For the alphabet of CA is the most convenient digital system. And this raises the question of whether form a complete set of arithmetic to convert the numbers? Resolving this issue is not entirely clear. (Try to specify arithmetic operations on numbers 7 and 5, leading to a number 3 or giving out the number 1 number 6.)
Is not there a way allowing an arbitrary transformation of the numbers? Such a transformation can be described by the notion of function. The values ​​of some functions can be obtained from the argument values ​​using known mathematical operations. Convenient to specify the function analytically, a symbolic record of these actions, but it is not possible for any function. More universally tabular functions. Any such table can be placed in the memory of computers, and to use it, rather a single command, which allows to move the operand of a single cell memory (including the Rhone and the registers are external to the computer device) to another. Such teams are called forward commands. In general, they must have two addresses: Cell source and destination operand. Let us imagine that the values ​​placed in cells with a memory address equal to the corresponding values ​​of the arguments. Then to find the function value is sufficient to place the corresponding argument in RON and use it as an indirect source operand address in the command transfer. As a result of its implementation will be the value function in a cell (or GPR) at the second in command at. Working with specifying the table - one of the most important applications of indirect addressing.
Despite its simplicity, the above mechanism becomes ineffective when the length of operands. So, to double operations, even if the operands consist of one decimal digit in the memory to take 100 (Yeh 10) cells to store the function for all possible combinations of operands. The natural desire to increase the speed causes the computer that uses a parallel presentation of information in the form of words (numbers), consisting of several characters (digits). In this case, the costs are exorbitantly high memory.
Fortunately, the simpler. Record numbers are usually multi-bit uses the same figures as for the single-digit. Therefore, any transformation of such numbers can be made "digit by digit", i.e., it reduces to the already transforming figures.