8^0) = 5*(64) + 3*(8) + 4*(1) = 320 + 24 + 4 = 348

Now let's convert 348(base 10) to binary:

Divide 348 by 2 repeatedly until we get a quotient of 0:

348 ÷ 2 = 174 (quotient 0)
174 ÷ 2 = 87 (quotient 0)
87 ÷ 2 = 43 (quotient 1)
43 ÷ 2 = 21 (quotient 1)
21 ÷ 2 = 10 (quotient 1)
10 ÷ 2 = 5 (quotient 0)
5 ÷ 2 = 2 (quotient 1)
2 ÷ 2 = 1 (quotient 0)
1 ÷ 2 = 0 (quotient 1)

Now, starting from the bottom, write down the remainders in reverse order:

348(base 10) = 101011100(base 2)