Decimal Number System
A 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 etc. If the Base value of a number system is 10. This is also known as base-10 or Decimal number system which has 10 characters from 0 to 9.
This is the weighted (or positional) number representation where value of each digit is determined by its position (or their weight) which is a power of 10 in a decimal 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 weight of the position in which the digit appears and then adding the products.
Example:
The number 2020 is interpreted as:
2020 = (2 × 10³) + (0 × 10²) + (2 × 10¹) + (0 × 10⁰) = 2000 + 0 + 20 + 0 = 2020
Decimal to Binary Conversion
Example :
The number 2020 in binary notation:
(2020)10 = (____)2
= (2020)10 = (1024 + 512 + 256 + 128 + 64 + 32 + 4)10 = (210x1 + 29x1 + 28x1 + 27x1 + 26x1 + 25x1 + 24x0 + 23x0 + 22x1 + 21x0+ 20x0)10 = (11111100100)2
Note : Right most bit is the least significant bit (LSB) and left most bit is the most significant bit (MSB). 
The range in Decimal number system expressed as their corresponding binary number.
Decimal Number | Binary Number |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
Also read about:
- Decimal to Binary Conversion and its implementation.
- Decimal to Octal Conversion and its implementation.
- Decimal to Hexadecimal Conversion and its implementation.
9’s and 10’s Complement of Decimal (Base-10) Number
Complements are used in number systems to simplify subtraction and error detection in digital systems. In the decimal system, the 9’s complement and 10’s complement are commonly used.
Steps to Find 9’s Complement:
- Write the given decimal number.
- Subtract each digit from 9.
Example : 9’s Complement of 2020
9 - 2 = 7
9 - 0 = 9
9 - 2 = 7
9 - 0 = 9Thus, the 9’s complement of 2020 is 7979.
Steps to Find 10’s Complement:
- Find the 9’s complement of the number.
- Add 1 to the least significant digit (LSB).
Example 1: 10’s Complement of 2020
- 9’s complement of 2020 = 7979
- Adding 1: 7979 + 1 = 7980
Thus, the 10’s complement of 2020 is 7980
