Binary and hexadecimal expansion

[nicnicman]

Homework Statement

Show that the binary expansion of a positive integer can be obtained form its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits.

Homework Equations

The Attempt at a Solution

I know that this is true but I have no idea how to show it. Any pointers?

 

[mfb]

If you have number given as $a_n 16^n + a_{n-1} 16^{n-1} + ... + a_0$, can you express it as binary number? This expression is unique, so once you find some way to represent the number you are done.