Subtract the largest power of 2 from 59, then do the same from the remainder you get:
59 = 32 + 27
27 = 16 + 11
Continuing in this fashion, you get
11 = 8 + 3
3 = 2 + 1
1 = 1 + 0
In other words, we've found
59 = 32 + 16 + 8 + 2 + 1
or
[tex]59=2^5+2^4+2^3+2^1+2^0[/tex]
which translates directly into binary:
[tex]59_{10}=111011_2[/tex]
