# Base-2 Numeral System

We have already studied that the computer works with 0 and 1 these are a part of BIT a bit has two types of conditions just like the switches which have two functions ON and OFF. Just for convenience, we call ON as 1 & 0 as OFF. These are called as bit this is the smallest unit called as a binary digit.

We usually work on a decimal system in which 0 to 9 these 10 numbers are there in a series and the whole work of addition subtraction division multiplication is done with these numbers or digits. In computers 0 and 1, these two numbers write all the information whatever is inputed in the device.

**BYTE**

- A single bit is not at all useful so when it joined with the other bits then only e a complete meaning is formed of any data or information for us this series of 8 bits is important which is known as byte this is the most important and essential unit the whole computer memory structure is counted in kilobyte and megabyte.
- All the activity is done with these bytes. The Stored information byte is a temporary thing for a computer that can be used in any form, so the computer does two important work along with the data, the first one is work with the digits, or we can say as a mathematical calculation is performed with the numbers and with the science it performs a different activity, in a byte, we can store data in two ways number system or sign System.
- In reality, two forms of data have no difference in byte the only thing is how to use for knowing that bite has a number or a sign we have to know what is the usage we are going to do with that data.

#### Binary Numbers

- As we know that in the decimal system we perform the execution of the number from right to left like the number 1, 10, 100, 1000, 10000, 100000, 1000000, etc.
- This is known as ones, tens, a hundred, a thousand, ten thousand, lakh, ten lakh, etc. The meaning of this the number system has a base of 10 because This has 10 digits 0,1,2,3,4,5,6,7,8 and 9.
- But the binary number system has a base of 2 because all the digits are counted into two numbers are 0 and 1 due to this when we write the whole binary number system the bits place is executed from right to left and the value is two times like 1,2,4,8,16,32,64,128 etc.
- Keep in mind that the bits series is from right to left and initially it is started from zero the best has a relation with the series each bit’s digital value is 2. Example bit series has 3 that has a value of 2 means 8 just like this other bits can be understood.
- In the computer all the series are kept in binary form only and in this form, they are added subtracted divided multiplied or any other arithmetical operation is performed through this. Any number can be written as binary, so no difference is there.
- Any decimal system can be converted to Binary System it has a special way, but it is out of the subject of this article that is why we are leaving that in this we will only talk about the first 16 decimal system which is equal to binary digits.

Decimal System | Binary System |

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |

For converting any Binary System into the decimal system every bit is added for that in reality only one-bit places are added because zero bit has no value for example diary system 1101 has 31 bites in which the first has a value of 8 seconds has a value of 4 and the third has a value of fun after adding these we get 13 as a result that is why Binary System 1101 is equal to decimal system 13.

We store one letter for sign in one bite like ok if we will write ASHA BISHT and want to store this then we require 10 bytes. In this 9 letters are there and one empty space each empty space to have a different byte in which it is stored as shown below:

A | S | H | A | B | I | S | H | T |

So we know that each bite has 8 bits and each bit has two value 0 and 1 that is why according to the mathematical rules 1 byte has 2 power 8 bits that mean 256 different groups can be formed which means 1 byte has zero to 255 means total value 256 series will be shown it has another meaning that one bite has 256 different signs or letters stored in it.

Letter | ASCII CODE | EBCDIC CODE |

A | 01000001 | 11000001 |

B | 01000010 | 11000010 |

C | 01000011 | 11000100 |

D | 01000101 | 11000101 |

Letters and signs are stored in bytes which has a special way called Coding System. The two known systems are ASCII or American Standard Code For Information Interchange or EBCDIC or Extended Binary Decimal Interchange Code.

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