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Introduction to Number Systems

We, humans, use words, numbers, and characters to communicate with each other. However, computers can not understand this language. Hence the data is converted to an electronic signal when we reach data. Each pulse is known as code, and ASCII translates the code to a numeric format. It creates a numerical value that digits for each digit, symbol, and character that a system understands. The numerical value of a digit in a number can be specified using The number, The position of the digit in the number, The base of the system. Therefore to understand computer language or communicate with the system, one needs to know the number systems.

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Types of Number Systems

1. Binary Number System

In this system, there are two types of electronic pulses. If there is no electronic pulse then the digit is represented by ‘0’ and If there is an electronic pulse present then it’s 1′. Single binary digit is a bit. A sequence of four bits (1001) is a nibble and a sequence of eight bits(11001010) is called a byte. Binary represents a specific power of the base (2) of the number system. Example, 20. The last position in a binary number represents an x power of the base (2). Example, 2x where x represents the last position -1.

Example

Binary Number: 110012

Step 3: 2610

2. Octal Number System

Octal system uses eight digits 0, 1, 2, 3, 4, 5, 6, 7 hence base is 8. Each position in an octal number indicates a 0 power of the base (8). So it is also known as base 8 number system. Eg. 80. The last position in an octal number represents an x power of the base (8). Eg.8x where x represents the last position -1.

Example

Octal Number: 120718

120718 can be written as 12071

Step 1: ((1 x 84) + (2 x 83) + (0 x 82) + (7 x 81) + (1 x 80)) 10

Step 2: (4096 + 1024 + 0 + 56 + 1) 10

Step 3: 5177

3. Decimal Number System

Example

Decimal Number: 123710

123710 can be written as 1237

Step 1: (1 x 103)+ (2 x 102)+ (3 x 101)+ (7 x l00) 10

Step 2: (1 x 1000)+ (2 x 100)+ (3 x 10)+ (7 x 1) 10

Step 3: (1000 + 200 + 30 + 7) 10

Step 4: 1237

4. Hexadecimal Number System

Example

Hexadecimal Number: 19FDA16

19FDE16 can be written as 19FDA

Step 1: ((1 x 164) + (9 x 163) + (F x 162) + (D x 161) + (A x 160)) 10

Step 2: ((1 x 164) + (9 x 163) + (15 x 162) + (13 x 161) + (10 x 160)) 10

Step 3: (65536+ 36864 + 3840 + 208 + 10) 10

Step 4: 106458

Conclusion

In this article, we have seen a Number system that is used to communicate with a computer along with decimal conversion. I hope you will find this article helpful.