The Decimal number system consists has ten values ranging from 0 to 9.The Binary system consists of only two values 0 and 1.

Number conversions are very useful for Engineering, especially during first semester. This article is very useful to help students convert Binary Numbers to Decimal Numbers.It is preferred that engineering students also learn How to Decimal Numbers to Binary Numbers.

In order to differentiate decimal numbers with binary numbers Base values of 10 and 2 are given in subscripts such as Binary numbers are represented as 100111_{(2) }(read as 100111 to the base 2)and decimal numbers are represented as 39_{(10)} (read as 39 to the base 10).To convert binary numbers to decimal numbers just follow these simple steps:

Let us consider a binary number 100111_{(2)}.In Order to convert it to decimal number

- Identify the position of each value of the given Binary value
- Write down the Given Values below the respective positions
- Multiply the binary values with the respective weights.
- The weight of first position is 2 raised to power (position-1)
- For example the weight of second position is 2
^{(2-1)}=2^{1.} - Then just multiply the
*Binary value*with the*weights.* - Then add all the final values to get the
*decimal equivalent*of the*binary number*.

6^{th} | 5^{th} | 4^{th} | 3^{rd} | 2^{nd} | 1^{st} | Position |

1 | 0 | 0 | 1 | 1 | 1 | Given Binary value |

X2^{5} | X2^{4} | X2^{3} | X2^{2} | X2^{1} | X2^{0} | Weights |

1X32 | +0X16 | +0X8 | +1X4 | +1X2 | +1X1 | . |

32 | +0 | +0 | +4 | +2 | +1 | =39_{(10)} |

Therefore the decimal equivalent of 100111

_{(2) }=39

_{(10)}.

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