Roman C. answered • 04/20/13

Masters of Education Graduate with Mathematics Expertise

Recall the product rule of combinatorics:

If you must make n independent decisions, and the numbers of choices for those decisions are k_{1}, ... ,k_{n} respectively, then the number of ways for me to make the decisions is k_{1}*...*k_{n}

If you have the same number of choices for all these decisions, say k choices for each, then the number of ways of making all decisions is k^{n}

In your problem, you have four independent decisions, one for each bit. You have two choices for each, namely, a 0 or 1. Thus the number of ways is 2^{4} = 16. Clearly each of these 16 possibilities yield a different possibility so there are 16 nybbles.

Matthew S.

2^4 is 16, not 64.

04/23/13