On the basis of Sagnac interferometric structure, a simple novel ultrafast scheme of all-optical half-adder is proposed. The structure comprises two of the same balanced terahertz optical asymmetric demultiplexers (TOADs). One TOAD is utilized to achieve an all-optical XOR gate, which is logic SUM. The other is utilized to obtain an all-optical AND gate, which is logic CARRY. Logical SUM and CARRY are simultaneously realized at 80 Gbit/s. Through numerical analysis, the operating characteristics of the scheme are illustrated at 80 Gbit/s. Furthermore, the carrier recovery time of the semiconductor optical amplifier is no longer a crucial parameter to restrict the operation speed of this scheme.