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Verilog_Calculator_Matrix_Multiplication

This project shows how to make some basic matrix multiplication in Verilog.

Characteristics

There are some details about this implementation:

  1. Three by three matrixes are used.
  2. Each matrix input is a two byte container, so the maximum value (in decimal) it can hold is 65,535.

Scalability

If you need to increase the maximum value (65,535), then modify

reg [15:0] A1 [0:2][0:2];

to something like

reg [63:0] A1 [0:2][0:2];

in the case you want to work with 64 bits. Also remember to modify

input [143:0] A;

to

input [575:0] A;

(The value of 575 comes from having 9 spaces of 64 bits).

Similarly, if you need to modify the program to work with a n*n matrix, just modify

{A1[0][0],A1[0][1],A1[0][2],A1[1][0],A1[1][1],A1[1][2],A1[2][0],A1[2][1],A1[2][2]} = A;

in the calculator module to work with the correct amount of cells.

Visualization

This code was run in Xilinx ISE. When running the simulation, only the result was viewable as a one dimensional array. In order to fix this, in the simulation window:

  1. Add the matrixes from the Calculator.v to the simulation.
  2. Change the Radix to signed integer.
  3. Relaunch the simulation.

Run example

1D to 2D and 2D to 1D remapping

The transformation from 1D to 2D is done in the code

{A1[0][0],A1[0][1],A1[0][2],A1[1][0],A1[1][1],A1[1][2],A1[2][0],A1[2][1],A1[2][2]} = A;

where the 2D matrix A1 is populated from the 1D array A. Similarly, the remapping from 2D to 1D is done in

Result = {Res1[0][0],Res1[0][1],Res1[0][2],Res1[1][0],Res1[1][1],Res1[1][2],Res1[2][0],Res1[2][1],Res1[2][2]};

as 2D arrays cannot be outputs of modules.