Let's say you want a counter that counts more or less "randomly", you can use an LFSR.

Here's an example.

As you can see, an LFSR is a shift-register with some XOR gates. The one shown above is an 8-taps LFSR (it uses 8 flip-flops).

The output sequence starts as follow (assuming all the flip-flops start at '1'):

11111111 11000111 11011011 11010101 11010010 01101001 10001100 01000110 00100011 10101001 11101100 01110110 00111011 10100101 ...

Here's the LFSR source code.

moduleLFSR8_11D(inputclk,outputreg[7:0] LFSR = 255 // put here the initial value );wirefeedback = LFSR[7];always@(posedgeclk)beginLFSR[0] <= feedback; LFSR[1] <= LFSR[0]; LFSR[2] <= LFSR[1] ^ feedback; LFSR[3] <= LFSR[2] ^ feedback; LFSR[4] <= LFSR[3] ^ feedback; LFSR[5] <= LFSR[4]; LFSR[6] <= LFSR[5]; LFSR[7] <= LFSR[6];endendmodule

Notice that we made it start at 255. That's because 0 is a dead-end state, so we can choose any start value but 0. After that, the LFSR changes value at each clock cycle but never reaches 0, so it goes through only 255 8bit values (out of 256 possible combinations of a 8bit output) before starting again.

Now, instead of outputting the full eight bits, we could output just one bit (i.e. choose any of the flip-flops to make the output, keep the other seven internal). That generates a string of 255 '0' and '1' that looks random (although it repeats itself after 255 clocks). Useful for a noise generator...

You can tweak the LFSR:

- Select a different number of taps (we chose 8 above).
- Change the way the feedback network is wired - like change the number XOR gates, where they are placed, or replace XOR gates by XNOR.

Certain feedback configurations will create islands of possible values. For example, this LFSR looks similar to the first one but loops through only 30 values.

moduleLFSR8_105(inputclk,outputreg[7:0] LFSR = 255 );wirefeedback = LFSR[7];always@(posedgeclk)beginLFSR[0] <= feedback; LFSR[1] <= LFSR[0]; LFSR[2] <= LFSR[1] ^ feedback; LFSR[3] <= LFSR[2]; LFSR[4] <= LFSR[3]; LFSR[5] <= LFSR[4]; LFSR[6] <= LFSR[5]; LFSR[7] <= LFSR[6];endendmodule

It is also possible to add a bit of logic in the feedback so that the LFSR reaches all possible states.

moduleLFSR8_11D(inputclk,outputreg[7:0] LFSR = 255 );wirefeedback = LFSR[7] ^ (LFSR[6:0]==7'b0000000); // modified feedback allows to reach 256 states instead of 255always@(posedgeclk)beginLFSR[0] <= feedback; LFSR[1] <= LFSR[0]; LFSR[2] <= LFSR[1] ^ feedback; LFSR[3] <= LFSR[2] ^ feedback; LFSR[4] <= LFSR[3] ^ feedback; LFSR[5] <= LFSR[4]; LFSR[6] <= LFSR[5]; LFSR[7] <= LFSR[6];endendmodule

We made a small Windows utility that allows experimenting with LFSR designs.

Download it here.