A number system can be considered as a mathematical notation of numbers using a set of digits or symbols. In simpler words the number system is a method of representing numbers. Every number system is identified with the help of its base or radix. For example, Binary, Octal, Decimal and Hexadecimal Number systems are used in microprocessor programming.
Decimal Number System :
If the Base value of a number system is 10. This is also known as base-10 number system which has 10 symbols, these are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Position of every digit has a weight which is a power of 10.
then it is called the Decimal number system which has the most important role in the development of science and technology. This is the weighted (or positional) number representation, where value of each digit is determined by its position (or their weight) in a number.
Each position in the decimal system is 10 times more significant than the previous position, that means the numeric value of a decimal number is determined by multiplying each digit of the number by the value of the position in which the digit appears and then adding the products.
Example-1: The number 2020 is interpreted as:-
= (2020)10 = (1024 + 512 + 256 + 128 + 64 + 32 + 4)10 = (210x1+29x1+28x1+27x1+26x1+25x1+24x0+23x0+22x1+21x0+20x0)10 = (11111100100)2
= (2020)10 = (11111100100)2
Example-2: The number 2020.50 is interpreted as:-
= (2020.50)10 = (1024 + 512 + 256 + 128 + 64 + 32 + 4 + (1/2))10 = (210x1+29x1+28x1+27x1+26x1+25x1+24x0+23x0+22x1+21x0+20x0+2-1x1)10 = (11111100100.1)2
= (2020.50)10 = (11111100100.1)2
Right most bit is the least significant bit (LSB) and left most bit is the most significant bit (MSB).
In general, a number expressed in the base-r system has coefficients multiplied by power of r. The coefficient aj ranges from 0 to (r-1). Representing real number in base-r is as following below:
Where, a0, a1, … a(n-1) and an are integer part digits, n is the total number of integer digits.
a-1, a-2, … and a-m are fractional part digits, m is the total number of fractional digits.
Advantages and disadvantages of Decimal Number System :
- Advantages – easy readability, used by humans, and easy to manipulate.
- Disadvantages – wastage of space and time.
9’s and 10’s Complement of Decimal (Base-10) Number :
- Simply, 9’s Complement of a decimal number is the subtraction of it’s each digits from 9. For example, 9’s complement of decimal number 2005 is 9999 – 2005 = 7994.
- 10’s Complement of decimal number is 9’s complement of given number plus 1 to the least significant bit (LSB). For example 10’s complement of decimal number 2005 is (9999 – 2005) + 1 = 7995.
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- Classification of Number System
- Number System and Base Conversions
- Conversion of Binary number to Base 4 system
- Overflow in Arithmetic Addition in Binary Number System
- Program for Hexadecimal to Decimal
- Program for Decimal to Binary Conversion
- Program for Octal to Decimal Conversion
- Program for Decimal to Octal Conversion
- Program for Binary To Decimal Conversion
- Implementation of Digital System
- Specification of Digital System
- Common Bus System using multiplexers
- File Processing System (FPS)
- Levels of Memory in Operating System
- Characteristics and Benefits of Digital System
- Features of Distributed Operating System
- Difference Between Digital And Analog System
- Concurrent Processes in Operating System
- Deadlock Ignorance in Operating System
- Multiport Memory Multiprocessor System
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.