How many distinct kinds of computer-based numerical systems are there?

How many distinct kinds of computer-based numerical systems are there?
Statistically Sorted
Number systems are a sort of mathematical notation that converts numerical values into a form that can be understood by computers. A number symbolizes an objectively established and practically helpful value in the fields of counting, measurement, and mathematics. In addition to natural numbers, whole numbers, rational numbers, irrational numbers, and so on, numbers may be further subdivided in many other ways. Countless unique numbering schemes exist, each with its peculiarities and uses. Binary, octal, decimal, and hexadecimal are all examples of this.

From binary to octal to decimal to hexadecimal, all of those systems and more are represented here. We’ll go through how to do the conversions between the various number systems and use many of examples to really drive the point home.

First things first: some number theory basics.

Numbering systems are nothing more than conventions for writing numbers. The rules for representing numbers in writing are known as the numeration system. The most prevalent are the ones and zeroes representing the binary 0 and 1. Numbers 0 through 9 are often substituted for their counterparts in other numbering systems.

The Importance of Number Systems

Every number system relies on a shared vocabulary of signs, often digits, to represent numbers. The value of a number may be calculated from a single digit, its place in the number, and the base used. Arithmetic operations like addition, subtraction, and division are feasible because of the unique representation of the integers. Example: Explain the results of dividing 2000 by 3. All numbers written and read from memory in a computer are represented by the number system represented by the hardware.

The numerical systems that work with contemporary computers are listed below.

Quantitative representation based on binary digits

Numbers that go up to eight digits

System of numbers based on the decimal system

Numbers are written in hexadecimal (hex)

Binary notation represents numbers that can only take on one of two possible values.

Only the digits 0 and 1 may exist in a binary number system. There are no other numbers except 0 and 1 in this system. Since binary uses 0 and 1, the number 2 serves as its foundation.

the system of numbers based on eight

The octal system can represent a wide range of numbers with just zero through seven digits available. Here, digits go from 0 to 7, inclusive. The octal system, which consists of just eight digits, uses 8 as its foundational number.

The use of decimals

Only the ten (10) digits zero (0.0) through nine (9.9) are used in the decimal number system (9). Each of the digits from 0 to 9 has its special significance in this scheme (value). Since there can only be ten digits in the decimal system, 10 is the basis.

A numbering system derived from the hexadecimal system

In hexadecimal, every 16 letters (represented by 0 through 9) also represents a numeral (A–F). To utilize this method, we substitute the letters 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F for the decimal points. Since there are 16 letters in the English alphabet, hexadecimal also has 16 digits. Letter A is represented by the number 10, letter B by 11, letter C by 12, letter D by 13, letter E by 14, and letter F by 15.