The 4-bit CPU was designed to execute 18 distinct operations from a lookup table. It was tested by executing an instruction set that performed operations like load, store, add, and jump instructions. The accumulator and program counter displays were observed after each instruction to verify the correct operations. Various components like a RAM, ALU, program counter, and decoders were used in the design. The group members demonstrated different parts of the instruction set to verify the CPU was functioning properly.