http://www.zenoli.net/2007/03/quickly-convert-binary-to-decimal-in-your-head/#comment-293945

that was a neat trick!

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.
- Its your Decimal Equivalent.

**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.

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

thanks to @va1ts7_100

Well,the trick is quite self explanatory if you already know the method answered by @bradley .

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.

wlcm @rcsldav2107…

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…

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.

**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=N*10+digit, instead of N=N*2+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.

Good one…fast method…