50 = 5 × 10 + 0 × 1 (5
in the tens place, and 0 in units).
We can write each place as a power of ten:
50 = 5 × 10^1 + 0 × 10^0
Similarly for hexadecimal and binary, but then
using powers of 16 and 2 respectively.
We need to find the digits of the hexadecimal
form. Or in other words, we need to find a and b:
50 = a × 16 + b × 1
Simply divide 50 by 16 will get you a with some
remainder, which is a multiple in units, and thus b:
50 / 16 = 3 (=a), remainder 2.
[2 / 1 = 2 (=b), remainder 0]
Thus 50 in hexadecimal is "32".
For binary, we need to do the division a couple of
times more to find all digits.
50 = a × 32 + b × 16 + c × 8 + d × 4 + e × 2 + f ×
1
50 / 32 = 1 (=a), remainder 18
18 / 16 = 1 (=b), remainder 2
2 / 8 = 0 (=c), remainder 2
2 / 4 = 0 (=d), remainder 2
2 / 2 = 1 (=e), remainder 0
[0 / 1 = 0 (=f), remainder 0]
We find that 50 in binary is "110010".
