Notice the numbers of ancestors in each generation of the pedigree chart of Sigmund Christoph von Waldburg-Zeil-Trauchburg shown above. Anyone who works with family trees quickly becomes familiar with the idea of powers of 2. For, each of us has two parents, so working backwards, each generation has twice as many members as the one which follows. This sequence: 1, 2, 4, 8, 16, ... , 2n, ... of powers of 2 is an example of exponential growth, the base here being 2 instead of the more usual e = 2.71828 ... . The powers of 2 increase very rapidly. The concept is very important in computer science in counting the number of bits in a binary integer. In number theory, Fermat primes and Mersenne primes involve powers of 2.
