Important Computer Awareness Materials (Day-23) – Introduction of Computer Number System (part-1):
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Introduction of Computer Number System (part-1)
A set of values used to represent different quantities is known as Number System. For example, a number system can be used to represent the number of students in a class or number of viewers watching a certain TV program etc. The digital computer represents all kinds of data and information in binary numbers. It includes audio, graphics, video, text and numbers. The total number of digits used in a number system is called its base or radix. The base is written after the number as subscript.
Some important number systems are as follows.
- Decimal number system
- Binary number system
- Octal number system
- Hexadecimal number system
Decimal number System:
The Decimal Number System consists of ten digits from 0 to 9. These digits can be used to represent any numeric value. The base of decimal number system is 10. It is the most widely used number system. The value represented by individual digit depends on weight and position of the digit.
Binary Number System:
Digital computer represents all kinds of data and information in the binary system. Binary Number System consists of two digits 0 and 1. Its base is 2. Each digit or bit in binary number system can be 0 or 1. A combination of binary numbers may be used to represent different quantities like 1001. The positional value of each digit in binary number is twice the place value or face value of the digit of its right side. The weight of each position is a power of 2.
Octal Number System:
Octal Number System consists of eight digits from 0 to 7. The base of octal system is 8. Each digit position in this system represents a power of 8. Any digit in this system is always less than 8. Octal number system is used as a shorthand representation of long binary numbers. The number 6418 is not valid in this number system as 8 is not a valid digit.
Hexadecimal Number System:
The Hexadecimal Number System consists of 16 digits from 0 to 9 and A to F. The alphabets A to F represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position in hexadecimal system represents a power of 16. The number 76416 is valid hexadecimal number. It is different from 76410 which is seven hundred and sixty four. This number system provides shortcut method to represent long binary numbers.
The decimal system consists of 10 numerals or symbols. These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Right now you must be thinking, I learnt it by the first grade. But then there’s more to learn in simpler topics.
The decimal system is also called base-10 system.
It is a positional-value system. It means the value of a digit depends on its position.
Example: Consider a decimal number 736. The digit 7 actually represents 7 hundreds, 3 represents 3 tens and 6 represents 6 units. Then 7 carries the most weight of the three digits, it is referred to as the most significant digit (MSD). Then 2 carries the least weight, it is referred to as the least significant digit (LSD).
Note the concepts: most significant digit (MSD) and least significant digit (LSD)
Binary number system gained importance due to its application in the digital world. Computers run on digital binary data. In binary system there are only two symbols 0 and 1. Still, with only 0 and 1 any number, how so ever large can be represented.
Binary is also a positional number system.
In the binary system the term binary digit is often abbreviated to the term, bit. In other words, bit is a short form for binary digit. The left most bit has the largest weight is the most significant bit (MSB). The right most bit has the smallest weight is the least significant bit (LSB).
The leftmost 1 is the most significant bit (MSB)
The rightmost 0 is the least significant bit (LSB).