Question

The simplest types of programmable logic ICs are called PLDs, PALs, PLAs, and GALs. While each acronym represents a slightly different internal design architecture, these devices share a common feature of using inverters, AND gates, and OR gates to implement any desired combinational logic function. Explain how it is possible to generate any arbitrary logic function with just these gate types (inverter, AND, OR), without any others.

What principle or convention of Boolean algebra is used by these devices to do this?

Answer 1

Logic functions can be generated using inverters, AND, and OR gates based on the principle of functional completeness in Boolean algebra. These devices, integrated into ICs, make use of transistors to process binary code and enable the operation of various electronic devices.

Step-by-step explanation:

The ability to generate any arbitrary logic function using inverters, AND gates, and OR gates in devices such as PLDs, PALs, PLAs, and GALs is based on the principle of functional completeness in Boolean algebra. This principle states that any Boolean function can be constructed using only these three types of gates. An inverter is used to create a logical NOT operation, while AND and OR gates are used to achieve logical AND and logical OR operations respectively. By combining these gates, it is possible to build more complex circuits that can execute any combinational logic task.

Integrated circuits (ICs), commonly known as microchips, include a vast collection of transistors on a single piece of silicon. These ICs are fundamental in the operation of various modern electronic devices, from computers to smartphones and global communication networks. Transistors within these ICs act like on-off switches to process the binary code of digital signals.