The multiplication process is merely a series of logical ANDs and XORs. In the figure bellow, the vector [1001] is multiplied by the identity matrix I. This serves to demonstrate the technique of modulo-2 matrix multiplication, as well as to prove that dI = d.
Each row of the matrix corresponds to a bit in the data vector, with the top row being the most significant bit, and the bottom row being the least significant. The multiplication of the vector [1001] by the first column [1000] is :
1001 & 1000 = 1000
The addition modulo-2 of the vector [1000] is:
1^0^0^0 = 1
giving the first bit of the product vector.
|1 0 0 0 | |0 1 0 0 | [1 0 0 1] * |0 0 1 0 | = [1 0 0 1] |0 0 0 1 |
