How to convert binary number into decimal numBer

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We saw above that in the decimal number system, the weight of each digit from right to left increases by a factor of 10. In the binary number system, the weight of each digit increases by a factor of  2 as shown. Then the first digit has a weight of  1 ( 20 ), the second digit has a weight of  2 ( 21 ), the third a weight of  4 ( 22 ), the fourth a weight of  8 ( 23 ) and so on.

So for example, converting a Binary to Decimal number would be:

By adding together ALL the decimal number values from right to left at the positions that are represented by a “1” gives us:  (256) + (64) + (32) + (4) + (1) = 35710 or three hundred and fifty seven as a decimal number.

Then, we can convert binary to decimal by finding the decimal equivalent of the binary array of digits 1011001012 and expanding the binary digits into a series with a base of  2 giving an equivalent of 35710 in decimal or denary.

Note that in number conversion systems “subscripts” are used to indicate the relevant base numbering system, 10012 = 910. If no subscript is used after a number, then it is generally assumed to be decimal.