Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. Digital electronic circuits are usually made from large assemblies of logic gates, often packaged in integrated circuits.

Boolean algebra is a mathematical system that may be defined with a set of elements, a set of operators, and a number of unproved axioms or postulates. Boolean algebra is a convenient tool to study the logic design of digital systems. The complement of 0 is 1 and the complement of 1 is 0.

As you know decimal, binary, octal and hexadecimal number systems are positional value number systems. To convert binary, octal, and hexadecimal to a decimal number, we just need to add the product of each digit with its positional value.

Digital systems are said to be constructed by using logic gates. These gates are the AND, OR, NOT, NAND, NOR, EXOR and EXNOR gates. The basic operations are described below with the aid of truth tables. The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high.

Many of our household items make use of digital electronics. This could include laptops, televisions, remote controls and other entertainment systems, to kitchen appliances like dishwashers and washing machines. Computers are one of the most complex examples and will make use of numerous, complex circuits. Examples of such devices are computers, information appliances, digital cameras, digital televisions, flash memory, key USB memory, mobile phones, hard disks, and devices of computer memory.

In Minterm, we look for the functions where the output results in “1” while in Maxterm we look for functions where the output results in “0”. We perform Sum of minterm also known as Sum of products (SOP). We perform Product of Maxterm also known as Product of sum (POS).

In digital circuits, an adder–subtractor is a circuit that is capable of adding or subtracting numbers (in particular, binary). Quite similar to the half adder, a half subtractor subtracts two 1-bit binary numbers to give two outputs, difference and borrow. Since it neglects any borrow inputs and essentially performs half the function of a subtractor, it is known as the half subtractor. It is also possible to construct a circuit that performs both addition and subtraction at the same time.