Expressions in VHDL are much like expressions in other programming languages. An expression is a formula combining primaries with operators. Primaries include names of objects, literals, function calls and parenthesized expressions. Operators are listed in Table 2-1 in order of decreasing precedence.
The logical operators and, or, nand, nor, xor and not operate on values of type bit or boolean, and also on one-dimensional arrays of these types. For array operands, the operation is applied between corresponding elements of each array, yielding an array of the same length as the result. For bit and boolean operands, and, or, nand, and nor are 'short-circuit' operators, that is they only evaluate their right operand if the left operand does not determine the result. So and and nand only evaluate the right operand if the left operand is true or '1', and or and nor only evaluate the right operand if the left operand is false or '0'.
The relational operators =, /=, <, <=, > and >= must have both operands of the same type, and yield boolean results. The equality operators (= and /=) can have operands of any type. For composite types, two values are equal if all of their corresponding elements are equal. The remaining operators must have operands which are scalar types or one-dimensional arrays of discrete types.
The sign operators (+ and -) and the addition (+) and subtraction (-) operators have their usual meaning on numeric operands. The concatenation operator (&) operates on one-dimensional arrays to form a new array with the contents of the right operand following the contents of the left operand. It can also concatenate a single new element to an array, or two individual elements to form an array. The concatenation operator is most commonly used with strings.
The multiplication (*) and division (/) operators work on integer, floating point and physical types types. The modulus (mod) and remainder (rem) operators only work on integer types. The absolute value (abs) operator works on any numeric type. Finally, the exponentiation (**) operator can have an integer or floating point left operand, but must have an integer right operand. A negative right operand is only allowed if the left operand is a floating point number.
| Highest precedence: | ** | abs | not | |||
| * | / | mod | rem | |||
| + (sign) | - (sign) | |||||
| + | - | & | ||||
| = | /= | < | <= | > | >= | |
| Lowest precedence: | and | or | nand | nor | xor |
Table 7-1. Operators and precedence.