In this tutorial we will learn binary to decimal conversion for an integer number.

Before we dive into the main topic lets talk a little about Decimal and Binary Number System that we are going to work with in this tutorial.

A decimal number system consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. So, any number that we use in our daily life is actually in decimal number system.

A binary number system consists of only 2 digits: 0 and 1. And it is most commmonly used in computers.

to convert a binary number into decimal form we have to multiply

ones place by 2^{0}

tens place by 2^{1}

hundreds place by 2^{2}

and so onâ€¦

Convert binary number 1010_{(base 2)} into decimal form.

The following table shows the places, binary number and the multipliers for the corresponding places.

place | thousands | hundreds | tens | ones |

binary | 1 | 0 | 1 | 0 |

multiplier | 2^{3} | 2^{2} | 2^{1} | 2^{0} |

```
= 1x2
```^{3} + 0x2^{2} + 1x2^{1} + 0x2^{0}
= 8 + 0 + 2 + 0
= 10

So, the required decimal number is

1010_{(base 2)} = 10_{(base 10)}

Alternatively, (1010)_{2} = (10)_{10}

Where, (base 10) means the number is in decimal number system and (base 2) means the number is in binary number system.

Convert binary number 110101_{(base 2)} into decimal form.

The following table shows the places, binary number and the multipliers for the corresponding places.

place | hundred thousands | ten thousands | thousands | hundreds | tens | ones |

binary | 1 | 1 | 0 | 1 | 0 | 1 |

multiplier | 2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} |

```
= 1x2
```^{5} + 1x2^{4} + 0x2^{3} + 1x2^{2} + 0x2^{1} + 1x2^{0}
= 32 + 16 + 0 + 4 + 0 + 1
= 53

So, the required decimal number is

110101_{(base 2)} = 53_{(base 10)}

Alternatively, (110101)_{2} = (53)_{10}

Where, (base 10) means the number is in decimal number system and (base 2) means the number is in binary number system.

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