# combinations of binary digits for decimal numbers

1. Four bits are required to represent the ten decimal digits, and since there are 2^4 combinations of four binary digits, six combinations are not used and the code is said to contain redundancy.

2. The four binary digits can be allocated to ten decimal digits in a purely arbitrary manner and it is possible to generate 2.9 • 10^10 four-bit codes, only a few of which have any practical application.

Can anyone explain the second point?

• Where did you get this information from? I would disagree with the second point, as there are only 16 different combinations of 4 binary digits. I've no idea where 2.9E10 comes from – Matt Taylor Apr 16 '13 at 14:33
• I think this has something to do with the notion that if you brute force 10 digits of bcd, that's 40 bits. – gbarry Apr 16 '13 at 14:58
• @MattTaylor digital logic design 4th edition- binary codes for decimal digits... – bkcpro Apr 16 '13 at 15:33

• permutations and combinations: the correct answer is $\frac{16!}{6!}$ = 16*15*14*13*...7 = 29,059430400 – placeholder Apr 16 '13 at 15:31