Reduction operators¶

When do we need reduction operators?¶

You're already familiar with bitwise operations between two values, e.g., a & b or a ^ b. Sometimes, you want to create a wide gate that operates on all of the bits of one vector, like (a[0] & a[1] & a[2] & a[3] ... ), which gets tedious if the vector is long.

The reduction operators can do AND, OR, and XOR of the bits of a vector, producing one bit of output:

Verilog
& a[3:0]     // AND: a[3]&a[2]&a[1]&a[0]. Equivalent to (a[3:0] == 4'hf)
| b[3:0]     // OR:  b[3]|b[2]|b[1]|b[0]. Equivalent to (b[3:0] != 4'h0)
^ c[2:0]     // XOR: c[2]^c[1]^c[0]

These are unary operators that have only one operand (similar to the NOT operators ! and ~). You can also invert the outputs of these to create NAND, NOR, and XNOR gates, e.g., (~& d[7:0]).

Now you can revisit 4-input gates and 100-input gates.

Practice¶

Problem statement¶

Parity checking is often used as a simple method of detecting errors when transmitting data through an imperfect channel. Create a circuit that will compute a parity bit for a 8-bit byte (which will add a 9th bit to the byte). We will use "even" parity, where the parity bit is just the XOR of all 8 data bits.

Verilog
module top_module (
    input [7:0] in,
    output parity); 

endmodule

Solution¶

Verilog
module top_module (
    input [7:0] in,
    output parity); 
    assign parity=^in;
endmodule