Firmware
Firmware is like computer software, only written specifically for embedded electronics. It defines what actions are taken depending on a series of inputs, determining how the electronic device functions.
An entire variety of programming languages are available on the market today, with Assembly and C being the most popular, although Assembly is losing ground due to the complexity of newer electronics. In essence, Assembly is the language closest to the actual hardware, providing an enormous amount of control, with the disadvantage of complexity. It is mostly used where timing is critical, or in less complex projects.
Aside from programming, programmable logic such as FPGA's offer Synthesis, in which case there are no bits set, but connections are made between logic ports, in essence creating a new truly digital component. This is the strength of programmable logic, as it's capable of operating both very fast, and in parallel, as opposed to microcontrollers, which have to run through their programs step by step.