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The last two examples illustrate what happens if x is a rather small number. In the second from last example, x = 1.110111⋯111 × 2 −50 ; 15 bits altogether. The binary is replaced very crudely by a single power of 2 (in this example, 2 −49) and its decimal equivalent is used.
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an operation with a ...
A binary operation is a rule for combining the arguments and to produce. In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, a binary operation on a set is a binary function ...
Distributive property. In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra. For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition.
A binary number is a number expressed in the base -2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the ...
A bitwise AND is a binary operation that takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0). For ...
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