Binary to Decimal conversion is an important concept in Digital Electronic. Because Computer understands binary number system and we are familiar with decimal number system. Before understanding binary to decimal conversion, we must aware with our decimal number system and also binary number system.

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## What is Decimal Number System?

“Decimal Number System” or “Denary Number System” is based on “Base 10”. Here in decimal number system total 10 symbol (0, 1, 2, 3, 4, 5, 6, 7, 8 & 9) used. Means in Decimal Number System each digit takes any one possible value from 0 to 9. This decimal number system also has most significant and least significant “Digits”. As it is a Base-10 system so each digit has 10 times higher value from previous digit.

Value of any number in Decimal System will be equal to the sum of digit multiplied by their position value. For Example value of number 213 in decimal will be..

(2×100) + (1×10) + (3×1) = 213 or

(2×10^{2}) + (1×10^{1}) + (3×10^{0}) = 213

## What is Binary Number System?

**Binary Number System** is used in digital system or you can say it is used in computer system because in computer we can store data in two forms. Either there will be a Data bit or there will not be a Data bit and this is called 0 and 1 stage. Probably this was main reason for invention of **Binary Number System. **

**Binary Number System **is a based on “Base-2”. Here in Binary number System total 2 symbols (0 & 1) used. Means in Binary Number System each digit takes any one possible value from 0 or 1. This binary number system also has most significant and least significant “Digits” as other number systems. As it is a Base-2 system so each digit has 2 times higher value from previous digit.

In this number system numbers are represented in string of 0 & 1.

For example 1101

(1×8) + (1×4) + (0x2) + (1×1) = 13 (in decimal)

(1×2^{4}) + (1×2^{2}) + (0x2^{1}) + (1×2^{1}) = 13 (in decimal)

So as given in above example, it is a **Binary to Decimal** number conversion.

In computer language single digit of Binary number system is called “Bit”. Others groups common names are given in table.

Number of Binary Digits (bits) |
Common Name |

1 | Bit |

4 | Nibble |

8 | Byte |

16 | Word |

32 | Double Word |

64 | Quad Word |

As you know that computer memory is also measured in binary bits and bytes. A brief of data memory sizes is given in table.

Number of Bytes |
Common Name |

1,024 (2^{10}) |
kilobyte (kb) |

1,048,576 (2^{20}) |
Megabyte (Mb) |

1,073,741,824 (2^{30}) |
Gigabyte (Gb) |

A very long number! (2^{40}) |
Terabyte (Tb) |

## Conversion of numbers (from Decimal to Binary and Binary to Decimal)

Decimal to Binary conversion is very easy and can be done on your figure tip. This method is called “divide by 2 technique”. Here as in given table we are going to convert decimal number 13 in to binary number.

Number | 13 | |||

Divide by 2 | ||||

Result | 6 | Remainder | 1 | LSB |

Divide by 2 | ||||

Result | 3 | Remainder | 0 | |

Divide by 2 | ||||

Result | 1 | Remainder | 1 | |

Divide by 2 | ||||

Result | 0 | Remainder | 1 | MSB |

So divide your decimal number by 2 and put remainder in to Least Significant Bit and result again divide by 2, same as previous put remainder in to second least significant bit and repeat this process until final result equals 0.

Finally decimal 13 will be 1101 in binary.

For binary to decimal conversion “sum of Weight” method is perfect and easy to use. Here for conversion simply we have to add all digit value as per its position. For example 1101

(1×8) + (1×4) + (0x2) + (1×1) = 13 (in decimal)

(1×2^{4}) + (1×2^{2}) + (0x2^{1}) + (1×2^{1}) = 13 (in decimal)

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**Binary to Decimal** or **Decimal to Binary** both conversion is very simple but during conversion don`t mix these numbers system because in binary system 1 0 means value 2 but if you mix these number system you can consider 1 0 as ten.

To solve this problem you can use subscript. For example 1 0 _{2 }means binary 1 0 and if there is no subscript means it is a decimal number system digit so 10 means value ten.

Today we are aware with many processors but binary system is the backbone of processors and data storage units. No doubt binary number can’t be used in practical life but it is also true that we can’t use computer without binary number system. As in practical life we are familiar with Decimal number system that’s why conversion from binary to decimal and decimal to binary becomes an important concept.

Enjoy Learning…