XOR XNOR Gates

Part of the Fundamentals section of Coddy's Verilog journey — lesson 41 of 90.

This lesson covers two additional logic gates: XOR (exclusive OR) and XNOR (exclusive NOR). These gates are useful for comparing bits and parity checking.

XOR Gate

The XOR gate outputs 1 when the inputs are different.

Truth Table (2-input):

a	b	out
0	0	0
0	1	1
1	0	1
1	1	0

Verilog gate primitive:

xor(out, a, b);

Continuous assignment equivalent:

assign out = a ^ b;

XNOR Gate

The XNOR gate outputs 1 when the inputs are the same. It is the opposite of XOR.

Truth Table (2-input):

a	b	out
0	0	1
0	1	0
1	0	0
1	1	1

Verilog gate primitive:

xnor(out, a, b);

Continuous assignment equivalent:

assign out = a ~^ b;   // or ~(a ^ b)

Multiple Inputs

XOR and XNOR gates can have more than 2 inputs. The output is:

XOR: 1 if an odd number of inputs are 1
XNOR: 1 if an even number of inputs are 1

xor(out, a, b, c);      // 3-input XOR
xnor(out, p, q, r, s);  // 4-input XNOR

Example (3-input XOR):

a	b	c	out
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	0
1	1	0	0
1	1	1	1

Common Uses

Use	Example
Compare if two bits are different	`xor(diff, a, b)`
Compare if two bits are the same	`xnor(same, a, b)`
Parity generation (odd number of 1's)	`xor(parity, data[0], data[1], data[2], data[3])`
Parity checking (even number of 1's)	`xnor(parity, data[0], data[1], data[2], data[3])`

Code Example

module xor_xnor_demo (
  input a, b,
  output xor_out,
  output xnor_out
);
  xor(xor_out, a, b);
  xnor(xnor_out, a, b);
endmodule

Summary Table

Gate	Output 1 when	Primitive	Operator
XOR	Inputs are different	`xor(out, a, b)`	`^`
XNOR	Inputs are the same	`xnor(out, a, b)`	`~^`

Challenge

Add the missing gate primitives based on the tasks.

What to do:

Create an XOR gate with output xor_result and inputs x and y
Create an XNOR gate with output xnor_result and inputs x and y

Cheat sheet

XOR outputs 1 when inputs are different. XNOR outputs 1 when inputs are the same.

Gate	Output 1 when	Primitive	Operator
XOR	Inputs are different	`xor(out, a, b)`	`^`
XNOR	Inputs are the same	`xnor(out, a, b)`	`~^`

For multiple inputs: XOR outputs 1 if an odd number of inputs are 1; XNOR outputs 1 if an even number of inputs are 1.

xor(out, a, b, c);      // 3-input XOR
xnor(out, p, q, r, s);  // 4-input XNOR

Try it yourself

module xor_xnor_challenge (
  input x,
  input y,
  output xor_result,
  output xnor_result
);
  
  // TODO: Add XOR gate (xor_result = x ^ y)
  
  // TODO: Add XNOR gate (xnor_result = x ~^ y)

endmodule