# Binary and hexadecimal expansion

1. Dec 11, 2012

### nicnicman

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution
I know that this is true but I have no idea how to show it. Any pointers?

2. Dec 11, 2012

### Staff: Mentor

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.