10/25/2023 0 Comments Survivors the quest find watering can![]() If, for example, W = 128, each system state can be unequivocally labeled by a single positive integer in the range 1 through 128. A polyhedron die is a three-dimensional object with W flat surfaces. If a single cubical die is placed or tossed on a surface, the six possible states of the system are 1 through 6. ![]() Let’s begin our discussion of states with simple die systems. Thus, for example, ceiling function (6.2) = 7 bits or buckets no partly filled buckets or hanging chads are allowed. The binary transformation rule adopts the ceiling function of computer science, the provision that non-integer values of T are to be rounded up to the nearest integer. This equation has no fixed scientific meaning it is simply the rule for transforming any base-10 number W into a binary number T, analogous to a simple mathematical rule like A x B = B x A. The right side is read, “the base 2 logarithm of W”. Solving this equation for T yields the minimum number of bits (buckets or binary digits) needed to store the number W: T = Log 2W. As shown in my first figure, a T-bit binary number can represent base-10 integers up to the maximum number W = 2 T – 1. I adopt the symbol T (after computer scientist Alan Turing) to indicate the number of buckets in the line. Empty buckets are designated 0 and sand-filled buckets are designated 1 fractional fills are not allowed. Imagine sand buckets placed in a straight line on a beach.
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