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Instead, comparison operators generate BIT(1) values; '0'B represents false and '1'B represents true. The operands of, e.g., &, |, ¬, are converted to bit strings and the operations are performed on each bit. The element-expression of an IF statement is true if any bit is 1.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
T = true. F = false. The superscripts [0] to [15] is the number resulting from reading the four truth values as a binary number with F = 0 and T = 1. The Com row indicates whether an operator, op, is commutative - P op Q = Q op P. The Assoc row indicates whether an operator, op, is associative - (P op Q) op R = P op (Q op R).
The name is a portmanteau of binary digit. [1] The bit represents a logical state with one of two possible values. These values are most commonly represented as either " 1" or "0 ", but other representations such as true/false, yes/no, on/off, or +/− are also widely used.
in the skew binary number system, only the least-significant non-zero digit can have a value of 2, and the remaining digits have a value of 0 or 1; 1 for true, 2 for false, and 0 for unknown, unknowable/undecidable, irrelevant, or both; [16] 0 for false, 1 for true, and a third non-integer "maybe" symbol such as ?, #, 1 / 2 , [17] or xy ...
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
The result of R is TRUE (1) if exactly one of its arguments is TRUE, and FALSE (0) otherwise. All 8 combinations of values for x , y , z are examined, one per line. The fresh variables a ,..., f can be chosen to satisfy all clauses (exactly one green argument for each R ) in all lines except the first, where x ∨ y ∨ z is FALSE.
Logical conjunction is often used for bitwise operations, where 0 corresponds to false and 1 to true: 0 AND 0 = 0, 0 AND 1 = 0, 1 AND 0 = 0, 1 AND 1 = 1. The operation can also be applied to two binary words viewed as bitstrings of equal length, by taking the bitwise AND of each pair of bits at corresponding positions. For example: