Essential approaches involving photons are among the most common uses of parallel optical computation due to their recent invention, ease of production, and low cost. As a result, most researchers have concentrated their efforts on it. The Basic Arithmetic Unit BAU is built using a three-step approach that uses optical gates with three states to configure the circuitry for addition, subtraction, and multiplication. This is a new optical computing method based on the usage of a radix of (2): a binary number with a signed-digit (BSD) system that includes the numbers -1, 0, and 1. Light with horizontal polarization (LHP) (↔), light with no intensity (LNI) (⥀), and light with vertical polarization (LVP) (↨) is represented by -1, 0, and 1, respectively. This research proposes new processor designs for addition. As a result, the design can achieve m addition operations with an operand length of n bits simultaneously. To explain and justify the theoretical design idea, the three steps of adding a BSD are numerically simulated. The constructing process is thought to be more precise and faster because the time to add does not depend on the length of the word. For all entries, all bits are implemented simultaneously, boosting the system's efficiency. A simulation model for six addition processes with a total bit count of 15 bits across all entries is presented in this work performing in a one-time parallelism manner.