Binary to Decimal conversion of an integer number

Conversion

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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.

How to convert a binary number into decimal number?

to convert a binary number into decimal form we have to multiply
ones place by 20
tens place by 21
hundreds place by 22
and so on…

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

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

placethousandshundredstensones
binary1010
multiplier23222120

= 1x23  +  0x22  +  1x21  + 0x20
= 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.

placehundred
thousands
ten
thousands
thousandshundredstensones
binary110101
multiplier252423222120

= 1x25  +  1x24  +  0x23  + 1x22  +  0x21  + 1x20
= 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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