In this paper the design and implementation of a new parallel adder

SJ-MSD adder

in a ternary optical computer (i.e.TOC) are proposed. It is introduced that a sufficient conditions (Shen's sufficient theorem) which judging that a group of ternary logical transformations is able to build a MSD (Modified Signed Digit) addition. Five logical transformations S

1

S

2

J

1

J

2

and J

3

(i.e.SJ transformation) and a parallel carry-free MSD addition rule (i.e.SJ rule) are proposed to construct SJ-MSD adder. Meanwhile according to Shen's sufficient theorem

the reliability of the SJ transform

ation and SJ rule used to construct MSD parallel adder is proved. Subsequently

in the ternary optical computer prototype system SD16

the design and implement of SJ-MSD adder are discussed in detail. At the same time the implementation methods of pipeline addition and sharing one SJ-MSD adder for multiple data are expatiated. Some experiments of SJ-MSD adder is introduced. Compared with the previous TW-MSD adder

the SJ-MSD adder occupies processor bits less about 25%. So the optical processor’ efficiency is effectively improved.