Formal Definition
Operators provide a means to construct expressions.
Simplified Syntax
Arithmetic: + - * /
Modulus: %
Relational: < <= > >=
Logical: ! && ||
Logical equality: == !=
Case equality: === !==
Bit-wise: ~ & | ^ ~^ ^~
Reduction: & ~& | ~| ^ ~^ ^~
Shift: << >>
Conditional: ?:
Event or: or
Concatenations: {} {{}}
Description
Verilog HDL operators can be divided into several groups.
Operator | Description |
+ - ! ~ | Unary |
* / % | Arithmetic |
+ - (binary) | Binary |
<< >> | Shift |
< <= > => | Relational |
== != === !== | Equality |
& ~& | and nand |
^ ~^ ^~ | xor xnor |
| ~| | or nor |
&& | Logical and |
|| | Logical or |
?: | Conditional operator |
Table 13: Operator's priority
Arithmetic operators
The arithmetic operators can be used with all data types.
Operator | Description |
a + b | a plus b |
a - b | a minus b |
a * b | a multiply by b |
a / b | a divide by b |
a % b | a modulo b |
Table 14: Arithmetic operators
The modulus operator is not allowed for real data type variables. For the modulus operator, the result takes the sign of the first operand. Examples of using these operators are shown in Example 1.
Relational operators
The relational operators are used to compare expressions. The value returned by the relational operators is 0 if the expression evaluates to false and 1 if expression evaluates to true.
Operator | Description |
a < b | a less than b |
a > b | a greater than b |
a <= b | a less than or equal to b |
a => b | a greater than or equal to b |
Table 15: Relational operators
Examples of using the relational operators are shown in Example 2.
Equality operators
The equality operators are used to compare expressions. If a comparison fails, then the result will be 0, otherwise it will be 1.
If both operands of logical equality (==) or logical inequality (!=) contain unknown (x) or a high-impedance (z) value, then the result of comparison will be unknown (x). Otherwise it will be true or false.
If operands of case equality (===) or case inequality (!==) contain unknown (x) or a high-impedance (z) value, then the result will be calculated bit by bit.
Examples of using the equality operators are shown in Example 3.
Logical operators
The logical operators are used to connect expressions.
Operator | Description |
a && b | a and b |
a || b | a or b |
!a | not a |
Table 16: Logical operators
The result for these operators is 0 (when false), 1 (when true), and unknown (x - when ambiguous). The negation operator (!) turns a nonzero or true value of the operand into 0, zero or false value into 1, and ambiguous value of operator results in x (unknown value).
Examples of using the logical operators are shown in Example 4.
Bit-wise operators
The bit-wise operators calculate each bit of results by evaluating the logical expression on a pair of corresponding operand bits.
& | 0 | 1 | x | z |
0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | x | x |
x | 0 | x | x | x |
z | 0 | x | x | x |
Table 17: Bit-wise and operator
| | 0 | 1 | x | z |
0 | 0 | 1 | x | x |
1 | 1 | 1 | 1 | 1 |
x | x | 1 | x | x |
z | x | 1 | x | x |
Table 18: Bit-wise or operator
^ | 0 | 1 | x | z |
0 | 0 | 1 | x | x |
1 | 1 | 0 | x | x |
x | x | x | x | x |
z | x | x | x | x |
Table 19: Bit-wise exclusive or operator
~^ ^~ | 0 | 1 | x | z |
0 | 1 | 0 | x | x |
1 | 0 | 1 | x | x |
x | x | x | x | x |
z | x | x | x | x |
Table 20: Bit-wise exclusive nor operator
~ | Result |
0 | 1 |
1 | 0 |
x | X |
z | X |
Table 21: Bit-wise negation operator
Examples of using the bit-wise operators are shown in Example 5.
Reduction operators
The reduction operator produces a 1-bit result. This result is calculated by recursively applying bit-wise operation on all bits of the operand. At each step of this recursive calculation the logical bit-wise operation is performed on the result of a previous operation and on the next bit of the operand. The operation is repeated for all bits of the operand.
Examples of using the reduction operators are in shown Example 6.
Shift operators
The shift operators perform left and right shifts on their left operand by the number of positions specified by their right operand. All vacated bits are filled with zeroes. If the expression that specifies the number of bits to shift (right operand) has unknown (x) or high-impedance (z) value, then result will be unknown.
Examples of using the shift operators are in shown Example 7.
Conditional operator
The conditional operator is described in the Conditional operator section.
Concatenations
Concatenations are described in the Concatenations section.
Event or operator
The event or operator is described in the section on Procedural timing controls.
Examples
Example 1
reg [3:0] a, b;
a = 4;
b = 3;
a + b = 7
a - b = 1
a * b = 12
a / b = 1
a % b = 1
5 % 2 = 1
5 % -2 = 1
-5 % 2 = -1
-5 % -2 = -1
Example 2
reg [3:0] a, b;
a = 4'b1100;
b = 4'b0110;
a < b // false - 0
a > 8 // true - 1
a <= b // false - 0
a >= 10 // true - 1
a < 4'b1zzz // unknown - x
a < 4'b1x01 // unknown - x
Example 3
reg [3:0] a, b;
a = 4'b1100;
b = 4'b101x;
a == 4'b1100 // true - 1
a != 4'b1100 // false - 0
a == 4'b1z10 // false - 0
a != 4'b100x // true - 1
b == 4'b101x // unknown - x
b != 4'b101x // unknown - x
b === 4'b101x // true - 1
b !== 4'b101x // false - 0
Example 4
reg [3:0] a, b;
a = 4'b1100;
b = 4'b0000;
!a // 0 - false
!b // 1 - true
a && b // 0 - false
a || b // 1 - true
Example 5
reg [7:0] a, b;
a = 8'b1010xzxz;
b = 8'b10010011;
a & b = 8'b100000xx;
a | b = 8'b1011xx11;
a ^ b = 8'b0011xxxx;
a ~^ b = 8'b1100xxxx;
~ a = 8'b0101xxxx;
Example 6
value | & | ~& | | | ~| | ^ | ~^ | ^~ |
4'b0000 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
4'b0001 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
4'b0011 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
4'b0111 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
4'b1111 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
4'b01xx | 0 | 1 | 1 | 0 | x | x | x |
4'b01z0 | 0 | 1 | 1 | 0 | x | x | x |
Table 22: Reduction operators
Example 7
reg [3:0] a;
a = 4'b1111;
a << 3 = 4'b1000
a >> 3 = 4'b0001
a << 1'bz = 4'bxxxx
a >> 1'bx = 4'bxxxx
Important Notes
- Some of the operators cannot be used with reals.
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