Digital Signal Processing 101

APPENDIX EBinary Field Arithmetic

Binary field arithmetic is used in coding. The basic rules are very simple. Addition is as follows:

This also corresponds to the exclusive OR or XOR operator in digital logic. Subtraction results are identical to addition; there is no distinction between the two operations.

Multiplication is as follows:

Division is not defined or allowed.

Linearity means that if two input codewords are input to a system, X₁ and X₂, the output result is the same as if the sum of two codewords X₁+X₂ were input instead. A more mathematical ...