How many bits are needed to store one bcd digit?

You need 4 bits for one BCD digit, mate.

I reckon the simple way to think is this. A BCD digit is for the numbers 0 to 9. If you only use 3 bits, you can only make numbers up to 7 (which is 111 in binary). That is not enough for the digits 8 or 9.

So, you must use 4 bits. This gives you 16 possible combinations, which is more than enough to show the number 9 (1001). BCD only uses the bit patterns from 0000 to 1001. The other six patterns are just not used.

So, for a number like 38, you would need 8 bits total. Four for the 3, and four for the 8.

Hope that makes sense! Cheers.