This example shows how to include the IEEE std_logic_1164 library in VHDL code. First, the library is included to access the std_logic type. Then, a signal 'a' of type std_logic is declared and initialized to '0'. Later, the signal 'a' is assigned the value '1'. The execution table traces these steps showing how the signal value changes from undefined to '0' and finally to '1'. Including the IEEE library is essential because it defines the std_logic type and its behavior. Without it, the code will not compile. Assignments to std_logic signals update their values, which can be observed during simulation.