Understanding VHDL Operators

The following charts summarize the operators available in VHDL. As indicated, not all operators can be used for all data types, and the data type that results from an operation may differ from the type of the object on which the operation is performed.

Note: Operations defined for types Bit are also valid for type std_ulogic and std_logic.

Logical operators

The logical operators and, or, nand, nor, xor and xnor are used to describe Boolean logic operations, or perform bit-wise operations, on bits or arrays of bits.

Operator	Description	Operand Types	Result Types
and	And	Any Bit or Boolean type	Same Type
or	Or	Any Bit or Boolean type	Same Type
nand	Not And	Any Bit or Boolean type	Same Type
nor	Not Or	Any Bit or Boolean type	Same Type
xor	Exclusive OR	Any Bit or Boolean type	Same Type
xnor	Exclusive NOR	Any Bit or Boolean type	Same Type

Relational operators

Relational operators are used to test the relative values of two scalar types. The result of a relational operation is always a Boolean true or false value.

Operator	Description	Operand Types	Result Type
=	Equality	Any type	Boolean
/=	Inequality	Any type	Boolean
<	Less than	Any scalar type or discrete array	Boolean
<=	Less than or equal	Any scalar type or discrete array	Boolean
>	Greater than	Any scalar type or discrete array	Boolean
>=	Greater than or equal	Any scalar type or discrete array	Boolean

Adding operators

The adding operators can be used to describe arithmetic functions or, in the case of array types, concatenation operations.

Operator	Description	Operand Types	Result Type
+	Addition	Any numeric type	Same type
-	Subtraction	Any numeric type	Same type
&	Concatenation	Any numeric type	Same type
&	Concatenation	Any array or element type	Same array type

Multiplying operators

The multiplying operators can be used to describe mathematical functions on numeric types.

Note: Synthesis tools vary in their support for multiplying operators.

Operator	Description	Operand Types	Result Type
*	Multiplication	Left: any integer or floating point type. Right: same type	Same as left
*	Multiplication	Left: any physical type. Right: integer or real type.	Same as left
*	Multiplication	Left: integer or real type. Right: any physical type.	Same as right
/	Division	Left: any integer or floating point type. Right: same type	Same as left
/	Division	Left: any integer or floating point type. Right: same type	Same as left
/	Division	Left: integer or real type. Right: any physical type.	Same as right
mod	Modulus	Any integer type	Same type
rem	Remainder	Any integer type	Same type

Sign operators

Sign operators can be used to specify the sign (either postive or negative) of a numeric object or literal.

Operator	Description	Operand Types	Result Type
+	Identity	Any numeric type	Same type
-	Negation	Any numeric type	Same type

Miscellaneous operators

The exponentiation and absolute value operators can be applied to numeric types, in which case they result in the same numeric type. The logical negation operator results in the same type (bit or Boolean), but with the reverse logical polarity. The shift operators provide bit-wise shift and rotate operatons for arrays of type bit or Boolean.

Operator	Description	Operand Types	Result Type
**	Exponentiation	Left: any integer type Right: integer type	Same as left
**	Exponentiation	Left: any floating point type Right: integer type	Same as left
abs	Absolute value	Any numeric type	Same as left type
not	Logical negation	Any Bit or Boolean type	Same as left type
sll	Shift left logical	Left: Any one-dimensinal arrayof Bit or Boolean Right: integer type	Same as left type
srl	Shift right logical	Left: Any one-dimensinal arrayof Bit or Boolean Right: integer type	Same as left type
sla	Shift left arithmetic	Left: Any one-dimensinal arrayof Bit or Boolean Right: integer type	Same as left type
sra	Shift right arithmetic	Left: Any one-dimensinal arrayof Bit or Boolean Right: integer type	Same as left type
rol	Rotate left	Left: Any one-dimensinal arrayof Bit or Boolean Right: integer type	Same as left type
ror	Rotate right	Left: Any one-dimensinal arrayof Bit or Boolean Right: integer type	Same as left type