Question

what is 57 converted in binary

Answer 1

The easiest way to convert from base 10 to another base is to work backwards. Just divide your number by the base, remember that result, and output the remainder. Keep doing it until your result is zero.

Answer 2

In decimal you have from right to left the 1's place, the 10's place, the 100's place etc. Or in other words, 10^0, 10^1, 10^2 etc so 57 in decimal is 5 10's and 7 1's thus it is written as 57.

Other base numbering systems work the same.

In binary, from right to left you have the 1's, 2's, 4's, 8's, 16's, 32's, 64's etc or in other words 2^0, 2^1, 2^2, 2^3 etc. So 57 decimal in binary is 57-32=25 25-16=9 9-8=1 and 1-1=0. Thus you have 1 in the 32's, 16's, 8's and 1's places. So 111001 binary.

In octal, you have the 1's, the 8's, the 64's etc or in other words 8^0, 8^1, 8^2 etc so 57 decimal in octal is 57-(7*8)=1 1-1=0. Thus you have 7 in the 8's place and 1 in the 1's place or 71 octal.

In hexadecimal (base 16) you have the 1's, 16's, 256's etc or 16^0, 16^1, 16^2. So 57 decimal in hexadecimal would be 57-(3*16)=9 9-(9*1)=0. Thus you have 3 in the 16's place and 9 in the 1's place or 39 hex.

As you can hopefully see it is all the same essentially.

Answer 3

And always keep in mind that there are only 10 kinds of people in the world: Those who understand binary and those who don't.