What is Number System in Maths? A number system is defined as a system of writing for expressing numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, and division. The value of any digit in a number can be determined by
• The digit • Its position in the number • The base of the number system Types of Number System There are various types of the number system in mathematics. The four most common number system types are 1. Decimal number system (Base- 10) 2. Binary number system (Base- 2) 3. Octal number system (Base-8) 4. Hexadecimal number system (Base- 16) Decimal Number System (Base 10 Number System) Decimal number system has base 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is expressed in decimal numbers. The base of the decimal is 10. This shows that there are ten symbols, 0 to 9. Similarly, the system using the symbols 0, 1, two will be of base 3, four symbols will be of base 4 and so on. Every position shows a particular power of the base (10). For example, the decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in the hundreds position, and 1 in the thousands place whose value can be written as (1×1000) + (4×100) + (5×10) + (7×1) (1×103) + (4×102) + (5×101) + (7×1)
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Binary Number System (Base 2 Number System) The base 2 number system is also known as the Binary number system wherein, only two binary digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number. We can convert any system into binary and vice versa. For Example, to write (14)10 as a binary number. Solution:
Base 2 Number System Example ˆ (14)10 = 11102
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