Imagine yourself as a time traveler suddenly reaching the Indus valley civilization. The Indus Valley people don’t know the numbers. They use certain symbols and you have no clue about it. How do you buy or count something? How do you count the numbers more than thousands or lakhs? Complicated right. Thanks to our great mathematicians who made it easy for us by discovering the number systems. Let us learn more about this number system now.
What is a Number System?
Before learning the number system, let me tell you what a number is. A number refers to a mathematical value used for counting, measuring, or labeling things. Numerical calculations are performed with numbers. A number may be a natural number, a whole number, a rational number, or an irrational number. Zero is also a number that represents a null value.
A number system refers to the consistent use of digits and other symbols to represent numbers. In determining the place value of a number, a digit’s position in the number, as well as the number’s base, should all be considered. Numerical operations such as addition, subtraction, and division can be performed based on their unique representation.
Types of Number Systems
The number system is majorly categorized into four types. They are as follows
- Binary number system (Base- 2)
- Octal number system (Base-8)
- Decimal number system (Base- 10)
- Hexadecimal number system (Base- 16)
Binary Number System
A number system that uses only two digits, i.e. 0,1 is termed a binary number system. The individual digits of a binary number are called bits. So, a binary number 1001 has 4 bits. Binary is used by computers and other digital devices. The binary number system uses Base 2.
We can convert any number system into binary and vice versa.
Example: Convert (12)10 to a binary number.
To convert, you need to divide the given number by 2. So, 12/2 = 6 Remainder = 0.
Now again divide 6 by 2. i.e. 6/2 = 3 Remainder is 0 again. Repeat the steps, 3/2 = (2 1)+1. Hence the remainder is 1.
Here we make use of remainders from bottom to top to write the binary number.
Hence (12)10 = 11002.
Check: To convert back from binary to decimal,
1 23 + 1 22 + 0 + 0 = 8 + 4 + 0 + 0 = (12)10.
Octal Number System
A number system that uses digits from 0 to 7 is termed an octal number system. The octal number system uses base 8. Converting an octal number to any other number system is the same as a binary system.
Decimal Number System
Since decimal numbers consist of ten digits from 0 to 9, they have a base 10. Decimal number systems use units, tens, hundreds, thousands, and so on, as successive positions to the left of the decimal point. Each position represents a certain power of base 10.
Example: The decimal number 197 consists of the digit 7 in the units position, 9 in the tens place, and 1 in the hundreds position, whose value can be written as
(1 ×102) + (9 ×101) + (7×100)
(1×100) + (9×10) + (7×1)
100 + 90 + 7 = 197
Hexadecimal Number System
Hexadecimal originates from Hexa meaning 6 and decimal meaning 10. As a result, hexadecimal number systems have 16 digits. In addition to the digits 0 to 9, the first six letters of the alphabet are included here. I.e 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. In total 16 digits.
Conversion from hexadecimal to any other number system is similar to a binary number system.
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