A system for DNA gene assembly that utilizes a DNA symbol library and a DNA linker library. The symbol library has a number of DNA symbols each having a first overhanging end and a second overhanging end different than and non-complimentary to the first end, the first and second ends being the same nucleotides for each DNA symbol. The linker library has pairs of DNA linkers, a first linker of a pair having a first end and a second end and a second linker of the pair having a first end and a second end, the first end of the first linker being the same nucleotides for each first linker and the second end of the second linker being the same nucleotides for each second linker, wherein the second end of the first linker and the first end of the second linker have complementary nucleotides. The first linker joins to the first end of a DNA symbol and the second linker joins to the second end of another DNA symbol.