 # binary to decimal best approach. check this out..!

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that was a neat trick!

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Well I have a pretty nice way too to convert a Binary Number to its Decimal Equivalent

Here are the steps:

• Write your number on a paper with the digits spaced by a finger length.
• Starting from the Right Hand Side, write “1” below the first digit.
• Then from RHS to LHS multiply by 2 and write it below.
• Add the numbers that you have written below 1s.

Example:
Convert 10010 Binary no. to its Base 10 equivalent.

``````         1    0    0    1    1

16   8    4    2    1
``````

Now we add 16,2,1. So Decimal Equivalent = 16+2+1 = 19

I think your solution is also tricky and good.

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very good trick …when you want to convert large number quick than it is work very fast…
thanks to @va1ts7_100

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I’ve come up with a theoritical proof one below.

Consider a binary number data to be of the form A101.

Here A can be any binary data
(If A is 1011 , X will be 1011101).

By @bradley method, value of A000 can be calculated(let it be k).

So the value of X(A101) will be - k+(2^2)+(2^0)

Now verifying the trick.

-Consider the trick to be working fine)

-Value of A is k/(2^3)

-Value of A101 is ((k/(2^3)*2+1)*2)*2+1

-Simplifying it we get-k+(2^2)+(2^0)

-This is the correct result.

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what does mental number one mean?

• sometimes i feel very hard(in case to be very quick i.e. aptitude ) to calculate decimal number using @bradely method…

*it is good if you want very quick answer than you should go with va1ts7_100
*bcz it does not require to much calculation…

@bradely because you first find all digit value like 16+2+1 than do one more addition…

• but first link provide ans in one scan with very easy to add number.

happy coding…

Thanks va1ts7_100,

it’s a nice way to convert binary to decimal but i can’t understand how to decrease time complexity

to use this method . it is very feasible when we are converting binary to decimal in our mind but it

can’t help in decreasing complexity.

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@deepakmourya

yeap…it use same time complexity as other methods…too \$ \$only advantage only mind calculation will be easy…

I guess all those who parsed strings to integers manually - should be familiar with this trick. You are doing exactly same when parsing string to decimal - the only difference is that you have base10, therefore you have to do N=N10+digit, instead of N=N2+digit.

@deepakmourya, if you need faster method - you should use divide and conquer with FFT multiplication. Solve your problem for left part of substring, for right part of substring, then multiply result for left part by 10^L and add these two numbers.

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Good one…fast method…

wlcm @rcsldav2107 thanks… 