Binary Coded Decimal (BCD) is the same as binary for 0-9, but then it carries to 10 and not to 0A. So this is exactly what you want. A single 74185 chip will decode up to 6 bits of binary to 2 digits of BCD.
(You have to add one or two BCD-7segment decoder/drivers)
Of course you could use a microcontroller or a programmable logic chip, as discussed http://www.electronics-related.com/usenet/basics/show/29703-1.php.
Other alternatives:
- simply use 5 Leds and learn to read binary
- use a BCD-7seg decoder/driver with defined output for input a-f and learn to read this (74247, iirc)
- two digit octal display with two standard BCD-7seg decoder/drivers