The Question:
$$F08C_{16}=\_\_\_\_\_\_\_\;_2$$$A=10, B=11, C=12, D=13, E=14,$ and $F=15$.
I can do it with a calculator, multiplying the $C$ by $16^0$, the $8$ by $16^1$, etc then getting it into base $2$. I would get $12+128+0+61440=61580$, then converting it into base $2$, I would get $1111000010001100$. Is there any way to do this without a calculator?
Because $2^4=16$ each hex digit corresponds to four binary bits. Just convert each hex digit, so $C_{16}=1100_2$ and so on. This only works directly when one base is a power of the other. You can go from hex to octal by going through binary.