Basic Binary Arithmetic

Basic arithmetic of logical expression is a key part of digital electronics. Arithmetic of digital electronic includes mostly what we always use in general mathematical operations like Addition, subtraction etc. However, there are some operations that not available in conventional mathematics. Digital electronics uses Boolean Algebra for all its mathematical operations. Also, the way how numbers are written and manipulated is different. For example, digital electronics has no negative sign and no negative numbers but it can handle and work with negative numbers. Basic binary arithmetic included addition, subtraction and complements.

Like any other engineering discipline, digital electronics also requires mathematics to manipulate numbers to design small but efficient systems and predict the operations of the system in future. In digital electronics, we use binary and hexadecimal number system. Most of the mathematics in digital electronics is executed using binary number system and this poses a problem. Conventional mathematical and arithmetic are designed to suit decimal number system. To solve this problem, digital electronics use a mathematical discipline that was invented long before modern era but is perfect for digital electronics. It is known as Boolean Algebra. We are going to use Boolean algebra to perform simple arithmetic like addition and counting in binary number system. But before that we are going to get familiar with important aspect of binary number manipulation called “Addition”, “Complement” and “Subtraction”.