Bitwise Operators

Part of the Fundamentals section of Coddy's Verilog journey — lesson 23 of 90.

Bitwise operators perform operations on each individual bit of a number. Unlike arithmetic operators (+, -, *, /) that treat numbers as whole values, bitwise operators work bit-by-bit.

Available Bitwise Operators

Operator	Operation	What It Does
`&`	AND	Output bit is 1 only if both input bits are 1
`\|`	OR	Output bit is 1 if at least one input bit is 1
`^`	XOR	Output bit is 1 if input bits are different
`~`	NOT	Flips all bits (0 becomes 1, 1 becomes 0)

When you use bitwise operators, Verilog treats the numbers as binary behind the scenes.

reg [3:0] a, b;

a = 4'd10;      // Decimal 10 = binary 1010
b = 4'd12;      // Decimal 12 = binary 1100
c = a & b;      // Works the same as using binary directly

You can write numbers in decimal, hex, or binary—Verilog converts them to binary for bitwise operations.

How Bitwise Works

Each operator works on pairs of bits (or single bits for NOT):

Example with 4-bit numbers:

a = 1010  (binary)
b = 1100  (binary)

AND:  a & b = 1000
      (1&1=1, 0&1=0, 1&0=0, 0&0=0)

OR:   a | b = 1110
      (1|1=1, 0|1=1, 1|0=1, 0|0=0)

XOR:  a ^ b = 0110
      (1^1=0, 0^1=1, 1^0=1, 0^0=0)

NOT:  ~a = 0101
      (~1=0, ~0=1, ~1=0, ~0=1)

Code Example

module bitwise_demo;
  reg [3:0] a, b;
  reg [3:0] and_res, or_res, xor_res, not_res;
  
  initial begin
    a = 4'b1010;
    b = 4'b1100;
    
    and_res = a & b;   // 1010 & 1100 = 1000
    or_res  = a | b;   // 1010 | 1100 = 1110
    xor_res = a ^ b;   // 1010 ^ 1100 = 0110
    not_res = ~a;      // ~1010 = 0101
    
    $display("a = %b", a);
    $display("b = %b", b);
    $display("a & b = %b", and_res);
    $display("a | b = %b", or_res);
    $display("a ^ b = %b", xor_res);
    $display("~a    = %b", not_res);
    $finish;
  end
endmodule

Output:

a = 1010
b = 1100
a & b = 1000
a | b = 1110
a ^ b = 0110
~a    = 0101

Challenge

Calculate the bitwise results for the given values.

What to do:

Calculate a & b and store in and_res
Calculate a | b and store in or_res
Calculate a ^ b and store in xor_res
Calculate ~a and store in not_res

Cheat sheet

Bitwise operators work on each individual bit of a number:

Operator	Operation	Output bit is 1 when...
`&`	AND	Both input bits are 1
`\|`	OR	At least one input bit is 1
`^`	XOR	Input bits are different
`~`	NOT	Flips all bits (unary)

// a = 1010, b = 1100
a & b = 1000   // AND
a | b = 1110   // OR
a ^ b = 0110   // XOR
~a    = 0101   // NOT

Try it yourself

module bitwise_challenge;
  reg [3:0] a, b;
  reg [3:0] and_res, or_res, xor_res, not_res;
  
  initial begin
    a = 4'b1101;
    b = 4'b1011;
    
    and_res = ______;   // a & b
    or_res  = ______;   // a | b
    xor_res = ______;   // a ^ b
    not_res = ______;   // ~a
    
    $display("a = %b", a);
    $display("b = %b", b);
    $display("a & b = %b", and_res);
    $display("a | b = %b", or_res);
    $display("a ^ b = %b", xor_res);
    $display("~a    = %b", not_res);
    $finish;
  end
endmodule