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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.

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
ABresult
000
100
010
111

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.

functions

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\$.
PL/I    ALL(x) — Pl/I built-in function that performs a Boolean AND on all of the bits of the bit string x. If the data item x is not a bit string, then it is converted to a bit string. If the data item x is CHARACTER then the character string should contain only the characters '1' and '0'. If the data item x is arithmetic, then the item is changed into a positive fixed point binary integer (applying absolute value if needed) and the AND operation is performed on the bits of the integer ignoring the plus sign. The result returned is '1'B if all bits are '1'B and the result returned is '0'B if any bit is not a '1'B.

assembly language instructions

Logical instructions typically work on a bit by bit basis, although some processors use the entire contents of the operands as whole flags (zero or not zero input, zero or negative one output). Typical logical operations include logical negation or logical complement (NOT), logical and (AND), logical inclusive or (OR or IOR), and logical exclusive or (XOR or EOR). Logical tests are a comparison of a value to a bit string (or operand treated as a bit string) of all zeros. Some processors have an instruction that sets or clears a bit or byte in registers or memory based on the processor condition codes.

• AND And Logical; Motorola 680x0, Motorola 68300; performs a logical AND of a source operand with a destination operand and stores the result in the destination operand (8, 16, or 32 bits), one of the two operands must be a data register, the other operand can be the contents of any register or memory location; sets or clears flags
• ANDI And Immediate; Motorola 680x0, Motorola 68300; performs a logical AND of the contents of a register or memory location (8, 16, or 32 bits) with an immediate; sets or clears flags
• AND Logical AND; Intel 80x86; performs a logical AND between two registers, a register and contents of a memory location, or an immediate operand and either the contents of a register or the contents of a memory location; byte (8 bits), word (16 bits), or doubleword (32 bits); sets or clears flags

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