Number systems are a mathematical notations that are used to express and represent numbers. This method uses a consistent and specific set of digits or symbols to represent a certain quantity. And its position is a very sensitive element as one wrong misplacement can change the entirety of the value.

Its base determines the total number of unique symbols used in the system, and the position of the digit determines the actual value, which is the power of the base. For example, a decimal number 123, the '1' represents 1 x 10^2. These number systems allows the unique representation of every number, and facilities arithmetic operations.

The four most common types of number systems, specifically in computing and modern mathematics are:

• Decimal has a base of 10, and uses numbers from 0 to 9. And each position has a power of 10 (10^0, 10^1).
• Binary has a base of 2, and has only two digits used, 0 and 1. Each position has a power of 2 (2^0, 2^1).
• Octal has a base of 8, using the digits: 0 until 7, and has a place value of 8.
• Hexadecimal uses a base of 16, and using numbers: 0 to 9, and letters: A to F. A to F represents numbers 10 to 15 in a single character, and its position has a power of 16.

Each number systems serves its own purpose and has man primary uses and significance. More specifically:

• Decimal (base-10) is the universal human counting and communication.
• Binary (base-2) is the foundation of all digital electronics and computing.
• Octal (base-8) is a compact representation of binary data in computing.
• Hexadecimal (base-16) is the mst common shorthand for representing large binary numbers in computing.