Reduction Operators

Operator	Description
&	and
~&	nand
|	or
~|	nor
^	xor
^~ or ~^	xnor

• Reduction operators are unary.
• They perform a bit-wise operation on a single operand to produce a single bit result.
• Reduction unary NAND and NOR operators operate as AND and OR respectively, but with their outputs negated.
  • Unknown bits are treated as described before.

Example

  1 module reduction_operators();

  2

  3 initial begin

  4   // Bit Wise AND reduction

  5   $display (" &  4'b1001 = %b", (&  4'b1001));

  6   $display (" &  4'bx111 = %b", (&  4'bx111));

  7   $display (" &  4'bz111 = %b", (&  4'bz111));

  8   // Bit Wise NAND reduction

  9   $display (" ~& 4'b1001 = %b", (~& 4'b1001));

 10   $display (" ~& 4'bx001 = %b", (~& 4'bx001));

 11   $display (" ~& 4'bz001 = %b", (~& 4'bz001));

 12   // Bit Wise OR reduction

 13   $display (" |  4'b1001 = %b", (|  4'b1001));

 14   $display (" |  4'bx000 = %b", (|  4'bx000));

 15   $display (" |  4'bz000 = %b", (|  4'bz000));

 16   // Bit Wise NOR reduction

 17   $display (" ~| 4'b1001 = %b", (~| 4'b1001));

 18   $display (" ~| 4'bx001 = %b", (~| 4'bx001));

 19   $display (" ~| 4'bz001 = %b", (~| 4'bz001));

 20   // Bit Wise XOR reduction

 21   $display (" ^  4'b1001 = %b", (^  4'b1001));

 22   $display (" ^  4'bx001 = %b", (^  4'bx001));

 23   $display (" ^  4'bz001 = %b", (^  4'bz001));

 24   // Bit Wise XNOR

 25   $display (" ~^ 4'b1001 = %b", (~^ 4'b1001));

 26   $display (" ~^ 4'bx001 = %b", (~^ 4'bx001));

 27   $display (" ~^ 4'bz001 = %b", (~^ 4'bz001));

 28    #10  $finish;

 29 end

 30

 31 endmodule
  &  4'b1001 = 0

  &  4'bx111 = x

  &  4'bz111 = x

  ~& 4'b1001 = 1

  ~& 4'bx001 = 1

  ~& 4'bz001 = 1

  |  4'b1001 = 1

  |  4'bx000 = x

  |  4'bz000 = x

  ~| 4'b1001 = 0

  ~| 4'bx001 = 0

  ~| 4'bz001 = 0

  ^  4'b1001 = 0

  ^  4'bx001 = x

  ^  4'bz001 = x

  ~^ 4'b1001 = 1

  ~^ 4'bx001 = x

  ~^ 4'bz001 = x

Shift Operators

Operator	Description
<<	left shift
>>	right shift

• The left operand is shifted by the number of bit positions given by the right operand.
• The vacated bit positions are filled with zeroes.

Example

  1 module shift_operators();

  2

  3 initial begin

  4   // Left Shift

  5   $display (" 4'b1001 << 1 = %b", (4'b1001 << 1));

  6   $display (" 4'b10x1 << 1 = %b", (4'b10x1 << 1));

  7   $display (" 4'b10z1 << 1 = %b", (4'b10z1 << 1));

  8   // Right Shift

  9   $display (" 4'b1001 >> 1 = %b", (4'b1001 >> 1));

 10   $display (" 4'b10x1 >> 1 = %b", (4'b10x1 >> 1));

 11   $display (" 4'b10z1 >> 1 = %b", (4'b10z1 >> 1));

 12    #10  $finish;

 13 end

 14

 15 endmodule

  4'b1001 << 1 = 0010

  4'b10x1 << 1 = 0x10

  4'b10z1 << 1 = 0z10

  4'b1001 >> 1 = 0100

  4'b10x1 >> 1 = 010x

  4'b10z1 >> 1 = 010z

Concatenation Operator

• Concatenations are expressed using the brace characters { and }, with commas separating the expressions within.
  • Example: + {a, b[3:0], c, 4'b1001} // if a and c are 8-bit numbers, the results has 24 bits
• Unsized constant numbers are not allowed in concatenations.

Example

 1 module concatenation_operator();

 2

 3 initial begin

 4   // concatenation

 5   $display (" {4'b1001,4'b10x1}  = %b", {4'b1001,4'b10x1});

 6    #10  $finish;

 7 end

 8

 9 endmodule
  {4'b1001,4'b10x1}  = 100110x1

Replication Operator
Replication operator is used to replicate a group of bits n times. Say you have a 4 bit variable and you want to replicate it 4 times to get a 16 bit variable: then we can use the replication operator.

Operator	Description
{n{m}}	Replicate value m, n times

• Repetition multipliers (must be constants) can be used:
  • {3{a}} // this is equivalent to {a, a, a}
• Nested concatenations and replication operator are possible:
  • {b, {3{c, d}}} // this is equivalent to {b, c, d, c, d, c, d}

Example

  1 module replication_operator();

  2

  3 initial begin

  4   // replication

  5   $display (" {4{4'b1001}}      = %b", {4{4'b1001}});

  6   // replication and concatenation

  7   $display (" {4{4'b1001,1'bz}} = %b", {4{4'b1001,1'bz}});

  8    #10  $finish;

  9 end

 10

 11 endmodule

  {4{4'b1001}       = 1001100110011001

  {4{4'b1001,1'bz}  = 1001z1001z1001z1001z

Conditional Operators

• The conditional operator has the following C-like format:
  • cond_expr ? true_expr : false_expr
• The true_expr or the false_expr is evaluated and used as a result depending on what cond_expr evaluates to (true or false).

Example

1 module conditional_operator();   2   3 wire out;   4 reg enable,data;   5 // Tri state buffer   6 assign out = (enable) ? data : 1'bz;   7   8 initial begin   9   $display ("time\t enable data out");  10   $monitor ("%g\t %b      %b    %b",$time,enable,data,out);  11   enable = 0;  12   data = 0;  13    #1  data = 1;  14    #1  data = 0;  15    #1  enable = 1;  16    #1  data = 1;  17    #1  data = 0;  18    #1  enable = 0;  19    #10  $finish;  20 end  21  22 endmodule

time         enable data out

 0             0      0    z

 1             0      1    z

 2             0      0    z

 3             1      0    0

 4             1      1    1

 5             1      0    0

 6             0      0    z

Operator Precedence

Operator	Symbols
Unary, Multiply, Divide, Modulus	!, ~, *, /, %
Add, Subtract, Shift	+, - ,
Relation, Equality	,=,==,!=,===,!==
Reduction	&, !&,^,^~,|,~|
Logic	&&, ||
Conditional	? :

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