All-optical non-inverted half-subtracter, half-adder, comparator, and decoder are pointed out based on a single semiconductor optical amplifier. We have replaced the continuous wave probe light with the clock pulse sequences light, which guarantees the non-inverted code output. All-optical AND, NOR, XNOR, XOR, A  •    B¯  , and   A¯    •  B logic gates are realized by four-wave mixing and cross-gain modulation of SOA, which are used to drive half-subtracter, half-adder, comparator, and decoder with 10  Gb  /  s return-to-zero code. Extinction ratio (ER) and optical signal-to-noise ratio (OSNR) are improved by a depolarizer. Compared with no depolarizer, for A  =  B output of comparator, it corresponds to XNOR; ER and OSNR are improved by about 1 dB. For d₀ output of decoder, it corresponds to NOR; ER and OSNR are improved to 1.1 dB compared with the original value. However, for borrow of half-subtracter, greater than and less than of comparator, d₁ and d₂ of decoder, it corresponds to A  •    B¯   and   A¯    •  B; ER and OSNR show only slight deterioration about 0.4 dB. For carry of half-adder and d₃ of the decoder, it corresponds to AND; OSNR has hardly changed and ER has improved by about 2 dB. It has potential applications in more complex optical computing and optical signal processing systems.