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Boolean AND

summary

    This subchapter looks at Boolean AND.

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Boolean AND

    This subchapter looks at Boolean AND.

    Please note the differences between a logical Boolean operation, an integer Boolean operation, and a bit-wise Boolean operation. Note that terminology varies, so you will eventually see references using these terms different than presented here.

    In the case of a logical Boolean AND, the result is a logical BOOLEAN type of either TRUE or FALSE. Some languages, such as C, do not have a built-in Boolean type. There are several different and incompatible encodings for TRUE and FALSE (see table below).

    In the case of an integer Boolean AND, the AND is performed on the two integers as whole numbers. The result can be inaccurate if the integer is not in a specified form (the legal options usually being [ZERO and ONE] or [ZERO and NEGATIVE ONE]. This works best with -1 and 0 as TURE and FALSE (or vice versa). There are several different and incompatible encodings for TRUE and FALSE (see table below).

some languages		TRUE		FALSE
C		1		0
C		non-zero		zero
		negative		zero or positive
		-1		0
		0		1

    in the case of a bit-wise Boolean AND, a logical AND is performed on each corresponding bit of the two bit strings (or two single bits).

AND

    AND requires both objects to be true for the result to be true. The AND works like a pair of switches in series. Both switches must be closed for current to flow.

    AND is conisdered to be Boolean multiplication and is represented by the middle dot symbol: · (such as A·B). As in ordinary algebra, AND (Boolean multiplication) can be written by dropping the middle dot (such as AB). There is no Boolean division operation.

    The truth table for AND is as follows:

AND

A	B	result
0	0	0
1	0	0
0	1	0
1	1	1

    The AND gate in logic circuits looks like:

    The AND operation (Boolean multiplication) has the same results as ordinary arithmetic multiplication..

    The AND operation has a result of 0 when any of its input variables is 0.

    The AND operation has a result of 1 only when both of its input variables are 1.

AND operator (for IF-THEN-ELSE)

    Most programming languages use the AND operator in conditional expressions to test if two parts of the conditional expression are both true.

BASIC    AND — BASIC operator used in the IF-THEN statements as a logical operator.

AND operator (returning numeric value)

    Some languages allow the use of the AND operator to return a numeric value.

BASIC    AND — Optional BASIC operator used in as a logical operator returning a numeric value. If the AND condition is met, a -1 is returned. If the AND condition fails, then a 0 is returned. Example: PRINT A=15 AND B=33

AND operator (bit wise binary)

    Some languages allow the use of the AND operator as a bit wise binary operator.

BASIC    AND — Optional BASIC operator used in as a bit wise bianry operator.

AND functions

    Some languages have an AND function.

APL    AND ∧(x) — APL dyadic function that returns the logical AND of two scalars, vectors, or matrices. Form is A∧B. This function can be used with two arrays, vectors, or matrices to logically AND all of the corresponding elements of the two arrays, vectors, or matrices; or with an array, matrix, or vector and a scalar to logically AND the scalar to every element of the array, vector, or matrix with the value of the scalar; or with two scalars to logically AND the two scalars. Each element of the operation must intiially have the value of one (1) or zero (0). One is TRUE and zero is FALSE.
BASIC    AND — Wang BASIC 2200B function. Form is AND(p$,q$) or AND(p$,q). In the first form, the two string variables are bit-wise ANDed on a character by character basis. In the second form, the two-digit hexadecimal constant is bit-wise ANDed with each character in the character string P$.
LISP    AND(x) — LISP predicate function that takes zero or more arguments of type NIL or nonNIL and returns either NIL or nonNIL. Arguments are evalutaed left to right. Evaluation stops at the first NIL and remaining arguments are not evaluated, returning NIL. If NIL is not encountered, then the function returns the value of the last argument.

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