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Information is physical. using .net framework toaccess gs1 datamatrix barcode on asp.net web,windows application About Micro QR Code This means that the crea Visual Studio .NET 2d Data Matrix barcode tion, erasure, manipulation, or processing of information involves physical laws. This represents a new awareness, which contrasts with the classical background of Shannon s information theory, and calls for more questions, answers, and paradoxes.

These are to be found in quantum information theory (QIT), which will be addressed shortly. At this stage, we must at least be convinced that there is more to information than a mere mathematical or ethereal de nition, as we have been used and trained through education to believe intuitively. Landauer s principle brings up another interesting question, which concerns computing.

When one performs hand calculations on a blackboard, one is obliged at some point to erase it, while saving the last results and other useful parameters somewhere in the corner of the blackboard. Very large blackboards, with different folding or sliding panels, could t a full math course. But the information must be cleared for the next course.

This shows that processing information (computation) requires information erasure, because of the nite size of the memory. A computer that would keep and store the information regarding all of its intermediate calculation steps (namely the memory contents at each step, or the full record of the memory changes) would rapidly choke on its own garbage. Such a necessary erasure yet obliterates the information of the computing history, which makes the computation irreversible.

For computation, the term irreversible means that the computed information output cannot lead one to know the information input to the computation.5 The concept of computing irreversibility, however, seems to be in contradiction with the laws of physics. Indeed, if one fully knows the state of a system at a given time t, for instance, the distribution of molecules and their velocities inside a closed box,.

For instance, the additi on of two integer numbers a and b, given the fact that the input information (a, b) is then erased, is irreversible: to any output c correspond c + 1 possible input pairs. If a and b are real numbers, the number of input-pair possibilities is in nite. Another example of irreversibility is the operation of functional derivation: given any input function f in = f (x), the output is f out = f (x).

Reversing the x algorithm yields f (x) = x f (x)dx = f (x) + C where C = f (x0 ) is an arbitrary constant. The knowl0 edge of f out = f (x), thus, makes it possible to know f = f (x) + C = f in (x) + C. This may represent and f differ from each other by an in nity of possible real constants C, which useful information, but f in illustrates the irreversibility of the computation algorithm.

. Reversible computation Memory Instructions Registers Data Control unit Figure 15.2 Von Neumann s generic computer architecture. the laws of mechanics ma 2d Data Matrix barcode for .NET ke it possible to compute the system at any time prior to t. This is like playing a video of a billiard ball game in reverse.

From this perspective, a physicist should suspect that it is possible to effect reversible computations, without any heat dissipation or entropy increase. This brings the issue of the existence of reversible logic. In the next two sections, I shall describe logic gates, which are used in the heart of computer microcircuits, and then show that it is possible to de ne reversible logic gates and circuits.

. From computer architecture to logic gates According to the 1945 de 2d Data Matrix barcode for .NET sign of computer architecture by von Neumann (VN),6 the core of a standard computer is made of a memory, and of an algorithmic and logical unit (ALU), as illustrated in Fig. 15.

2. It is seen that the VN architecture is completed with a control unit and the interfaces enabling the computer to communicate with the outside word and its peripherals. The memory is a device containing the instructions to initialize and run the computer with its interfaces and peripherals.

It includes the program to be performed, in the form of a stack of instructions, and the data before, during, and after.
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