An all-optical full adder using semiconductor optical amplifiers has been demonstrated at 10 Gbps for the first time. The full adder consisted of XOR and NOR gates only utilizes the mechanism of cross-gain modulation. The full adder utilize two logic functions of SUM and CARRY, which can be demonstrated by using two XOR gates and four NOR gates, respectively. By passing signal A as probe signal and signal B as pump signal into SOA-1, Boolean A NOT B can be obtained. Also, by changing the role of signals A and B for SOA-2, Boolean NOT A B can be acquired. Addition of Boolean A NOT B and NOT A B results in NOT A B + A NOT B , which is Boolean expression of logic XOR. By passing this XOR signal and signal C into the second XOR gate with the same principle, SUM signal of the full adder can be obtained. The Boolean expression of SUM can be expressed as A # B # C . With the first three NOR gates, Boolean NOT(A+B), NOT(B+C), and NOT(C+A) can be obtained. With the addition of these outputs, Boolean NOT(A+B) + NOT(B+C) + NOT(C+A) can be formed. By injecting these outputs through the last NOR gate with clock signal, CARRY signal of the full adder can be realized. The Boolean expression of CARRY can be expressed as AB +BC +CA. The extinction ratio is about 6.1dB.