Operators
Operator ---- used in ----> Expression

Syntax

See LRM section 7.2

Rules and Examples

The logical operators are predefined for bit, boolean, bit_vector, linear arrays of boolean, std_logic and std_logic_vector types. They return a value of the same type: 
and, or, nand, nor, xor, not
The equality and inequality operators are predefined for all types, and they return a boolean value: 
=   -- equal to
/=  -- not equal to

The other relational operators are predefined for all scalar types, and all one-dimensional array types. They also return a boolean value: 
<   -- less than
>   -- greater than
<=  -- less than or equal to
>=  -- greater than or equal to

For arrays of different lengthsm the predefined relational operators align the left-hand elements and compare corresponding positions. This can lead to unexpected results: 
constant ARR1 :bit_vector := "0011";
constant ARR2 :bit_vector := "01";
-- (ARR1 < ARR2) will return true

The & operator is used to concatenate (join) arrays, or join new elements to an array: 
Z_BUS(1 downto 0) <= '0' & B_BIT;
BYTE <= A_BUS & B_BUS;

Add, subtract, multiply and divide are defined for integer and real. Both operands must be the same type, and the result is also of the same type: 
signal INT1, INT2: integer := 0;
signal REAL1, REAL2: real := 6.7;
...
INT1  <= INT1 + 3;
REAL1 <= REAL2 - 2.2;
INT2  <= INT1 * REAL1;   --illegal
INT2  <= INT1 * INTEGER(REAL1);
REAL2 <= REAL1 / 42.3;

For physical types (e.g.time), assignments must be dimensionally consistant: 
variable TIME1,TIME2: time;
...
TIME1 := TIME2 * 2.5;
TIME1 := TIME2 / 4;
TIME1 := 3.6 ns + TIME2;
TIME1 := TIME2 * 6.67 ns;   --illegal

Other numeric operators are exponentiation (**), absolute value (abs), modulus (mod), and remainder (rem).

Synthesis Issues

Most predefined operators are synthesisable, providing they are used with types accepted by the synthesis tool. See also type declarations and overloading

The following are not usually synthesisable, except as part of a constant expression: exponentiation (**), division by other than 2, mod, rem.

Whats New in '93

xnor has been added to the logical operators in VHDL-94. New shift and rotate operators are defined for one-dimensional arrays of bit or boolean: 

sll -- shift left logical
srl -- shift right logical
sla -- shift left arithmetic
sra -- shift right arithmetic
rol -- rotate left
ror -- rotate right