The calculator would work by running a program in the 89C669. This is a microcontroller that is based on the 8051 core. These chips do nothing until programmed. The part must be programmed to scan the keyboard, interpret the keystrokes, perform the arithmetic, and display the results to the seven segment display.
The reason, no one has responded is that your request is too general. The specific microcode or program needed depends on the chips used and how they are hooked up. Unless someone else has built a calculator with exactly the same parts in exactly the same arrangement, the microcode you need will not be available. You would need to write it. Each different configuration is a unique set of microcode.
This may seem confusing as you can easily download new computer programs or code from the web and they work on your machine. The reason for this is that the hardware configuration of the machine is a fixed standard. Without the standard, this same unique code or program requirement would exist.