Counting up in binary/binary data type?

[NetHacker]

I wrote a program and part of the program counts up in binary. But it does it by counting up in integers and converting each integer to binary. Obviously, this can't go very high because of the limitations of the conversion loop I wrote. Is there a way to count up in binary without counting up in integers and converting? Perhapse a binary data type which can go much higher than my converter? Thanks.