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The Motorola 6800 microprocessor was the first for which an undocumented assembly mnemonic HCF became widely known. The operation codes (opcodes—the portions of the machine language instructions that specify an operation to be performed) hexadecimal 9D and DD were reported and given the unofficial mnemonic HCF in a December 1977 article by Gerry Wheeler in BYTE magazine on undocumented ...
More generally, an a-by-b rectangle can be covered with square tiles of side length c only if c is a common divisor of a and b. For example, a 24-by-60 rectangular area can be divided into a grid of: 1-by-1 squares, 2-by-2 squares, 3-by-3 squares, 4-by-4 squares, 6-by-6 squares or 12-by-12 squares.
Recursive drawing of a Sierpiński Triangle through turtle graphics. In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. [1] [2] Recursion solves such recursive problems by using functions that call themselves from within their own code ...
A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...
In the second step, any natural number c that divides both a and b (in other words, any common divisor of a and b) divides the remainders r k. By definition, a and b can be written as multiples of c: a = mc and b = nc, where m and n are natural numbers. Therefore, c divides the initial remainder r 0, since r 0 = a − q 0 b = mc − q 0 nc = (m ...
In contemporary use, the term "computable function" has various definitions: according to Nigel J. Cutland, [10] it is a partial recursive function (which can be undefined for some inputs), while according to Robert I. Soare [11] it is a total recursive (equivalently, general recursive) function. This article follows the second of these ...
As with direct recursion, tail call optimization is necessary if the recursion depth is large or unbounded, such as using mutual recursion for multitasking. Note that tail call optimization in general (when the function called is not the same as the original function, as in tail-recursive calls) may be more difficult to implement than the ...
A total recursive function is a partial recursive function that is defined for every input. Every primitive recursive function is total recursive, but not all total recursive functions are primitive recursive. The Ackermann function A(m,n) is a well-known example of a total recursive function (in fact, provable total), that is not primitive ...