Polymorphysm of n-bit digital systems

n*max("n"bit)= full cycle of "n"bit digital system = (n-1)*("(n+1)"bit) + 1

Examples:

10*max(1 to 10) = 100 = 9*max(1 to 11) + 1

8*max(1 to 8) = 64 =  7*max(1 to 9) + 1

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x E (1 to n) =>
n*x=(n-1)*(x+1 ) -  n + x + 1